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32,020 | pingouin.regression | mediation_analysis | Mediation analysis using a bias-correct non-parametric bootstrap method.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x : str
Column name in data containing the predictor variable.
The predictor variable must be continuous.
m : str or list of str
Column name(s) in data containing the mediator variable(s).
The mediator(s) can be continuous or binary (e.g. 0 or 1).
This function supports multiple parallel mediators.
y : str
Column name in data containing the outcome variable.
The outcome variable must be continuous.
covar : None, str, or list
Covariate(s). If not None, the specified covariate(s) will be included
in all regressions.
alpha : float
Significance threshold. Used to determine the confidence interval,
:math:`\text{CI} = [\alpha / 2 ; 1 - \alpha / 2]`.
n_boot : int
Number of bootstrap iterations for confidence intervals and p-values
estimation. The greater, the slower.
seed : int or None
Random state seed.
logreg_kwargs : dict or None
Dictionary with optional arguments passed to :py:func:`pingouin.logistic_regression`
return_dist : bool
If True, the function also returns the indirect bootstrapped beta
samples (size = n_boot). Can be plotted for instance using
:py:func:`seaborn.distplot()` or :py:func:`seaborn.kdeplot()`
functions.
Returns
-------
stats : :py:class:`pandas.DataFrame`
Mediation summary:
* ``'path'``: regression model
* ``'coef'``: regression estimates
* ``'se'``: standard error
* ``'CI[2.5%]'``: lower confidence interval
* ``'CI[97.5%]'``: upper confidence interval
* ``'pval'``: two-sided p-values
* ``'sig'``: statistical significance
See also
--------
linear_regression, logistic_regression
Notes
-----
Mediation analysis [1]_ is a *"statistical procedure to test
whether the effect of an independent variable X on a dependent variable
Y (i.e., X → Y) is at least partly explained by a chain of effects of the
independent variable on an intervening mediator variable M and of the
intervening variable on the dependent variable (i.e., X → M → Y)"* [2]_.
The **indirect effect** (also referred to as average causal mediation
effect or ACME) of X on Y through mediator M quantifies the estimated
difference in Y resulting from a one-unit change in X through a sequence of
causal steps in which X affects M, which in turn affects Y.
It is considered significant if the specified confidence interval does not
include 0. The path 'X --> Y' is the sum of both the indirect and direct
effect. It is sometimes referred to as total effect.
A linear regression is used if the mediator variable is continuous and a
logistic regression if the mediator variable is dichotomous (binary).
Multiple parallel mediators are also supported.
This function will only work well if the outcome variable is continuous.
It does not support binary or ordinal outcome variable. For more
advanced mediation models, please refer to the
`lavaan <http://lavaan.ugent.be/tutorial/mediation.html>`_ or `mediation
<https://cran.r-project.org/web/packages/mediation/mediation.pdf>`_ R
packages, or the `PROCESS macro
<https://www.processmacro.org/index.html>`_ for SPSS.
The two-sided p-value of the indirect effect is computed using the
bootstrap distribution, as in the mediation R package. However, the p-value
should be interpreted with caution since it is not constructed
conditioned on a true null hypothesis [3]_ and varies depending on the
number of bootstrap samples and the random seed.
Note that rows with missing values are automatically removed.
Results have been tested against the R mediation package and this tutorial
https://data.library.virginia.edu/introduction-to-mediation-analysis/
References
----------
.. [1] Baron, R. M. & Kenny, D. A. The moderator–mediator variable
distinction in social psychological research: Conceptual, strategic,
and statistical considerations. J. Pers. Soc. Psychol. 51, 1173–1182
(1986).
.. [2] Fiedler, K., Schott, M. & Meiser, T. What mediation analysis can
(not) do. J. Exp. Soc. Psychol. 47, 1231–1236 (2011).
.. [3] Hayes, A. F. & Rockwood, N. J. Regression-based statistical
mediation and moderation analysis in clinical research:
Observations, recommendations, and implementation. Behav. Res.
Ther. 98, 39–57 (2017).
Code originally adapted from https://github.com/rmill040/pymediation.
Examples
--------
1. Simple mediation analysis
>>> from pingouin import mediation_analysis, read_dataset
>>> df = read_dataset('mediation')
>>> mediation_analysis(data=df, x='X', m='M', y='Y', alpha=0.05,
... seed=42)
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.561015 0.094480 4.391362e-08 0.373522 0.748509 Yes
1 Y ~ M 0.654173 0.085831 1.612674e-11 0.483844 0.824501 Yes
2 Total 0.396126 0.111160 5.671128e-04 0.175533 0.616719 Yes
3 Direct 0.039604 0.109648 7.187429e-01 -0.178018 0.257226 No
4 Indirect 0.356522 0.083313 0.000000e+00 0.219818 0.537654 Yes
2. Return the indirect bootstrapped beta coefficients
>>> stats, dist = mediation_analysis(data=df, x='X', m='M', y='Y',
... return_dist=True)
>>> print(dist.shape)
(500,)
3. Mediation analysis with a binary mediator variable
>>> mediation_analysis(data=df, x='X', m='Mbin', y='Y', seed=42).round(3)
path coef se pval CI[2.5%] CI[97.5%] sig
0 Mbin ~ X -0.021 0.116 0.857 -0.248 0.206 No
1 Y ~ Mbin -0.135 0.412 0.743 -0.952 0.682 No
2 Total 0.396 0.111 0.001 0.176 0.617 Yes
3 Direct 0.396 0.112 0.001 0.174 0.617 Yes
4 Indirect 0.002 0.050 0.960 -0.072 0.146 No
4. Mediation analysis with covariates
>>> mediation_analysis(data=df, x='X', m='M', y='Y',
... covar=['Mbin', 'Ybin'], seed=42).round(3)
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.559 0.097 0.000 0.367 0.752 Yes
1 Y ~ M 0.666 0.086 0.000 0.495 0.837 Yes
2 Total 0.420 0.113 0.000 0.196 0.645 Yes
3 Direct 0.064 0.110 0.561 -0.155 0.284 No
4 Indirect 0.356 0.086 0.000 0.209 0.553 Yes
5. Mediation analysis with multiple parallel mediators
>>> mediation_analysis(data=df, x='X', m=['M', 'Mbin'], y='Y',
... seed=42).round(3)
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.561 0.094 0.000 0.374 0.749 Yes
1 Mbin ~ X -0.005 0.029 0.859 -0.063 0.052 No
2 Y ~ M 0.654 0.086 0.000 0.482 0.825 Yes
3 Y ~ Mbin -0.064 0.328 0.846 -0.715 0.587 No
4 Total 0.396 0.111 0.001 0.176 0.617 Yes
5 Direct 0.040 0.110 0.721 -0.179 0.258 No
6 Indirect M 0.356 0.085 0.000 0.215 0.538 Yes
7 Indirect Mbin 0.000 0.010 0.952 -0.017 0.025 No
| @pf.register_dataframe_method
def mediation_analysis(
data=None,
x=None,
m=None,
y=None,
covar=None,
alpha=0.05,
n_boot=500,
seed=None,
return_dist=False,
logreg_kwargs=None,
):
"""Mediation analysis using a bias-correct non-parametric bootstrap method.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x : str
Column name in data containing the predictor variable.
The predictor variable must be continuous.
m : str or list of str
Column name(s) in data containing the mediator variable(s).
The mediator(s) can be continuous or binary (e.g. 0 or 1).
This function supports multiple parallel mediators.
y : str
Column name in data containing the outcome variable.
The outcome variable must be continuous.
covar : None, str, or list
Covariate(s). If not None, the specified covariate(s) will be included
in all regressions.
alpha : float
Significance threshold. Used to determine the confidence interval,
:math:`\\text{CI} = [\\alpha / 2 ; 1 - \\alpha / 2]`.
n_boot : int
Number of bootstrap iterations for confidence intervals and p-values
estimation. The greater, the slower.
seed : int or None
Random state seed.
logreg_kwargs : dict or None
Dictionary with optional arguments passed to :py:func:`pingouin.logistic_regression`
return_dist : bool
If True, the function also returns the indirect bootstrapped beta
samples (size = n_boot). Can be plotted for instance using
:py:func:`seaborn.distplot()` or :py:func:`seaborn.kdeplot()`
functions.
Returns
-------
stats : :py:class:`pandas.DataFrame`
Mediation summary:
* ``'path'``: regression model
* ``'coef'``: regression estimates
* ``'se'``: standard error
* ``'CI[2.5%]'``: lower confidence interval
* ``'CI[97.5%]'``: upper confidence interval
* ``'pval'``: two-sided p-values
* ``'sig'``: statistical significance
See also
--------
linear_regression, logistic_regression
Notes
-----
Mediation analysis [1]_ is a *"statistical procedure to test
whether the effect of an independent variable X on a dependent variable
Y (i.e., X → Y) is at least partly explained by a chain of effects of the
independent variable on an intervening mediator variable M and of the
intervening variable on the dependent variable (i.e., X → M → Y)"* [2]_.
The **indirect effect** (also referred to as average causal mediation
effect or ACME) of X on Y through mediator M quantifies the estimated
difference in Y resulting from a one-unit change in X through a sequence of
causal steps in which X affects M, which in turn affects Y.
It is considered significant if the specified confidence interval does not
include 0. The path 'X --> Y' is the sum of both the indirect and direct
effect. It is sometimes referred to as total effect.
A linear regression is used if the mediator variable is continuous and a
logistic regression if the mediator variable is dichotomous (binary).
Multiple parallel mediators are also supported.
This function will only work well if the outcome variable is continuous.
It does not support binary or ordinal outcome variable. For more
advanced mediation models, please refer to the
`lavaan <http://lavaan.ugent.be/tutorial/mediation.html>`_ or `mediation
<https://cran.r-project.org/web/packages/mediation/mediation.pdf>`_ R
packages, or the `PROCESS macro
<https://www.processmacro.org/index.html>`_ for SPSS.
The two-sided p-value of the indirect effect is computed using the
bootstrap distribution, as in the mediation R package. However, the p-value
should be interpreted with caution since it is not constructed
conditioned on a true null hypothesis [3]_ and varies depending on the
number of bootstrap samples and the random seed.
Note that rows with missing values are automatically removed.
Results have been tested against the R mediation package and this tutorial
https://data.library.virginia.edu/introduction-to-mediation-analysis/
References
----------
.. [1] Baron, R. M. & Kenny, D. A. The moderator–mediator variable
distinction in social psychological research: Conceptual, strategic,
and statistical considerations. J. Pers. Soc. Psychol. 51, 1173–1182
(1986).
.. [2] Fiedler, K., Schott, M. & Meiser, T. What mediation analysis can
(not) do. J. Exp. Soc. Psychol. 47, 1231–1236 (2011).
.. [3] Hayes, A. F. & Rockwood, N. J. Regression-based statistical
mediation and moderation analysis in clinical research:
Observations, recommendations, and implementation. Behav. Res.
Ther. 98, 39–57 (2017).
Code originally adapted from https://github.com/rmill040/pymediation.
Examples
--------
1. Simple mediation analysis
>>> from pingouin import mediation_analysis, read_dataset
>>> df = read_dataset('mediation')
>>> mediation_analysis(data=df, x='X', m='M', y='Y', alpha=0.05,
... seed=42)
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.561015 0.094480 4.391362e-08 0.373522 0.748509 Yes
1 Y ~ M 0.654173 0.085831 1.612674e-11 0.483844 0.824501 Yes
2 Total 0.396126 0.111160 5.671128e-04 0.175533 0.616719 Yes
3 Direct 0.039604 0.109648 7.187429e-01 -0.178018 0.257226 No
4 Indirect 0.356522 0.083313 0.000000e+00 0.219818 0.537654 Yes
2. Return the indirect bootstrapped beta coefficients
>>> stats, dist = mediation_analysis(data=df, x='X', m='M', y='Y',
... return_dist=True)
>>> print(dist.shape)
(500,)
3. Mediation analysis with a binary mediator variable
>>> mediation_analysis(data=df, x='X', m='Mbin', y='Y', seed=42).round(3)
path coef se pval CI[2.5%] CI[97.5%] sig
0 Mbin ~ X -0.021 0.116 0.857 -0.248 0.206 No
1 Y ~ Mbin -0.135 0.412 0.743 -0.952 0.682 No
2 Total 0.396 0.111 0.001 0.176 0.617 Yes
3 Direct 0.396 0.112 0.001 0.174 0.617 Yes
4 Indirect 0.002 0.050 0.960 -0.072 0.146 No
4. Mediation analysis with covariates
>>> mediation_analysis(data=df, x='X', m='M', y='Y',
... covar=['Mbin', 'Ybin'], seed=42).round(3)
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.559 0.097 0.000 0.367 0.752 Yes
1 Y ~ M 0.666 0.086 0.000 0.495 0.837 Yes
2 Total 0.420 0.113 0.000 0.196 0.645 Yes
3 Direct 0.064 0.110 0.561 -0.155 0.284 No
4 Indirect 0.356 0.086 0.000 0.209 0.553 Yes
5. Mediation analysis with multiple parallel mediators
>>> mediation_analysis(data=df, x='X', m=['M', 'Mbin'], y='Y',
... seed=42).round(3)
path coef se pval CI[2.5%] CI[97.5%] sig
0 M ~ X 0.561 0.094 0.000 0.374 0.749 Yes
1 Mbin ~ X -0.005 0.029 0.859 -0.063 0.052 No
2 Y ~ M 0.654 0.086 0.000 0.482 0.825 Yes
3 Y ~ Mbin -0.064 0.328 0.846 -0.715 0.587 No
4 Total 0.396 0.111 0.001 0.176 0.617 Yes
5 Direct 0.040 0.110 0.721 -0.179 0.258 No
6 Indirect M 0.356 0.085 0.000 0.215 0.538 Yes
7 Indirect Mbin 0.000 0.010 0.952 -0.017 0.025 No
"""
# Sanity check
assert isinstance(x, (str, int)), "y must be a string or int."
assert isinstance(y, (str, int)), "y must be a string or int."
assert isinstance(m, (list, str, int)), "Mediator(s) must be a list, string or int."
assert isinstance(covar, (type(None), str, list, int))
if isinstance(m, (str, int)) | (data=None, x=None, m=None, y=None, covar=None, alpha=0.05, n_boot=500, seed=None, return_dist=False, logreg_kwargs=None) | [
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|
32,021 | pingouin.parametric | mixed_anova | Mixed-design (split-plot) ANOVA.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
within : string
Name of column containing the within-subject factor
(repeated measurements).
subject : string
Name of column containing the between-subject identifier.
between : string
Name of column containing the between factor.
correction : string or boolean
If True, return Greenhouse-Geisser corrected p-value.
If `'auto'` (default), compute Mauchly's test of sphericity to
determine whether the p-values needs to be corrected.
effsize : str
Effect size. Must be one of 'np2' (partial eta-squared), 'n2'
(eta-squared) or 'ng2'(generalized eta-squared).
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Names of the factor considered
* ``'ddof1'``: Degrees of freedom (numerator)
* ``'ddof2'``: Degrees of freedom (denominator)
* ``'F'``: F-values
* ``'p-unc'``: Uncorrected p-values
* ``'np2'``: Partial eta-squared effect sizes
* ``'eps'``: Greenhouse-Geisser epsilon factor (= index of sphericity)
* ``'p-GG-corr'``: Greenhouse-Geisser corrected p-values
* ``'W-spher'``: Sphericity test statistic
* ``'p-spher'``: p-value of the sphericity test
* ``'sphericity'``: sphericity of the data (boolean)
See Also
--------
anova, rm_anova, pairwise_tests
Notes
-----
Data are expected to be in long-format (even the repeated measures).
If your data is in wide-format, you can use the :py:func:`pandas.melt()`
function to convert from wide to long format.
Missing values are automatically removed using a strict listwise approach (= complete-case
analysis). In other words, any subject with one or more missing value(s) is completely removed
from the dataframe prior to running the test. This could drastically decrease the power of the
ANOVA if many missing values are present. In that case, we strongly recommend using linear
mixed effect modelling, which can handle missing values in repeated measures.
.. warning :: If the between-subject groups are unbalanced (= unequal sample sizes),
a type II ANOVA will be computed. Note however that SPSS, JAMOVI and JASP by default
return a type III ANOVA, which may lead to slightly different results.
Examples
--------
For more examples, please refer to the `Jupyter notebooks
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/01_ANOVA.ipynb>`_
Compute a two-way mixed model ANOVA.
>>> from pingouin import mixed_anova, read_dataset
>>> df = read_dataset('mixed_anova')
>>> aov = mixed_anova(dv='Scores', between='Group',
... within='Time', subject='Subject', data=df)
>>> aov.round(3)
Source SS DF1 DF2 MS F p-unc np2 eps
0 Group 5.460 1 58 5.460 5.052 0.028 0.080 NaN
1 Time 7.628 2 116 3.814 4.027 0.020 0.065 0.999
2 Interaction 5.167 2 116 2.584 2.728 0.070 0.045 NaN
Same but reporting a generalized eta-squared effect size. Notice how we
can also apply this function directly as a method of the dataframe, in
which case we do not need to specify ``data=df`` anymore.
>>> df.mixed_anova(dv='Scores', between='Group', within='Time',
... subject='Subject', effsize="ng2").round(3)
Source SS DF1 DF2 MS F p-unc ng2 eps
0 Group 5.460 1 58 5.460 5.052 0.028 0.031 NaN
1 Time 7.628 2 116 3.814 4.027 0.020 0.042 0.999
2 Interaction 5.167 2 116 2.584 2.728 0.070 0.029 NaN
| @pf.register_dataframe_method
def mixed_anova(
data=None, dv=None, within=None, subject=None, between=None, correction="auto", effsize="np2"
):
"""Mixed-design (split-plot) ANOVA.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
within : string
Name of column containing the within-subject factor
(repeated measurements).
subject : string
Name of column containing the between-subject identifier.
between : string
Name of column containing the between factor.
correction : string or boolean
If True, return Greenhouse-Geisser corrected p-value.
If `'auto'` (default), compute Mauchly's test of sphericity to
determine whether the p-values needs to be corrected.
effsize : str
Effect size. Must be one of 'np2' (partial eta-squared), 'n2'
(eta-squared) or 'ng2'(generalized eta-squared).
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Names of the factor considered
* ``'ddof1'``: Degrees of freedom (numerator)
* ``'ddof2'``: Degrees of freedom (denominator)
* ``'F'``: F-values
* ``'p-unc'``: Uncorrected p-values
* ``'np2'``: Partial eta-squared effect sizes
* ``'eps'``: Greenhouse-Geisser epsilon factor (= index of sphericity)
* ``'p-GG-corr'``: Greenhouse-Geisser corrected p-values
* ``'W-spher'``: Sphericity test statistic
* ``'p-spher'``: p-value of the sphericity test
* ``'sphericity'``: sphericity of the data (boolean)
See Also
--------
anova, rm_anova, pairwise_tests
Notes
-----
Data are expected to be in long-format (even the repeated measures).
If your data is in wide-format, you can use the :py:func:`pandas.melt()`
function to convert from wide to long format.
Missing values are automatically removed using a strict listwise approach (= complete-case
analysis). In other words, any subject with one or more missing value(s) is completely removed
from the dataframe prior to running the test. This could drastically decrease the power of the
ANOVA if many missing values are present. In that case, we strongly recommend using linear
mixed effect modelling, which can handle missing values in repeated measures.
.. warning :: If the between-subject groups are unbalanced (= unequal sample sizes),
a type II ANOVA will be computed. Note however that SPSS, JAMOVI and JASP by default
return a type III ANOVA, which may lead to slightly different results.
Examples
--------
For more examples, please refer to the `Jupyter notebooks
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/01_ANOVA.ipynb>`_
Compute a two-way mixed model ANOVA.
>>> from pingouin import mixed_anova, read_dataset
>>> df = read_dataset('mixed_anova')
>>> aov = mixed_anova(dv='Scores', between='Group',
... within='Time', subject='Subject', data=df)
>>> aov.round(3)
Source SS DF1 DF2 MS F p-unc np2 eps
0 Group 5.460 1 58 5.460 5.052 0.028 0.080 NaN
1 Time 7.628 2 116 3.814 4.027 0.020 0.065 0.999
2 Interaction 5.167 2 116 2.584 2.728 0.070 0.045 NaN
Same but reporting a generalized eta-squared effect size. Notice how we
can also apply this function directly as a method of the dataframe, in
which case we do not need to specify ``data=df`` anymore.
>>> df.mixed_anova(dv='Scores', between='Group', within='Time',
... subject='Subject', effsize="ng2").round(3)
Source SS DF1 DF2 MS F p-unc ng2 eps
0 Group 5.460 1 58 5.460 5.052 0.028 0.031 NaN
1 Time 7.628 2 116 3.814 4.027 0.020 0.042 0.999
2 Interaction 5.167 2 116 2.584 2.728 0.070 0.029 NaN
"""
assert effsize in ["n2", "np2", "ng2"], "effsize must be n2, np2 or ng2."
# Check that only a single within and between factor are provided
one_is_list = isinstance(within, list) or isinstance(between, list)
both_are_str = isinstance(within, (str, int)) and isinstance(between, (str, int))
if one_is_list or not both_are_str:
raise ValueError(
"within and between factors must both be strings referring to a column in the data. "
"Specifying multiple within and between factors is currently not supported. "
"For more information, see: https://github.com/raphaelvallat/pingouin/issues/136"
)
# Check data
data = _check_dataframe(
dv=dv, within=within, between=between, data=data, subject=subject, effects="interaction"
)
# Pivot and melt the table. This has several effects:
# 1) Force missing values to be explicit (a NaN cell is created)
# 2) Automatic collapsing to the mean if multiple within factors are present
# 3) If using dropna, remove rows with missing values (listwise deletion).
# The latter is the same behavior as JASP (= strict complete-case analysis).
data_piv = data.pivot_table(index=[subject, between], columns=within, values=dv, observed=True)
data_piv = data_piv.dropna()
data = data_piv.melt(ignore_index=False, value_name=dv).reset_index()
# Check that subject IDs do not overlap between groups: the subject ID
# should have a unique range / set of values for each between-subject
# group e.g. group1= 1 --> 20 and group2 = 21 --> 40.
if not (data.groupby([subject, within], observed=True)[between].nunique() == 1).all():
raise ValueError(
"Subject IDs cannot overlap between groups: each "
"group in `%s` must have a unique set of "
"subject IDs, e.g. group1 = [1, 2, 3, ..., 10] "
"and group2 = [11, 12, 13, ..., 20]" % between
)
# SUMS OF SQUARES
grandmean = data[dv].mean(numeric_only=True)
ss_total = ((data[dv] - grandmean) ** 2).sum()
# Extract main effects of within and between factors
aov_with = rm_anova(
dv=dv, within=within, subject=subject, data=data, correction=correction, detailed=True
)
aov_betw = anova(dv=dv, between=between, data=data, detailed=True)
ss_betw = aov_betw.at[0, "SS"]
ss_with = aov_with.at[0, "SS"]
# Extract residuals and interactions
grp = data.groupby([between, within], observed=True, group_keys=False)[dv]
# ssresall = residuals within + residuals between
ss_resall = grp.apply(lambda x: (x - x.mean()) ** 2).sum()
# Interaction
ss_inter = ss_total - (ss_resall + ss_with + ss_betw)
ss_reswith = aov_with.at[1, "SS"] - ss_inter
ss_resbetw = ss_total - (ss_with + ss_betw + ss_reswith + ss_inter)
# DEGREES OF FREEDOM
n_obs = data.groupby(within, observed=True)[dv].count().max()
df_with = aov_with.at[0, "DF"]
df_betw = aov_betw.at[0, "DF"]
df_resbetw = n_obs - data.groupby(between, observed=True)[dv].count().count()
df_reswith = df_with * df_resbetw
df_inter = aov_with.at[0, "DF"] * aov_betw.at[0, "DF"]
# MEAN SQUARES
ms_betw = aov_betw.at[0, "MS"]
ms_with = aov_with.at[0, "MS"]
ms_resbetw = ss_resbetw / df_resbetw
ms_reswith = ss_reswith / df_reswith
ms_inter = ss_inter / df_inter
# F VALUES
f_betw = ms_betw / ms_resbetw
f_with = ms_with / ms_reswith
f_inter = ms_inter / ms_reswith
# P-values
p_betw = f(df_betw, df_resbetw).sf(f_betw)
p_with = f(df_with, df_reswith).sf(f_with)
p_inter = f(df_inter, df_reswith).sf(f_inter)
# Effects sizes (see Bakeman 2005)
if effsize == "n2":
# Standard eta-squared
ef_betw = ss_betw / ss_total
ef_with = ss_with / ss_total
ef_inter = ss_inter / ss_total
elif effsize == "ng2":
# Generalized eta-square
ef_betw = ss_betw / | (data=None, dv=None, within=None, subject=None, between=None, correction='auto', effsize='np2') | [
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|
32,022 | pingouin.multicomp | multicomp | P-values correction for multiple comparisons.
Parameters
----------
pvals : array_like
Uncorrected p-values.
alpha : float
Significance level.
method : string
Method used for testing and adjustment of p-values. Can be either the
full name or initial letters. Available methods are:
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
* ``'none'``: pass-through option (no correction applied)
Returns
-------
reject : array, boolean
True for hypothesis that can be rejected for given alpha.
pvals_corrected : array
P-values corrected for multiple testing.
Notes
-----
This function is similar to the `p.adjust
<https://stat.ethz.ch/R-manual/R-devel/library/stats/html/p.adjust.html>`_
R function.
The correction methods include the Bonferroni correction (``'bonf'``)
in which the p-values are multiplied by the number of comparisons.
Less conservative methods are also included such as Sidak (1967)
(``'sidak'``), Holm (1979) (``'holm'``), Benjamini & Hochberg (1995)
(``'fdr_bh'``), and Benjamini & Yekutieli (2001) (``'fdr_by'``),
respectively.
The first three methods are designed to give strong control of the
family-wise error rate. Note that the Holm's method is usually preferred.
The ``'fdr_bh'`` and ``'fdr_by'`` methods control the false discovery rate,
i.e. the expected proportion of false discoveries amongst the rejected
hypotheses. The false discovery rate is a less stringent condition than
the family-wise error rate, so these methods are more powerful than the
others.
The **Bonferroni** [1]_ adjusted p-values are defined as:
.. math::
\widetilde {p}_{{(i)}}= n \cdot p_{{(i)}}
where :math:`n` is the number of *finite* p-values (i.e. excluding NaN).
The **Sidak** [2]_ adjusted p-values are defined as:
.. math::
\widetilde {p}_{{(i)}}= 1 - (1 - p_{{(i)}})^{n}
The **Holm** [3]_ adjusted p-values are the running maximum of the sorted
p-values divided by the corresponding increasing alpha level:
.. math::
\widetilde {p}_{{(i)}}=\max _{{j\leq i}}\left\{(n-j+1)p_{{(j)}}
\right\}_{{1}}
The **Benjamini–Hochberg** procedure (BH step-up procedure, [4]_)
controls the false discovery rate (FDR) at level :math:`\alpha`.
It works as follows:
1. For a given :math:`\alpha`, find the largest :math:`k` such that
:math:`P_{(k)}\leq \frac {k}{n}\alpha.`
2. Reject the null hypothesis for all
:math:`H_{(i)}` for :math:`i = 1, \ldots, k`.
The BH procedure is valid when the :math:`n` tests are independent, and
also in various scenarios of dependence, but is not universally valid.
The **Benjamini–Yekutieli** procedure (BY, [5]_) controls the FDR under
arbitrary dependence assumptions. This refinement modifies the threshold
and finds the largest :math:`k` such that:
.. math::
P_{(k)} \leq \frac{k}{n \cdot c(n)} \alpha
References
----------
.. [1] Bonferroni, C. E. (1935). Il calcolo delle assicurazioni su gruppi
di teste. Studi in onore del professore salvatore ortu carboni, 13-60.
.. [2] Šidák, Z. K. (1967). "Rectangular Confidence Regions for the Means
of Multivariate Normal Distributions". Journal of the American
Statistical Association. 62 (318): 626–633.
.. [3] Holm, S. (1979). A simple sequentially rejective multiple test
procedure. Scandinavian Journal of Statistics, 6, 65–70.
.. [4] Benjamini, Y., and Hochberg, Y. (1995). Controlling the false
discovery rate: a practical and powerful approach to multiple testing.
Journal of the Royal Statistical Society Series B, 57, 289–300.
.. [5] Benjamini, Y., and Yekutieli, D. (2001). The control of the false
discovery rate in multiple testing under dependency. Annals of
Statistics, 29, 1165–1188.
Examples
--------
FDR correction of an array of p-values
>>> import pingouin as pg
>>> pvals = [.50, .003, .32, .054, .0003]
>>> reject, pvals_corr = pg.multicomp(pvals, method='fdr_bh')
>>> print(reject, pvals_corr)
[False True False False True] [0.5 0.0075 0.4 0.09 0.0015]
Holm correction with missing values
>>> import numpy as np
>>> pvals[2] = np.nan
>>> reject, pvals_corr = pg.multicomp(pvals, method='holm')
>>> print(reject, pvals_corr)
[False True False False True] [0.5 0.009 nan 0.108 0.0012]
| def multicomp(pvals, alpha=0.05, method="holm"):
"""P-values correction for multiple comparisons.
Parameters
----------
pvals : array_like
Uncorrected p-values.
alpha : float
Significance level.
method : string
Method used for testing and adjustment of p-values. Can be either the
full name or initial letters. Available methods are:
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
* ``'none'``: pass-through option (no correction applied)
Returns
-------
reject : array, boolean
True for hypothesis that can be rejected for given alpha.
pvals_corrected : array
P-values corrected for multiple testing.
Notes
-----
This function is similar to the `p.adjust
<https://stat.ethz.ch/R-manual/R-devel/library/stats/html/p.adjust.html>`_
R function.
The correction methods include the Bonferroni correction (``'bonf'``)
in which the p-values are multiplied by the number of comparisons.
Less conservative methods are also included such as Sidak (1967)
(``'sidak'``), Holm (1979) (``'holm'``), Benjamini & Hochberg (1995)
(``'fdr_bh'``), and Benjamini & Yekutieli (2001) (``'fdr_by'``),
respectively.
The first three methods are designed to give strong control of the
family-wise error rate. Note that the Holm's method is usually preferred.
The ``'fdr_bh'`` and ``'fdr_by'`` methods control the false discovery rate,
i.e. the expected proportion of false discoveries amongst the rejected
hypotheses. The false discovery rate is a less stringent condition than
the family-wise error rate, so these methods are more powerful than the
others.
The **Bonferroni** [1]_ adjusted p-values are defined as:
.. math::
\\widetilde {p}_{{(i)}}= n \\cdot p_{{(i)}}
where :math:`n` is the number of *finite* p-values (i.e. excluding NaN).
The **Sidak** [2]_ adjusted p-values are defined as:
.. math::
\\widetilde {p}_{{(i)}}= 1 - (1 - p_{{(i)}})^{n}
The **Holm** [3]_ adjusted p-values are the running maximum of the sorted
p-values divided by the corresponding increasing alpha level:
.. math::
\\widetilde {p}_{{(i)}}=\\max _{{j\\leq i}}\\left\\{(n-j+1)p_{{(j)}}
\\right\\}_{{1}}
The **Benjamini–Hochberg** procedure (BH step-up procedure, [4]_)
controls the false discovery rate (FDR) at level :math:`\\alpha`.
It works as follows:
1. For a given :math:`\\alpha`, find the largest :math:`k` such that
:math:`P_{(k)}\\leq \\frac {k}{n}\\alpha.`
2. Reject the null hypothesis for all
:math:`H_{(i)}` for :math:`i = 1, \\ldots, k`.
The BH procedure is valid when the :math:`n` tests are independent, and
also in various scenarios of dependence, but is not universally valid.
The **Benjamini–Yekutieli** procedure (BY, [5]_) controls the FDR under
arbitrary dependence assumptions. This refinement modifies the threshold
and finds the largest :math:`k` such that:
.. math::
P_{(k)} \\leq \\frac{k}{n \\cdot c(n)} \\alpha
References
----------
.. [1] Bonferroni, C. E. (1935). Il calcolo delle assicurazioni su gruppi
di teste. Studi in onore del professore salvatore ortu carboni, 13-60.
.. [2] Šidák, Z. K. (1967). "Rectangular Confidence Regions for the Means
of Multivariate Normal Distributions". Journal of the American
Statistical Association. 62 (318): 626–633.
.. [3] Holm, S. (1979). A simple sequentially rejective multiple test
procedure. Scandinavian Journal of Statistics, 6, 65–70.
.. [4] Benjamini, Y., and Hochberg, Y. (1995). Controlling the false
discovery rate: a practical and powerful approach to multiple testing.
Journal of the Royal Statistical Society Series B, 57, 289–300.
.. [5] Benjamini, Y., and Yekutieli, D. (2001). The control of the false
discovery rate in multiple testing under dependency. Annals of
Statistics, 29, 1165–1188.
Examples
--------
FDR correction of an array of p-values
>>> import pingouin as pg
>>> pvals = [.50, .003, .32, .054, .0003]
>>> reject, pvals_corr = pg.multicomp(pvals, method='fdr_bh')
>>> print(reject, pvals_corr)
[False True False False True] [0.5 0.0075 0.4 0.09 0.0015]
Holm correction with missing values
>>> import numpy as np
>>> pvals[2] = np.nan
>>> reject, pvals_corr = pg.multicomp(pvals, method='holm')
>>> print(reject, pvals_corr)
[False True False False True] [0.5 0.009 nan 0.108 0.0012]
"""
# Safety check
assert isinstance(pvals, (list, np.ndarray, Series)), "pvals must be list or array"
assert isinstance(alpha, float), "alpha must be a float."
assert isinstance(method, str), "method must be a string."
assert 0 < alpha < 1, "alpha must be between 0 and 1."
pvals = np.asarray(pvals)
if method.lower() in ["b", "bonf", "bonferroni"]:
reject, pvals_corrected = bonf(pvals, alpha=alpha)
elif method.lower() in ["h", "holm"]:
reject, pvals_corrected = holm(pvals, alpha=alpha)
elif method.lower() in ["s", "sidak"]:
reject, pvals_corrected = sidak(pvals, alpha=alpha)
elif method.lower() in ["fdr", "fdr_bh", "bh"]:
reject, pvals_corrected = fdr(pvals, alpha=alpha, method="fdr_bh")
elif method.lower() in ["fdr_by", "by"]:
reject, pvals_corrected = fdr(pvals, alpha=alpha, method="fdr_by")
elif method.lower() == "none":
pvals_corrected = pvals
with np.errstate(invalid="ignore"):
reject = np.less(pvals_corrected, alpha)
else:
raise ValueError("Multiple comparison method not recognized")
return reject, pvals_corrected
| (pvals, alpha=0.05, method='holm') | [
0.03242960944771767,
0.0028958774637430906,
-0.031100353226065636,
0.011646808125078678,
-0.010143483057618141,
-0.048528365790843964,
0.006234840024262667,
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0.008007179945707321,
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0.00532229570671916,
0.03131134435534477,
0.013071009889245033,
-0.06574538350105286,
0.04287375509738922,
0.006403634324669838,
0.029306912794709206,
-0.011815601959824562,
0.007215957157313824,
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0.01929529942572117,
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0.08389077335596085,
0.04456169903278351,
0.005818129051476717,
0.04074272885918617,
0.0003272038302384317,
-0.02639521099627018,
0.034265246242284775,
0.013587942346930504,
0.03175443038344383,
-0.023778898641467094,
0.013830584473907948,
0.0072212317027151585,
-0.005754831247031689,
0.042071983218193054,
0.00425414415076375,
-0.10102339833974838,
0.02190106175839901,
0.015803366899490356,
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0.02941240929067135,
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0.04006754979491234,
0.028547339141368866,
0.08173865079879761,
0.003399623092263937,
0.02996099181473255,
0.0048897601664066315,
-0.026142019778490067,
0.02175336703658104,
0.010111834853887558,
-0.010897782631218433,
0.1168900653719902,
0.03447623923420906,
0.025087054818868637,
-0.0035130316391587257,
-0.08608510345220566,
-0.013271452859044075,
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0.04329574108123779,
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0.01649964414536953,
-0.02310372143983841,
0.0022180627565830946,
-0.03899148851633072,
-0.029939891770482063,
0.01101382914930582,
0.014495211653411388,
0.0008657302241772413,
-0.04274716228246689,
-0.006630451884120703,
0.0516088604927063,
0.02609982155263424,
0.03213421627879143,
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0.0028800528962165117,
0.033294677734375,
0.05924680456519127,
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|
32,024 | pingouin.multivariate | multivariate_normality | Henze-Zirkler multivariate normality test.
Parameters
----------
X : np.array
Data matrix of shape (n_samples, n_features).
alpha : float
Significance level.
Returns
-------
hz : float
The Henze-Zirkler test statistic.
pval : float
P-value.
normal : boolean
True if X comes from a multivariate normal distribution.
See Also
--------
normality : Test the univariate normality of one or more variables.
homoscedasticity : Test equality of variance.
sphericity : Mauchly's test for sphericity.
Notes
-----
The Henze-Zirkler test [1]_ has a good overall power against alternatives
to normality and works for any dimension and sample size.
Adapted to Python from a Matlab code [2]_ by Antonio Trujillo-Ortiz and
tested against the
`MVN <https://cran.r-project.org/web/packages/MVN/MVN.pdf>`_ R package.
Rows with missing values are automatically removed.
References
----------
.. [1] Henze, N., & Zirkler, B. (1990). A class of invariant consistent
tests for multivariate normality. Communications in Statistics-Theory
and Methods, 19(10), 3595-3617.
.. [2] Trujillo-Ortiz, A., R. Hernandez-Walls, K. Barba-Rojo and L.
Cupul-Magana. (2007). HZmvntest: Henze-Zirkler's Multivariate
Normality Test. A MATLAB file.
Examples
--------
>>> import pingouin as pg
>>> data = pg.read_dataset('multivariate')
>>> X = data[['Fever', 'Pressure', 'Aches']]
>>> pg.multivariate_normality(X, alpha=.05)
HZResults(hz=0.540086101851555, pval=0.7173686509622386, normal=True)
| def multivariate_normality(X, alpha=0.05):
"""Henze-Zirkler multivariate normality test.
Parameters
----------
X : np.array
Data matrix of shape (n_samples, n_features).
alpha : float
Significance level.
Returns
-------
hz : float
The Henze-Zirkler test statistic.
pval : float
P-value.
normal : boolean
True if X comes from a multivariate normal distribution.
See Also
--------
normality : Test the univariate normality of one or more variables.
homoscedasticity : Test equality of variance.
sphericity : Mauchly's test for sphericity.
Notes
-----
The Henze-Zirkler test [1]_ has a good overall power against alternatives
to normality and works for any dimension and sample size.
Adapted to Python from a Matlab code [2]_ by Antonio Trujillo-Ortiz and
tested against the
`MVN <https://cran.r-project.org/web/packages/MVN/MVN.pdf>`_ R package.
Rows with missing values are automatically removed.
References
----------
.. [1] Henze, N., & Zirkler, B. (1990). A class of invariant consistent
tests for multivariate normality. Communications in Statistics-Theory
and Methods, 19(10), 3595-3617.
.. [2] Trujillo-Ortiz, A., R. Hernandez-Walls, K. Barba-Rojo and L.
Cupul-Magana. (2007). HZmvntest: Henze-Zirkler's Multivariate
Normality Test. A MATLAB file.
Examples
--------
>>> import pingouin as pg
>>> data = pg.read_dataset('multivariate')
>>> X = data[['Fever', 'Pressure', 'Aches']]
>>> pg.multivariate_normality(X, alpha=.05)
HZResults(hz=0.540086101851555, pval=0.7173686509622386, normal=True)
"""
from scipy.stats import lognorm
# Check input and remove missing values
X = np.asarray(X)
assert X.ndim == 2, "X must be of shape (n_samples, n_features)."
X = X[~np.isnan(X).any(axis=1)]
n, p = X.shape
assert n >= 3, "X must have at least 3 rows."
assert p >= 2, "X must have at least two columns."
# Covariance matrix
S = np.cov(X, rowvar=False, bias=True)
S_inv = np.linalg.pinv(S, hermitian=True).astype(X.dtype) # Preserving original dtype
difT = X - X.mean(0)
# Squared-Mahalanobis distances
Dj = np.diag(np.linalg.multi_dot([difT, S_inv, difT.T]))
Y = np.linalg.multi_dot([X, S_inv, X.T])
Djk = -2 * Y.T + np.repeat(np.diag(Y.T), n).reshape(n, -1) + np.tile(np.diag(Y.T), (n, 1))
# Smoothing parameter
b = 1 / (np.sqrt(2)) * ((2 * p + 1) / 4) ** (1 / (p + 4)) * (n ** (1 / (p + 4)))
# Is matrix full-rank (columns are linearly independent)?
if np.linalg.matrix_rank(S) == p:
hz = n * (
1 / (n**2) * np.sum(np.sum(np.exp(-(b**2) / 2 * Djk)))
- 2
* ((1 + (b**2)) ** (-p / 2))
* (1 / n)
* (np.sum(np.exp(-((b**2) / (2 * (1 + (b**2)))) * Dj)))
+ ((1 + (2 * (b**2))) ** (-p / 2))
)
else:
hz = n * 4
wb = (1 + b**2) * (1 + 3 * b**2)
a = 1 + 2 * b**2
# Mean and variance
mu = 1 - a ** (-p / 2) * (1 + p * b**2 / a + (p * (p + 2) * (b**4)) / (2 * a**2))
si2 = (
2 * (1 + 4 * b**2) ** (-p / 2)
+ 2
* a ** (-p)
* (1 + (2 * p * b**4) / a**2 + (3 * p * (p + 2) * b**8) / (4 * a**4))
- 4
* wb ** (-p / 2)
* (1 + (3 * p * b**4) / (2 * wb) + (p * (p + 2) * b**8) / (2 * wb**2))
)
# Lognormal mean and variance
pmu = np.log(np.sqrt(mu**4 / (si2 + mu**2)))
psi = np.sqrt(np.log1p(si2 / mu**2))
# P-value
pval = lognorm.sf(hz, psi, scale=np.exp(pmu))
normal = True if pval > alpha else False
HZResults = namedtuple("HZResults", ["hz", "pval", "normal"])
return HZResults(hz=hz, pval=pval, normal=normal)
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|
32,025 | pingouin.multivariate | multivariate_ttest | Hotelling T-squared test (= multivariate T-test)
Parameters
----------
X : np.array
First data matrix of shape (n_samples, n_features).
Y : np.array or None
Second data matrix of shape (n_samples, n_features). If ``Y`` is a 1D
array of shape (n_features), a one-sample test is performed where the
null hypothesis is defined in ``Y``. If ``Y`` is None, a one-sample
is performed against np.zeros(n_features).
paired : boolean
Specify whether the two observations are related (i.e. repeated
measures) or independent. If ``paired`` is True, ``X`` and ``Y`` must
have exactly the same shape.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'T2'``: T-squared value
* ``'F'``: F-value
* ``'df1'``: first degree of freedom
* ``'df2'``: second degree of freedom
* ``'p-val'``: p-value
See Also
--------
multivariate_normality : Multivariate normality test.
ttest : Univariate T-test.
Notes
-----
The Hotelling 's T-squared test [1]_ is the multivariate counterpart of
the T-test.
Rows with missing values are automatically removed using the
:py:func:`remove_na` function.
Tested against the `Hotelling
<https://cran.r-project.org/web/packages/Hotelling/Hotelling.pdf>`_ R
package.
References
----------
.. [1] Hotelling, H. The Generalization of Student's Ratio. Ann. Math.
Statist. 2 (1931), no. 3, 360--378.
See also http://www.real-statistics.com/multivariate-statistics/
Examples
--------
Two-sample independent Hotelling T-squared test
>>> import pingouin as pg
>>> data = pg.read_dataset('multivariate')
>>> dvs = ['Fever', 'Pressure', 'Aches']
>>> X = data[data['Condition'] == 'Drug'][dvs]
>>> Y = data[data['Condition'] == 'Placebo'][dvs]
>>> pg.multivariate_ttest(X, Y)
T2 F df1 df2 pval
hotelling 4.228679 1.326644 3 32 0.282898
Two-sample paired Hotelling T-squared test
>>> pg.multivariate_ttest(X, Y, paired=True)
T2 F df1 df2 pval
hotelling 4.468456 1.314252 3 15 0.306542
One-sample Hotelling T-squared test with a specified null hypothesis
>>> null_hypothesis_means = [37.5, 70, 5]
>>> pg.multivariate_ttest(X, Y=null_hypothesis_means)
T2 F df1 df2 pval
hotelling 253.230991 74.479703 3 15 3.081281e-09
| def multivariate_ttest(X, Y=None, paired=False):
"""Hotelling T-squared test (= multivariate T-test)
Parameters
----------
X : np.array
First data matrix of shape (n_samples, n_features).
Y : np.array or None
Second data matrix of shape (n_samples, n_features). If ``Y`` is a 1D
array of shape (n_features), a one-sample test is performed where the
null hypothesis is defined in ``Y``. If ``Y`` is None, a one-sample
is performed against np.zeros(n_features).
paired : boolean
Specify whether the two observations are related (i.e. repeated
measures) or independent. If ``paired`` is True, ``X`` and ``Y`` must
have exactly the same shape.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'T2'``: T-squared value
* ``'F'``: F-value
* ``'df1'``: first degree of freedom
* ``'df2'``: second degree of freedom
* ``'p-val'``: p-value
See Also
--------
multivariate_normality : Multivariate normality test.
ttest : Univariate T-test.
Notes
-----
The Hotelling 's T-squared test [1]_ is the multivariate counterpart of
the T-test.
Rows with missing values are automatically removed using the
:py:func:`remove_na` function.
Tested against the `Hotelling
<https://cran.r-project.org/web/packages/Hotelling/Hotelling.pdf>`_ R
package.
References
----------
.. [1] Hotelling, H. The Generalization of Student's Ratio. Ann. Math.
Statist. 2 (1931), no. 3, 360--378.
See also http://www.real-statistics.com/multivariate-statistics/
Examples
--------
Two-sample independent Hotelling T-squared test
>>> import pingouin as pg
>>> data = pg.read_dataset('multivariate')
>>> dvs = ['Fever', 'Pressure', 'Aches']
>>> X = data[data['Condition'] == 'Drug'][dvs]
>>> Y = data[data['Condition'] == 'Placebo'][dvs]
>>> pg.multivariate_ttest(X, Y)
T2 F df1 df2 pval
hotelling 4.228679 1.326644 3 32 0.282898
Two-sample paired Hotelling T-squared test
>>> pg.multivariate_ttest(X, Y, paired=True)
T2 F df1 df2 pval
hotelling 4.468456 1.314252 3 15 0.306542
One-sample Hotelling T-squared test with a specified null hypothesis
>>> null_hypothesis_means = [37.5, 70, 5]
>>> pg.multivariate_ttest(X, Y=null_hypothesis_means)
T2 F df1 df2 pval
hotelling 253.230991 74.479703 3 15 3.081281e-09
"""
from scipy.stats import f
x = np.asarray(X)
assert x.ndim == 2, "x must be of shape (n_samples, n_features)"
if Y is None:
y = np.zeros(x.shape[1])
# Remove rows with missing values in x
x = x[~np.isnan(x).any(axis=1)]
else:
nx, kx = x.shape
y = np.asarray(Y)
assert y.ndim in [1, 2], "Y must be 1D or 2D."
if y.ndim == 1:
# One sample with specified null
assert y.size == kx
else:
# Two-sample
err = "X and Y must have the same number of features (= columns)."
assert y.shape[1] == kx, err
if paired:
err = "X and Y must have the same number of rows if paired."
assert y.shape[0] == nx, err
# Remove rows with missing values in both x and y
x, y = remove_na(x, y, paired=paired, axis="rows")
# Shape of arrays
nx, k = x.shape
ny = y.shape[0]
assert nx >= 5, "At least five samples are required."
if y.ndim == 1 or paired is True:
n = nx
if y.ndim == 1:
# One sample test
cov = np.cov(x, rowvar=False)
diff = x.mean(0) - y
else:
# Paired two sample
cov = np.cov(x - y, rowvar=False)
diff = x.mean(0) - y.mean(0)
inv_cov = np.linalg.pinv(cov, hermitian=True)
t2 = (diff @ inv_cov) @ diff * n
else:
n = nx + ny - 1
x_cov = np.cov(x, rowvar=False)
y_cov = np.cov(y, rowvar=False)
pooled_cov = ((nx - 1) * x_cov + (ny - 1) * y_cov) / (n - 1)
inv_cov = np.linalg.pinv((1 / nx + 1 / ny) * pooled_cov, hermitian=True)
diff = x.mean(0) - y.mean(0)
t2 = (diff @ inv_cov) @ diff
# F-value, degrees of freedom and p-value
fval = t2 * (n - k) / (k * (n - 1))
df1 = k
df2 = n - k
pval = f.sf(fval, df1, df2)
# Create output dictionnary
stats = {"T2": t2, "F": fval, "df1": df1, "df2": df2, "pval": pval}
stats = pd.DataFrame(stats, index=["hotelling"])
return _postprocess_dataframe(stats)
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|
32,026 | pingouin.nonparametric | mwu | Mann-Whitney U Test (= Wilcoxon rank-sum test). It is the non-parametric
version of the independent T-test.
Parameters
----------
x, y : array_like
First and second set of observations. ``x`` and ``y`` must be
independent.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". See :py:func:`scipy.stats.mannwhitneyu` for
more details.
**kwargs : dict
Additional keywords arguments that are passed to :py:func:`scipy.stats.mannwhitneyu`.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'U-val'``: U-value
* ``'alternative'``: tail of the test
* ``'p-val'``: p-value
* ``'RBC'`` : rank-biserial correlation
* ``'CLES'`` : common language effect size
See also
--------
scipy.stats.mannwhitneyu, wilcoxon, ttest
Notes
-----
The Mann–Whitney U test [1]_ (also called Wilcoxon rank-sum test) is a
non-parametric test of the null hypothesis that it is equally likely that
a randomly selected value from one sample will be less than or greater
than a randomly selected value from a second sample. The test assumes
that the two samples are independent. This test corrects for ties and by
default uses a continuity correction (see :py:func:`scipy.stats.mannwhitneyu` for details).
The rank biserial correlation [2]_ is the difference between
the proportion of favorable evidence minus the proportion of unfavorable
evidence.
The common language effect size is the proportion of pairs where ``x`` is
higher than ``y``. It was first introduced by McGraw and Wong (1992) [3]_.
Pingouin uses a brute-force version of the formula given by Vargha and
Delaney 2000 [4]_:
.. math:: \text{CL} = P(X > Y) + .5 \times P(X = Y)
The advantage is of this method are twofold. First, the brute-force
approach pairs each observation of ``x`` to its ``y`` counterpart, and
therefore does not require normally distributed data. Second, the formula
takes ties into account and therefore works with ordinal data.
When tail is ``'less'``, the CLES is then set to :math:`1 - \text{CL}`,
which gives the proportion of pairs where ``x`` is *lower* than ``y``.
References
----------
.. [1] Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of
two random variables is stochastically larger than the other.
The annals of mathematical statistics, 50-60.
.. [2] Kerby, D. S. (2014). The simple difference formula: An approach to
teaching nonparametric correlation. Comprehensive Psychology,
3, 11-IT.
.. [3] McGraw, K. O., & Wong, S. P. (1992). A common language effect size
statistic. Psychological bulletin, 111(2), 361.
.. [4] Vargha, A., & Delaney, H. D. (2000). A Critique and Improvement of
the “CL” Common Language Effect Size Statistics of McGraw and Wong.
Journal of Educational and Behavioral Statistics: A Quarterly
Publication Sponsored by the American Educational Research
Association and the American Statistical Association, 25(2),
101–132. https://doi.org/10.2307/1165329
Examples
--------
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.uniform(low=0, high=1, size=20)
>>> y = np.random.uniform(low=0.2, high=1.2, size=20)
>>> pg.mwu(x, y, alternative='two-sided')
U-val alternative p-val RBC CLES
MWU 97.0 two-sided 0.00556 0.515 0.2425
Compare with SciPy
>>> import scipy
>>> scipy.stats.mannwhitneyu(x, y, use_continuity=True, alternative='two-sided')
MannwhitneyuResult(statistic=97.0, pvalue=0.0055604599321374135)
One-sided test
>>> pg.mwu(x, y, alternative='greater')
U-val alternative p-val RBC CLES
MWU 97.0 greater 0.997442 0.515 0.2425
>>> pg.mwu(x, y, alternative='less')
U-val alternative p-val RBC CLES
MWU 97.0 less 0.00278 0.515 0.7575
Passing keyword arguments to :py:func:`scipy.stats.mannwhitneyu`:
>>> pg.mwu(x, y, alternative='two-sided', method='exact')
U-val alternative p-val RBC CLES
MWU 97.0 two-sided 0.004681 0.515 0.2425
| def mwu(x, y, alternative="two-sided", **kwargs):
"""Mann-Whitney U Test (= Wilcoxon rank-sum test). It is the non-parametric
version of the independent T-test.
Parameters
----------
x, y : array_like
First and second set of observations. ``x`` and ``y`` must be
independent.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". See :py:func:`scipy.stats.mannwhitneyu` for
more details.
**kwargs : dict
Additional keywords arguments that are passed to :py:func:`scipy.stats.mannwhitneyu`.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'U-val'``: U-value
* ``'alternative'``: tail of the test
* ``'p-val'``: p-value
* ``'RBC'`` : rank-biserial correlation
* ``'CLES'`` : common language effect size
See also
--------
scipy.stats.mannwhitneyu, wilcoxon, ttest
Notes
-----
The Mann–Whitney U test [1]_ (also called Wilcoxon rank-sum test) is a
non-parametric test of the null hypothesis that it is equally likely that
a randomly selected value from one sample will be less than or greater
than a randomly selected value from a second sample. The test assumes
that the two samples are independent. This test corrects for ties and by
default uses a continuity correction (see :py:func:`scipy.stats.mannwhitneyu` for details).
The rank biserial correlation [2]_ is the difference between
the proportion of favorable evidence minus the proportion of unfavorable
evidence.
The common language effect size is the proportion of pairs where ``x`` is
higher than ``y``. It was first introduced by McGraw and Wong (1992) [3]_.
Pingouin uses a brute-force version of the formula given by Vargha and
Delaney 2000 [4]_:
.. math:: \\text{CL} = P(X > Y) + .5 \\times P(X = Y)
The advantage is of this method are twofold. First, the brute-force
approach pairs each observation of ``x`` to its ``y`` counterpart, and
therefore does not require normally distributed data. Second, the formula
takes ties into account and therefore works with ordinal data.
When tail is ``'less'``, the CLES is then set to :math:`1 - \\text{CL}`,
which gives the proportion of pairs where ``x`` is *lower* than ``y``.
References
----------
.. [1] Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of
two random variables is stochastically larger than the other.
The annals of mathematical statistics, 50-60.
.. [2] Kerby, D. S. (2014). The simple difference formula: An approach to
teaching nonparametric correlation. Comprehensive Psychology,
3, 11-IT.
.. [3] McGraw, K. O., & Wong, S. P. (1992). A common language effect size
statistic. Psychological bulletin, 111(2), 361.
.. [4] Vargha, A., & Delaney, H. D. (2000). A Critique and Improvement of
the “CL” Common Language Effect Size Statistics of McGraw and Wong.
Journal of Educational and Behavioral Statistics: A Quarterly
Publication Sponsored by the American Educational Research
Association and the American Statistical Association, 25(2),
101–132. https://doi.org/10.2307/1165329
Examples
--------
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.uniform(low=0, high=1, size=20)
>>> y = np.random.uniform(low=0.2, high=1.2, size=20)
>>> pg.mwu(x, y, alternative='two-sided')
U-val alternative p-val RBC CLES
MWU 97.0 two-sided 0.00556 0.515 0.2425
Compare with SciPy
>>> import scipy
>>> scipy.stats.mannwhitneyu(x, y, use_continuity=True, alternative='two-sided')
MannwhitneyuResult(statistic=97.0, pvalue=0.0055604599321374135)
One-sided test
>>> pg.mwu(x, y, alternative='greater')
U-val alternative p-val RBC CLES
MWU 97.0 greater 0.997442 0.515 0.2425
>>> pg.mwu(x, y, alternative='less')
U-val alternative p-val RBC CLES
MWU 97.0 less 0.00278 0.515 0.7575
Passing keyword arguments to :py:func:`scipy.stats.mannwhitneyu`:
>>> pg.mwu(x, y, alternative='two-sided', method='exact')
U-val alternative p-val RBC CLES
MWU 97.0 two-sided 0.004681 0.515 0.2425
"""
x = np.asarray(x)
y = np.asarray(y)
# Remove NA
x, y = remove_na(x, y, paired=False)
# Check tails
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
if "tail" in kwargs:
raise ValueError(
"Since Pingouin 0.4.0, the 'tail' argument has been renamed to 'alternative'."
)
uval, pval = scipy.stats.mannwhitneyu(x, y, alternative=alternative, **kwargs)
# Effect size 1: Common Language Effect Size
# CLES is tail-specific and calculated according to the formula given in
# Vargha and Delaney 2000 which works with ordinal data.
diff = x[:, None] - y
# cles = max((diff < 0).sum(), (diff > 0).sum()) / diff.size
# Tail = 'greater', with ties set to 0.5
# Note that tail = 'two-sided' gives same output as tail = 'greater'
cles = np.where(diff == 0, 0.5, diff > 0).mean()
cles = 1 - cles if alternative == "less" else cles
# Effect size 2: rank biserial correlation (Wendt 1972)
rbc = 1 - (2 * uval) / diff.size # diff.size = x.size * y.size
# Fill output DataFrame
stats = pd.DataFrame(
{"U-val": uval, "alternative": alternative, "p-val": pval, "RBC": rbc, "CLES": cles},
index=["MWU"],
)
return _postprocess_dataframe(stats)
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|
32,028 | pingouin.distribution | normality | Univariate normality test.
Parameters
----------
data : :py:class:`pandas.DataFrame`, series, list or 1D np.array
Iterable. Can be either a single list, 1D numpy array,
or a wide- or long-format pandas dataframe.
dv : str
Dependent variable (only when ``data`` is a long-format dataframe).
group : str
Grouping variable (only when ``data`` is a long-format dataframe).
method : str
Normality test. `'shapiro'` (default) performs the Shapiro-Wilk test
using :py:func:`scipy.stats.shapiro`, `'normaltest'` performs the
omnibus test of normality using :py:func:`scipy.stats.normaltest`, `'jarque_bera'` performs
the Jarque-Bera test using :py:func:`scipy.stats.jarque_bera`.
The Omnibus and Jarque-Bera tests are more suitable than the Shapiro test for
large samples.
alpha : float
Significance level.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W'``: Test statistic.
* ``'pval'``: p-value.
* ``'normal'``: True if ``data`` is normally distributed.
See Also
--------
homoscedasticity : Test equality of variance.
sphericity : Mauchly's test for sphericity.
Notes
-----
The Shapiro-Wilk test calculates a :math:`W` statistic that tests whether a
random sample :math:`x_1, x_2, ..., x_n` comes from a normal distribution.
The :math:`W` statistic is calculated as follows:
.. math::
W = \frac{(\sum_{i=1}^n a_i x_{i})^2}
{\sum_{i=1}^n (x_i - \overline{x})^2}
where the :math:`x_i` are the ordered sample values (in ascending
order) and the :math:`a_i` are constants generated from the means,
variances and covariances of the order statistics of a sample of size
:math:`n` from a standard normal distribution. Specifically:
.. math:: (a_1, ..., a_n) = \frac{m^TV^{-1}}{(m^TV^{-1}V^{-1}m)^{1/2}}
with :math:`m = (m_1, ..., m_n)^T` and :math:`(m_1, ..., m_n)` are the
expected values of the order statistics of independent and identically
distributed random variables sampled from the standard normal distribution,
and :math:`V` is the covariance matrix of those order statistics.
The null-hypothesis of this test is that the population is normally
distributed. Thus, if the p-value is less than the
chosen alpha level (typically set at 0.05), then the null hypothesis is
rejected and there is evidence that the data tested are not normally
distributed.
The result of the Shapiro-Wilk test should be interpreted with caution in
the case of large sample sizes. Indeed, quoting from
`Wikipedia <https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test>`_:
*"Like most statistical significance tests, if the sample size is
sufficiently large this test may detect even trivial departures from
the null hypothesis (i.e., although there may be some statistically
significant effect, it may be too small to be of any practical
significance); thus, additional investigation of the effect size is
typically advisable, e.g., a Q–Q plot in this case."*
Note that missing values are automatically removed (casewise deletion).
References
----------
* Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test
for normality (complete samples). Biometrika, 52(3/4), 591-611.
* https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
Examples
--------
1. Shapiro-Wilk test on a 1D array.
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.normal(size=100)
>>> pg.normality(x)
W pval normal
0 0.98414 0.274886 True
2. Omnibus test on a wide-format dataframe with missing values
>>> data = pg.read_dataset('mediation')
>>> data.loc[1, 'X'] = np.nan
>>> pg.normality(data, method='normaltest').round(3)
W pval normal
X 1.792 0.408 True
M 0.492 0.782 True
Y 0.349 0.840 True
Mbin 839.716 0.000 False
Ybin 814.468 0.000 False
W1 24.816 0.000 False
W2 43.400 0.000 False
3. Pandas Series
>>> pg.normality(data['X'], method='normaltest')
W pval normal
X 1.791839 0.408232 True
4. Long-format dataframe
>>> data = pg.read_dataset('rm_anova2')
>>> pg.normality(data, dv='Performance', group='Time')
W pval normal
Time
Pre 0.967718 0.478773 True
Post 0.940728 0.095157 True
5. Same but using the Jarque-Bera test
>>> pg.normality(data, dv='Performance', group='Time', method="jarque_bera")
W pval normal
Time
Pre 0.304021 0.858979 True
Post 1.265656 0.531088 True
| def normality(data, dv=None, group=None, method="shapiro", alpha=0.05):
"""Univariate normality test.
Parameters
----------
data : :py:class:`pandas.DataFrame`, series, list or 1D np.array
Iterable. Can be either a single list, 1D numpy array,
or a wide- or long-format pandas dataframe.
dv : str
Dependent variable (only when ``data`` is a long-format dataframe).
group : str
Grouping variable (only when ``data`` is a long-format dataframe).
method : str
Normality test. `'shapiro'` (default) performs the Shapiro-Wilk test
using :py:func:`scipy.stats.shapiro`, `'normaltest'` performs the
omnibus test of normality using :py:func:`scipy.stats.normaltest`, `'jarque_bera'` performs
the Jarque-Bera test using :py:func:`scipy.stats.jarque_bera`.
The Omnibus and Jarque-Bera tests are more suitable than the Shapiro test for
large samples.
alpha : float
Significance level.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W'``: Test statistic.
* ``'pval'``: p-value.
* ``'normal'``: True if ``data`` is normally distributed.
See Also
--------
homoscedasticity : Test equality of variance.
sphericity : Mauchly's test for sphericity.
Notes
-----
The Shapiro-Wilk test calculates a :math:`W` statistic that tests whether a
random sample :math:`x_1, x_2, ..., x_n` comes from a normal distribution.
The :math:`W` statistic is calculated as follows:
.. math::
W = \\frac{(\\sum_{i=1}^n a_i x_{i})^2}
{\\sum_{i=1}^n (x_i - \\overline{x})^2}
where the :math:`x_i` are the ordered sample values (in ascending
order) and the :math:`a_i` are constants generated from the means,
variances and covariances of the order statistics of a sample of size
:math:`n` from a standard normal distribution. Specifically:
.. math:: (a_1, ..., a_n) = \\frac{m^TV^{-1}}{(m^TV^{-1}V^{-1}m)^{1/2}}
with :math:`m = (m_1, ..., m_n)^T` and :math:`(m_1, ..., m_n)` are the
expected values of the order statistics of independent and identically
distributed random variables sampled from the standard normal distribution,
and :math:`V` is the covariance matrix of those order statistics.
The null-hypothesis of this test is that the population is normally
distributed. Thus, if the p-value is less than the
chosen alpha level (typically set at 0.05), then the null hypothesis is
rejected and there is evidence that the data tested are not normally
distributed.
The result of the Shapiro-Wilk test should be interpreted with caution in
the case of large sample sizes. Indeed, quoting from
`Wikipedia <https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test>`_:
*"Like most statistical significance tests, if the sample size is
sufficiently large this test may detect even trivial departures from
the null hypothesis (i.e., although there may be some statistically
significant effect, it may be too small to be of any practical
significance); thus, additional investigation of the effect size is
typically advisable, e.g., a Q–Q plot in this case."*
Note that missing values are automatically removed (casewise deletion).
References
----------
* Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test
for normality (complete samples). Biometrika, 52(3/4), 591-611.
* https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
Examples
--------
1. Shapiro-Wilk test on a 1D array.
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.normal(size=100)
>>> pg.normality(x)
W pval normal
0 0.98414 0.274886 True
2. Omnibus test on a wide-format dataframe with missing values
>>> data = pg.read_dataset('mediation')
>>> data.loc[1, 'X'] = np.nan
>>> pg.normality(data, method='normaltest').round(3)
W pval normal
X 1.792 0.408 True
M 0.492 0.782 True
Y 0.349 0.840 True
Mbin 839.716 0.000 False
Ybin 814.468 0.000 False
W1 24.816 0.000 False
W2 43.400 0.000 False
3. Pandas Series
>>> pg.normality(data['X'], method='normaltest')
W pval normal
X 1.791839 0.408232 True
4. Long-format dataframe
>>> data = pg.read_dataset('rm_anova2')
>>> pg.normality(data, dv='Performance', group='Time')
W pval normal
Time
Pre 0.967718 0.478773 True
Post 0.940728 0.095157 True
5. Same but using the Jarque-Bera test
>>> pg.normality(data, dv='Performance', group='Time', method="jarque_bera")
W pval normal
Time
Pre 0.304021 0.858979 True
Post 1.265656 0.531088 True
"""
assert isinstance(data, (pd.DataFrame, pd.Series, list, np.ndarray))
assert method in ["shapiro", "normaltest", "jarque_bera"]
if isinstance(data, pd.Series):
data = data.to_frame()
col_names = ["W", "pval"]
func = getattr(scipy.stats, method)
if isinstance(data, (list, np.ndarray)):
data = np.asarray(data)
assert data.ndim == 1, "Data must be 1D."
assert data.size > 3, "Data must have more than 3 samples."
data = remove_na(data)
stats = pd.DataFrame(func(data)).T
stats.columns = col_names
stats["normal"] = np.where(stats["pval"] > alpha, True, False)
else:
# Data is a Pandas DataFrame
if dv is None and group is None:
# Wide-format
# Get numeric data only
numdata = data._get_numeric_data()
stats = numdata.apply(lambda x: func(x.dropna()), result_type="expand", axis=0).T
stats.columns = col_names
stats["normal"] = np.where(stats["pval"] > alpha, True, False)
else:
# Long-format
stats = pd.DataFrame([])
assert group in data.columns
assert dv in data.columns
grp = data.groupby(group, observed=True, sort=False)
cols = grp.groups.keys()
for idx, tmp in grp:
if tmp[dv].count() <= 3:
warnings.warn(f"Group {idx} has less than 4 valid samples. Returning NaN.")
st_grp = pd.DataFrame(
{"W": np.nan, "pval": np.nan, "normal": False}, index=[idx]
)
else:
st_grp = normality(tmp[dv].to_numpy(), method=method, alpha=alpha)
stats = pd.concat([stats, st_grp], axis=0, ignore_index=True)
stats.index = cols
stats.index.name = group
return _postprocess_dataframe(stats)
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|
32,030 | pingouin.pairwise | pairwise_corr | Pairwise (partial) correlations between columns of a pandas dataframe.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
columns : list or str
Column names in data:
* ``["a", "b", "c"]``: combination between columns a, b, and c.
* ``["a"]``: product between a and all the other numeric columns.
* ``[["a"], ["b", "c"]]``: product between ["a"] and ["b", "c"].
* ``[["a", "d"], ["b", "c"]]``: product between ["a", "d"] and
["b", "c"].
* ``[["a", "d"], None]``: product between ["a", "d"] and all other
numeric columns in dataframe.
If column is None, the function will return the pairwise correlation
between the combination of all the numeric columns in data.
See the examples section for more details on this.
covar : None, string or list
Covariate(s) for partial correlation. Must be one or more columns
in data. Use a list if there are more than one covariate. If
``covar`` is not None, a partial correlation will be computed using
:py:func:`pingouin.partial_corr` function.
.. important:: Only ``method='pearson'`` and ``method='spearman'``
are currently supported in partial correlation.
alternative : string
Defines the alternative hypothesis, or tail of the correlation. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return a one-sided
p-value. "greater" tests against the alternative hypothesis that the correlation is
positive (greater than zero), "less" tests against the hypothesis that the correlation is
negative.
method : string
Correlation type:
* ``'pearson'``: Pearson :math:`r` product-moment correlation
* ``'spearman'``: Spearman :math:`\rho` rank-order correlation
* ``'kendall'``: Kendall's :math:`\tau_B` correlation
(for ordinal data)
* ``'bicor'``: Biweight midcorrelation (robust)
* ``'percbend'``: Percentage bend correlation (robust)
* ``'shepherd'``: Shepherd's pi correlation (robust)
* ``'skipped'``: Skipped correlation (robust)
padjust : string
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
nan_policy : string
Can be ``'listwise'`` for listwise deletion of missing values
(= complete-case analysis) or ``'pairwise'`` (default) for the more
liberal pairwise deletion (= available-case analysis).
.. versionadded:: 0.2.9
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'X'``: Name(s) of first columns.
* ``'Y'``: Name(s) of second columns.
* ``'method'``: Correlation type.
* ``'covar'``: List of specified covariate(s), only when covariates are passed.
* ``'alternative'``: Tail of the test.
* ``'n'``: Sample size (after removal of missing values).
* ``'r'``: Correlation coefficients.
* ``'CI95'``: 95% parametric confidence intervals.
* ``'p-unc'``: Uncorrected p-values.
* ``'p-corr'``: Corrected p-values.
* ``'p-adjust'``: P-values correction method.
* ``'BF10'``: Bayes Factor of the alternative hypothesis (only for Pearson correlation)
* ``'power'``: achieved power of the test (= 1 - type II error).
Notes
-----
Please refer to the :py:func:`pingouin.corr()` function for a description
of the different methods. Missing values are automatically removed from the
data using a pairwise deletion.
This function is more flexible and gives a much more detailed
output than the :py:func:`pandas.DataFrame.corr()` method (i.e. p-values,
confidence interval, Bayes Factor...). This comes however at
an increased computational cost. While this should not be discernible for
a dataframe with less than 10,000 rows and/or less than 20 columns, this
function can be slow for very large datasets.
A faster alternative to get the r-values and p-values in a matrix format is
to use the :py:func:`pingouin.rcorr` function, which works directly as a
:py:class:`pandas.DataFrame` method (see example below).
This function also works with two-dimensional multi-index columns. In this
case, columns must be list(s) of tuple(s). Please refer to this `example
Jupyter notebook
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/04_Correlations.ipynb>`_
for more details.
If and only if ``covar`` is specified, this function will compute the
pairwise partial correlation between the variables. If you are only
interested in computing the partial correlation matrix (i.e. the raw
pairwise partial correlation coefficient matrix, without the p-values,
sample sizes, etc), a better alternative is to use the
:py:func:`pingouin.pcorr` function (see example 7).
Examples
--------
1. One-sided spearman correlation corrected for multiple comparisons
>>> import pandas as pd
>>> import pingouin as pg
>>> pd.set_option('display.expand_frame_repr', False)
>>> pd.set_option('display.max_columns', 20)
>>> data = pg.read_dataset('pairwise_corr').iloc[:, 1:]
>>> pg.pairwise_corr(data, method='spearman', alternative='greater', padjust='bonf').round(3)
X Y method alternative n r CI95% p-unc p-corr p-adjust power
0 Neuroticism Extraversion spearman greater 500 -0.325 [-0.39, 1.0] 1.000 1.000 bonf 0.000
1 Neuroticism Openness spearman greater 500 -0.028 [-0.1, 1.0] 0.735 1.000 bonf 0.012
2 Neuroticism Agreeableness spearman greater 500 -0.151 [-0.22, 1.0] 1.000 1.000 bonf 0.000
3 Neuroticism Conscientiousness spearman greater 500 -0.356 [-0.42, 1.0] 1.000 1.000 bonf 0.000
4 Extraversion Openness spearman greater 500 0.243 [0.17, 1.0] 0.000 0.000 bonf 1.000
5 Extraversion Agreeableness spearman greater 500 0.062 [-0.01, 1.0] 0.083 0.832 bonf 0.398
6 Extraversion Conscientiousness spearman greater 500 0.056 [-0.02, 1.0] 0.106 1.000 bonf 0.345
7 Openness Agreeableness spearman greater 500 0.170 [0.1, 1.0] 0.000 0.001 bonf 0.985
8 Openness Conscientiousness spearman greater 500 -0.007 [-0.08, 1.0] 0.560 1.000 bonf 0.036
9 Agreeableness Conscientiousness spearman greater 500 0.161 [0.09, 1.0] 0.000 0.002 bonf 0.976
2. Robust two-sided biweight midcorrelation with uncorrected p-values
>>> pcor = pg.pairwise_corr(data, columns=['Openness', 'Extraversion',
... 'Neuroticism'], method='bicor')
>>> pcor.round(3)
X Y method alternative n r CI95% p-unc power
0 Openness Extraversion bicor two-sided 500 0.247 [0.16, 0.33] 0.000 1.000
1 Openness Neuroticism bicor two-sided 500 -0.028 [-0.12, 0.06] 0.535 0.095
2 Extraversion Neuroticism bicor two-sided 500 -0.343 [-0.42, -0.26] 0.000 1.000
3. One-versus-all pairwise correlations
>>> pg.pairwise_corr(data, columns=['Neuroticism']).round(3)
X Y method alternative n r CI95% p-unc BF10 power
0 Neuroticism Extraversion pearson two-sided 500 -0.350 [-0.42, -0.27] 0.000 6.765e+12 1.000
1 Neuroticism Openness pearson two-sided 500 -0.010 [-0.1, 0.08] 0.817 0.058 0.056
2 Neuroticism Agreeableness pearson two-sided 500 -0.134 [-0.22, -0.05] 0.003 5.122 0.854
3 Neuroticism Conscientiousness pearson two-sided 500 -0.368 [-0.44, -0.29] 0.000 2.644e+14 1.000
4. Pairwise correlations between two lists of columns (cartesian product)
>>> columns = [['Neuroticism', 'Extraversion'], ['Openness']]
>>> pg.pairwise_corr(data, columns).round(3)
X Y method alternative n r CI95% p-unc BF10 power
0 Neuroticism Openness pearson two-sided 500 -0.010 [-0.1, 0.08] 0.817 0.058 0.056
1 Extraversion Openness pearson two-sided 500 0.267 [0.18, 0.35] 0.000 5.277e+06 1.000
5. As a Pandas method
>>> pcor = data.pairwise_corr(covar='Neuroticism', method='spearman')
6. Pairwise partial correlation
>>> pg.pairwise_corr(data, covar=['Neuroticism', 'Openness'])
X Y method covar alternative n r CI95% p-unc
0 Extraversion Agreeableness pearson ['Neuroticism', 'Openness'] two-sided 500 -0.038737 [-0.13, 0.05] 0.388361
1 Extraversion Conscientiousness pearson ['Neuroticism', 'Openness'] two-sided 500 -0.071427 [-0.16, 0.02] 0.111389
2 Agreeableness Conscientiousness pearson ['Neuroticism', 'Openness'] two-sided 500 0.123108 [0.04, 0.21] 0.005944
7. Pairwise partial correlation matrix using :py:func:`pingouin.pcorr`
>>> data[['Neuroticism', 'Openness', 'Extraversion']].pcorr().round(3)
Neuroticism Openness Extraversion
Neuroticism 1.000 0.092 -0.360
Openness 0.092 1.000 0.281
Extraversion -0.360 0.281 1.000
8. Correlation matrix with p-values using :py:func:`pingouin.rcorr`
>>> data[['Neuroticism', 'Openness', 'Extraversion']].rcorr()
Neuroticism Openness Extraversion
Neuroticism - ***
Openness -0.01 - ***
Extraversion -0.35 0.267 -
| @pf.register_dataframe_method
def pairwise_corr(
data,
columns=None,
covar=None,
alternative="two-sided",
method="pearson",
padjust="none",
nan_policy="pairwise",
):
"""Pairwise (partial) correlations between columns of a pandas dataframe.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
columns : list or str
Column names in data:
* ``["a", "b", "c"]``: combination between columns a, b, and c.
* ``["a"]``: product between a and all the other numeric columns.
* ``[["a"], ["b", "c"]]``: product between ["a"] and ["b", "c"].
* ``[["a", "d"], ["b", "c"]]``: product between ["a", "d"] and
["b", "c"].
* ``[["a", "d"], None]``: product between ["a", "d"] and all other
numeric columns in dataframe.
If column is None, the function will return the pairwise correlation
between the combination of all the numeric columns in data.
See the examples section for more details on this.
covar : None, string or list
Covariate(s) for partial correlation. Must be one or more columns
in data. Use a list if there are more than one covariate. If
``covar`` is not None, a partial correlation will be computed using
:py:func:`pingouin.partial_corr` function.
.. important:: Only ``method='pearson'`` and ``method='spearman'``
are currently supported in partial correlation.
alternative : string
Defines the alternative hypothesis, or tail of the correlation. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return a one-sided
p-value. "greater" tests against the alternative hypothesis that the correlation is
positive (greater than zero), "less" tests against the hypothesis that the correlation is
negative.
method : string
Correlation type:
* ``'pearson'``: Pearson :math:`r` product-moment correlation
* ``'spearman'``: Spearman :math:`\\rho` rank-order correlation
* ``'kendall'``: Kendall's :math:`\\tau_B` correlation
(for ordinal data)
* ``'bicor'``: Biweight midcorrelation (robust)
* ``'percbend'``: Percentage bend correlation (robust)
* ``'shepherd'``: Shepherd's pi correlation (robust)
* ``'skipped'``: Skipped correlation (robust)
padjust : string
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
nan_policy : string
Can be ``'listwise'`` for listwise deletion of missing values
(= complete-case analysis) or ``'pairwise'`` (default) for the more
liberal pairwise deletion (= available-case analysis).
.. versionadded:: 0.2.9
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'X'``: Name(s) of first columns.
* ``'Y'``: Name(s) of second columns.
* ``'method'``: Correlation type.
* ``'covar'``: List of specified covariate(s), only when covariates are passed.
* ``'alternative'``: Tail of the test.
* ``'n'``: Sample size (after removal of missing values).
* ``'r'``: Correlation coefficients.
* ``'CI95'``: 95% parametric confidence intervals.
* ``'p-unc'``: Uncorrected p-values.
* ``'p-corr'``: Corrected p-values.
* ``'p-adjust'``: P-values correction method.
* ``'BF10'``: Bayes Factor of the alternative hypothesis (only for Pearson correlation)
* ``'power'``: achieved power of the test (= 1 - type II error).
Notes
-----
Please refer to the :py:func:`pingouin.corr()` function for a description
of the different methods. Missing values are automatically removed from the
data using a pairwise deletion.
This function is more flexible and gives a much more detailed
output than the :py:func:`pandas.DataFrame.corr()` method (i.e. p-values,
confidence interval, Bayes Factor...). This comes however at
an increased computational cost. While this should not be discernible for
a dataframe with less than 10,000 rows and/or less than 20 columns, this
function can be slow for very large datasets.
A faster alternative to get the r-values and p-values in a matrix format is
to use the :py:func:`pingouin.rcorr` function, which works directly as a
:py:class:`pandas.DataFrame` method (see example below).
This function also works with two-dimensional multi-index columns. In this
case, columns must be list(s) of tuple(s). Please refer to this `example
Jupyter notebook
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/04_Correlations.ipynb>`_
for more details.
If and only if ``covar`` is specified, this function will compute the
pairwise partial correlation between the variables. If you are only
interested in computing the partial correlation matrix (i.e. the raw
pairwise partial correlation coefficient matrix, without the p-values,
sample sizes, etc), a better alternative is to use the
:py:func:`pingouin.pcorr` function (see example 7).
Examples
--------
1. One-sided spearman correlation corrected for multiple comparisons
>>> import pandas as pd
>>> import pingouin as pg
>>> pd.set_option('display.expand_frame_repr', False)
>>> pd.set_option('display.max_columns', 20)
>>> data = pg.read_dataset('pairwise_corr').iloc[:, 1:]
>>> pg.pairwise_corr(data, method='spearman', alternative='greater', padjust='bonf').round(3)
X Y method alternative n r CI95% p-unc p-corr p-adjust power
0 Neuroticism Extraversion spearman greater 500 -0.325 [-0.39, 1.0] 1.000 1.000 bonf 0.000
1 Neuroticism Openness spearman greater 500 -0.028 [-0.1, 1.0] 0.735 1.000 bonf 0.012
2 Neuroticism Agreeableness spearman greater 500 -0.151 [-0.22, 1.0] 1.000 1.000 bonf 0.000
3 Neuroticism Conscientiousness spearman greater 500 -0.356 [-0.42, 1.0] 1.000 1.000 bonf 0.000
4 Extraversion Openness spearman greater 500 0.243 [0.17, 1.0] 0.000 0.000 bonf 1.000
5 Extraversion Agreeableness spearman greater 500 0.062 [-0.01, 1.0] 0.083 0.832 bonf 0.398
6 Extraversion Conscientiousness spearman greater 500 0.056 [-0.02, 1.0] 0.106 1.000 bonf 0.345
7 Openness Agreeableness spearman greater 500 0.170 [0.1, 1.0] 0.000 0.001 bonf 0.985
8 Openness Conscientiousness spearman greater 500 -0.007 [-0.08, 1.0] 0.560 1.000 bonf 0.036
9 Agreeableness Conscientiousness spearman greater 500 0.161 [0.09, 1.0] 0.000 0.002 bonf 0.976
2. Robust two-sided biweight midcorrelation with uncorrected p-values
>>> pcor = pg.pairwise_corr(data, columns=['Openness', 'Extraversion',
... 'Neuroticism'], method='bicor')
>>> pcor.round(3)
X Y method alternative n r CI95% p-unc power
0 Openness Extraversion bicor two-sided 500 0.247 [0.16, 0.33] 0.000 1.000
1 Openness Neuroticism bicor two-sided 500 -0.028 [-0.12, 0.06] 0.535 0.095
2 Extraversion Neuroticism bicor two-sided 500 -0.343 [-0.42, -0.26] 0.000 1.000
3. One-versus-all pairwise correlations
>>> pg.pairwise_corr(data, columns=['Neuroticism']).round(3)
X Y method alternative n r CI95% p-unc BF10 power
0 Neurotic | (data, columns=None, covar=None, alternative='two-sided', method='pearson', padjust='none', nan_policy='pairwise') | [
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|
32,031 | pingouin.pairwise | pairwise_gameshowell | Pairwise Games-Howell post-hoc test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame
dv : string
Name of column containing the dependent variable.
between: string
Name of column containing the between factor.
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
Returns
-------
stats : :py:class:`pandas.DataFrame`
Stats summary:
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'mean(A)'``: Mean of first measurement
* ``'mean(B)'``: Mean of second measurement
* ``'diff'``: Mean difference (= mean(A) - mean(B))
* ``'se'``: Standard error
* ``'T'``: T-values
* ``'df'``: adjusted degrees of freedom
* ``'pval'``: Games-Howell corrected p-values
* ``'hedges'``: Hedges effect size (or any effect size defined in
``effsize``)
See also
--------
pairwise_tests, pairwise_tukey
Notes
-----
Games-Howell [1]_ is very similar to the Tukey HSD post-hoc test but is much more robust to
heterogeneity of variances. While the Tukey-HSD post-hoc is optimal after a classic one-way
ANOVA, the Games-Howell is optimal after a Welch ANOVA. Please note that Games-Howell
is not valid for repeated measures ANOVA. Only one-way ANOVA design are supported.
Compared to the Tukey-HSD test, the Games-Howell test uses different pooled variances for
each pair of variables instead of the same pooled variance.
The T-values are defined as:
.. math::
t = \frac{\overline{x}_i - \overline{x}_j}
{\sqrt{(\frac{s_i^2}{n_i} + \frac{s_j^2}{n_j})}}
and the corrected degrees of freedom are:
.. math::
v = \frac{(\frac{s_i^2}{n_i} + \frac{s_j^2}{n_j})^2}
{\frac{(\frac{s_i^2}{n_i})^2}{n_i-1} +
\frac{(\frac{s_j^2}{n_j})^2}{n_j-1}}
where :math:`\overline{x}_i`, :math:`s_i^2`, and :math:`n_i` are the mean, variance and sample
size of the first group and :math:`\overline{x}_j`, :math:`s_j^2`, and :math:`n_j` the mean,
variance and sample size of the second group.
The p-values are then approximated using the Studentized range distribution
:math:`Q(\sqrt2|t_i|, r, v_i)`.
References
----------
.. [1] Games, Paul A., and John F. Howell. "Pairwise multiple comparison
procedures with unequal n's and/or variances: a Monte Carlo study."
Journal of Educational Statistics 1.2 (1976): 113-125.
.. [2] Gleason, John R. "An accurate, non-iterative approximation for
studentized range quantiles." Computational statistics & data
analysis 31.2 (1999): 147-158.
Examples
--------
Pairwise Games-Howell post-hocs on the Penguins dataset.
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> pg.pairwise_gameshowell(data=df, dv='body_mass_g',
... between='species').round(3)
A B mean(A) mean(B) diff se T df pval hedges
0 Adelie Chinstrap 3700.662 3733.088 -32.426 59.706 -0.543 152.455 0.85 -0.074
1 Adelie Gentoo 3700.662 5076.016 -1375.354 58.811 -23.386 249.643 0.00 -2.860
2 Chinstrap Gentoo 3733.088 5076.016 -1342.928 65.103 -20.628 170.404 0.00 -2.875
| def pairwise_gameshowell(data=None, dv=None, between=None, effsize="hedges"):
"""Pairwise Games-Howell post-hoc test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame
dv : string
Name of column containing the dependent variable.
between: string
Name of column containing the between factor.
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
Returns
-------
stats : :py:class:`pandas.DataFrame`
Stats summary:
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'mean(A)'``: Mean of first measurement
* ``'mean(B)'``: Mean of second measurement
* ``'diff'``: Mean difference (= mean(A) - mean(B))
* ``'se'``: Standard error
* ``'T'``: T-values
* ``'df'``: adjusted degrees of freedom
* ``'pval'``: Games-Howell corrected p-values
* ``'hedges'``: Hedges effect size (or any effect size defined in
``effsize``)
See also
--------
pairwise_tests, pairwise_tukey
Notes
-----
Games-Howell [1]_ is very similar to the Tukey HSD post-hoc test but is much more robust to
heterogeneity of variances. While the Tukey-HSD post-hoc is optimal after a classic one-way
ANOVA, the Games-Howell is optimal after a Welch ANOVA. Please note that Games-Howell
is not valid for repeated measures ANOVA. Only one-way ANOVA design are supported.
Compared to the Tukey-HSD test, the Games-Howell test uses different pooled variances for
each pair of variables instead of the same pooled variance.
The T-values are defined as:
.. math::
t = \\frac{\\overline{x}_i - \\overline{x}_j}
{\\sqrt{(\\frac{s_i^2}{n_i} + \\frac{s_j^2}{n_j})}}
and the corrected degrees of freedom are:
.. math::
v = \\frac{(\\frac{s_i^2}{n_i} + \\frac{s_j^2}{n_j})^2}
{\\frac{(\\frac{s_i^2}{n_i})^2}{n_i-1} +
\\frac{(\\frac{s_j^2}{n_j})^2}{n_j-1}}
where :math:`\\overline{x}_i`, :math:`s_i^2`, and :math:`n_i` are the mean, variance and sample
size of the first group and :math:`\\overline{x}_j`, :math:`s_j^2`, and :math:`n_j` the mean,
variance and sample size of the second group.
The p-values are then approximated using the Studentized range distribution
:math:`Q(\\sqrt2|t_i|, r, v_i)`.
References
----------
.. [1] Games, Paul A., and John F. Howell. "Pairwise multiple comparison
procedures with unequal n's and/or variances: a Monte Carlo study."
Journal of Educational Statistics 1.2 (1976): 113-125.
.. [2] Gleason, John R. "An accurate, non-iterative approximation for
studentized range quantiles." Computational statistics & data
analysis 31.2 (1999): 147-158.
Examples
--------
Pairwise Games-Howell post-hocs on the Penguins dataset.
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> pg.pairwise_gameshowell(data=df, dv='body_mass_g',
... between='species').round(3)
A B mean(A) mean(B) diff se T df pval hedges
0 Adelie Chinstrap 3700.662 3733.088 -32.426 59.706 -0.543 152.455 0.85 -0.074
1 Adelie Gentoo 3700.662 5076.016 -1375.354 58.811 -23.386 249.643 0.00 -2.860
2 Chinstrap Gentoo 3733.088 5076.016 -1342.928 65.103 -20.628 170.404 0.00 -2.875
"""
# Check the dataframe
data = _check_dataframe(dv=dv, between=between, effects="between", data=data)
# Reset index (avoid duplicate axis error)
data = data.reset_index(drop=True)
# Extract infos
ng = data[between].nunique()
grp = data.groupby(between, observed=True)[dv] # default is sort=True
# Careful: pd.unique does NOT sort whereas numpy does
# The line below should be equal to labels = np.unique(data[between])
# However, this does not work if between is a Categorical column, because
# Pandas applies a custom, not alphabetical, sorting.
# See https://github.com/raphaelvallat/pingouin/issues/111
labels = np.array(list(grp.groups.keys()))
n = grp.count().to_numpy()
gmeans = grp.mean(numeric_only=True).to_numpy()
gvars = grp.var(numeric_only=True).to_numpy() # numeric_only=True added in pandas 1.5
# Pairwise combinations
g1, g2 = np.array(list(combinations(np.arange(ng), 2))).T
mn = gmeans[g1] - gmeans[g2]
se = np.sqrt(gvars[g1] / n[g1] + gvars[g2] / n[g2])
tval = mn / np.sqrt(gvars[g1] / n[g1] + gvars[g2] / n[g2])
df = (gvars[g1] / n[g1] + gvars[g2] / n[g2]) ** 2 / (
(((gvars[g1] / n[g1]) ** 2) / (n[g1] - 1)) + (((gvars[g2] / n[g2]) ** 2) / (n[g2] - 1))
)
# Compute corrected p-values
pval = studentized_range.sf(np.sqrt(2) * np.abs(tval), ng, df)
pval = np.clip(pval, 0, 1)
# Uncorrected p-values
# from scipy.stats import t
# punc = t.sf(np.abs(tval), n[g1].size + n[g2].size - 2) * 2
# Effect size
# Method 1: Approximation
# d = tval * np.sqrt(1 / n[g1] + 1 / n[g2])
# ef = convert_effsize(d, "cohen", effsize, n[g1], n[g2])
# Method 2: Exact
ef = []
for idx_a, idx_b in zip(g1, g2):
ef.append(
compute_effsize(
grp.get_group(labels[idx_a]),
grp.get_group(labels[idx_b]),
paired=False,
eftype=effsize,
)
)
# Create dataframe
stats = pd.DataFrame(
{
"A": labels[g1],
"B": labels[g2],
"mean(A)": gmeans[g1],
"mean(B)": gmeans[g2],
"diff": mn,
"se": se,
"T": tval,
"df": df,
"pval": pval,
effsize: ef,
}
)
return _postprocess_dataframe(stats)
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|
32,032 | pingouin.pairwise | pairwise_tests | Pairwise tests.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
between : string or list with 2 elements
Name of column(s) containing the between-subject factor(s).
within : string or list with 2 elements
Name of column(s) containing the within-subject factor(s), i.e. the
repeated measurements.
subject : string
Name of column containing the subject identifier. This is mandatory
when ``within`` is specified.
parametric : boolean
If True (default), use the parametric :py:func:`ttest` function.
If False, use :py:func:`pingouin.wilcoxon` or :py:func:`pingouin.mwu`
for paired or unpaired samples, respectively.
marginal : boolean
If True (default), the between-subject pairwise T-test(s) will be calculated
after averaging across all levels of the within-subject factor in mixed
design. This is recommended to avoid violating the assumption of
independence and conflating the degrees of freedom by the
number of repeated measurements.
.. versionadded:: 0.3.2
alpha : float
Significance level
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return one-sided
p-values. "greater" tests against the alternative hypothesis that the mean of ``x``
is greater than the mean of ``y``.
padjust : string
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
correction : string or boolean
For independent two sample T-tests, specify whether or not to correct for
unequal variances using Welch separate variances T-test. If `'auto'`,
it will automatically uses Welch T-test when the sample sizes are
unequal, as recommended by Zimmerman 2004.
.. versionadded:: 0.3.2
nan_policy : string
Can be `'listwise'` for listwise deletion of missing values in repeated
measures design (= complete-case analysis) or `'pairwise'` for the
more liberal pairwise deletion (= available-case analysis). The former (default) is more
appropriate for post-hoc analysis following an ANOVA, however it can drastically reduce
the power of the test: any subject with one or more missing value(s) will be
completely removed from the analysis.
.. versionadded:: 0.2.9
return_desc : boolean
If True, append group means and std to the output dataframe
interaction : boolean
If there are multiple factors and ``interaction`` is True (default),
Pingouin will also calculate T-tests for the interaction term (see Notes).
.. versionadded:: 0.2.9
within_first : boolean
Determines the order of the interaction in mixed design. Pingouin will
return within * between when this parameter is set to True (default),
and between * within otherwise.
.. versionadded:: 0.3.6
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'Contrast'``: Contrast (= independent variable or interaction)
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'Paired'``: indicates whether the two measurements are paired or
independent
* ``'Parametric'``: indicates if (non)-parametric tests were used
* ``'T'``: T statistic (only if parametric=True)
* ``'U-val'``: Mann-Whitney U stat (if parametric=False and unpaired
data)
* ``'W-val'``: Wilcoxon W stat (if parametric=False and paired data)
* ``'dof'``: degrees of freedom (only if parametric=True)
* ``'alternative'``: tail of the test
* ``'p-unc'``: Uncorrected p-values
* ``'p-corr'``: Corrected p-values
* ``'p-adjust'``: p-values correction method
* ``'BF10'``: Bayes Factor
* ``'hedges'``: effect size (or any effect size defined in
``effsize``)
See also
--------
ttest, mwu, wilcoxon, compute_effsize, multicomp
Notes
-----
Data are expected to be in long-format. If your data is in wide-format,
you can use the :py:func:`pandas.melt` function to convert from wide to
long format.
If ``between`` or ``within`` is a list (e.g. ['col1', 'col2']),
the function returns 1) the pairwise T-tests between each values of the
first column, 2) the pairwise T-tests between each values of the second
column and 3) the interaction between col1 and col2. The interaction is
dependent of the order of the list, so ['col1', 'col2'] will not yield the
same results as ['col2', 'col1']. Furthermore, the interaction will only be
calculated if ``interaction=True``.
If ``between`` is a list with two elements, the output
model is between1 + between2 + between1 * between2.
Similarly, if ``within`` is a list with two elements, the output model is
within1 + within2 + within1 * within2.
If both ``between`` and ``within`` are specified, the output model is
within + between + within * between (= mixed design), unless
``within_first=False`` in which case the model becomes between + within +
between * within.
Missing values in repeated measurements are automatically removed using a
listwise (default) or pairwise deletion strategy. The former is more conservative, as any
subject with one or more missing value(s) will be completely removed from the dataframe prior
to calculating the T-tests. The ``nan_policy`` parameter can therefore have a huge impact
on the results.
Examples
--------
For more examples, please refer to the `Jupyter notebooks
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/01_ANOVA.ipynb>`_
1. One between-subject factor
>>> import pandas as pd
>>> import pingouin as pg
>>> pd.set_option('display.expand_frame_repr', False)
>>> pd.set_option('display.max_columns', 20)
>>> df = pg.read_dataset('mixed_anova.csv')
>>> pg.pairwise_tests(dv='Scores', between='Group', data=df).round(3)
Contrast A B Paired Parametric T dof alternative p-unc BF10 hedges
0 Group Control Meditation False True -2.29 178.0 two-sided 0.023 1.813 -0.34
2. One within-subject factor
>>> post_hocs = pg.pairwise_tests(dv='Scores', within='Time', subject='Subject', data=df)
>>> post_hocs.round(3)
Contrast A B Paired Parametric T dof alternative p-unc BF10 hedges
0 Time August January True True -1.740 59.0 two-sided 0.087 0.582 -0.328
1 Time August June True True -2.743 59.0 two-sided 0.008 4.232 -0.483
2 Time January June True True -1.024 59.0 two-sided 0.310 0.232 -0.170
3. Non-parametric pairwise paired test (wilcoxon)
>>> pg.pairwise_tests(dv='Scores', within='Time', subject='Subject',
... data=df, parametric=False).round(3)
Contrast A B Paired Parametric W-val alternative p-unc hedges
0 Time August January True False 716.0 two-sided 0.144 -0.328
1 Time August June True False 564.0 two-sided 0.010 -0.483
2 Time January June True False 887.0 two-sided 0.840 -0.170
4. Mixed design (within and between) with bonferroni-corrected p-values
>>> posthocs = pg.pairwise_tests(dv='Scores', within='Time', subject='Subject',
... between='Group', padjust='bonf', data=df)
>>> posthocs.round(3)
Contrast Time A B Paired Parametric T dof alternative p-unc p-corr p-adjust BF10 hedges
0 Time - August January True True -1.740 59.0 two-sided 0.087 0.261 bonf 0.582 -0.328
1 Time - August June True True -2.743 59.0 two-sided 0.008 0.024 bonf 4.232 -0.483
2 Time - January June True True -1.024 59.0 two-sided 0.310 0.931 bonf 0.232 -0.170
3 Group - Control Meditation False True -2.248 58.0 two-sided 0.028 NaN NaN 2.096 -0.573
4 Time * Group August Control Meditation False True 0.316 58.0 two-sided 0.753 1.000 bonf 0.274 0.081
5 Time * Group January Control Meditation False True -1.434 58.0 two-sided 0.157 0.471 bonf 0.619 -0.365
6 Time * Group June Control Meditation False True -2.744 58.0 two-sided 0.008 0.024 bonf 5.593 -0.699
5. Two between-subject factors. The order of the ``between`` factors matters!
>>> pg.pairwise_tests(dv='Scores', between=['Group', 'Time'], data=df).round(3)
Contrast Group A B Paired Parametric T dof alternative p-unc BF10 hedges
0 Group - Control Meditation False True -2.290 178.0 two-sided 0.023 1.813 -0.340
1 Time - August January False True -1.806 118.0 two-sided 0.074 0.839 -0.328
2 Time - August June False True -2.660 118.0 two-sided 0.009 4.499 -0.483
3 Time - January June False True -0.934 118.0 two-sided 0.352 0.288 -0.170
4 Group * Time Control August January False True -0.383 58.0 two-sided 0.703 0.279 -0.098
5 Group * Time Control August June False True -0.292 58.0 two-sided 0.771 0.272 -0.074
6 Group * Time Control January June False True 0.045 58.0 two-sided 0.964 0.263 0.011
7 Group * Time Meditation August January False True -2.188 58.0 two-sided 0.033 1.884 -0.558
8 Group * Time Meditation August June False True -4.040 58.0 two-sided 0.000 148.302 -1.030
9 Group * Time Meditation January June False True -1.442 58.0 two-sided 0.155 0.625 -0.367
6. Same but without the interaction, and using a directional test
>>> df.pairwise_tests(dv='Scores', between=['Group', 'Time'], alternative="less",
... interaction=False).round(3)
Contrast A B Paired Parametric T dof alternative p-unc BF10 hedges
0 Group Control Meditation False True -2.290 178.0 less 0.012 3.626 -0.340
1 Time August January False True -1.806 118.0 less 0.037 1.679 -0.328
2 Time August June False True -2.660 118.0 less 0.004 8.998 -0.483
3 Time January June False True -0.934 118.0 less 0.176 0.577 -0.170
| @pf.register_dataframe_method
def pairwise_tests(
data=None,
dv=None,
between=None,
within=None,
subject=None,
parametric=True,
marginal=True,
alpha=0.05,
alternative="two-sided",
padjust="none",
effsize="hedges",
correction="auto",
nan_policy="listwise",
return_desc=False,
interaction=True,
within_first=True,
):
"""Pairwise tests.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
between : string or list with 2 elements
Name of column(s) containing the between-subject factor(s).
within : string or list with 2 elements
Name of column(s) containing the within-subject factor(s), i.e. the
repeated measurements.
subject : string
Name of column containing the subject identifier. This is mandatory
when ``within`` is specified.
parametric : boolean
If True (default), use the parametric :py:func:`ttest` function.
If False, use :py:func:`pingouin.wilcoxon` or :py:func:`pingouin.mwu`
for paired or unpaired samples, respectively.
marginal : boolean
If True (default), the between-subject pairwise T-test(s) will be calculated
after averaging across all levels of the within-subject factor in mixed
design. This is recommended to avoid violating the assumption of
independence and conflating the degrees of freedom by the
number of repeated measurements.
.. versionadded:: 0.3.2
alpha : float
Significance level
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return one-sided
p-values. "greater" tests against the alternative hypothesis that the mean of ``x``
is greater than the mean of ``y``.
padjust : string
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
correction : string or boolean
For independent two sample T-tests, specify whether or not to correct for
unequal variances using Welch separate variances T-test. If `'auto'`,
it will automatically uses Welch T-test when the sample sizes are
unequal, as recommended by Zimmerman 2004.
.. versionadded:: 0.3.2
nan_policy : string
Can be `'listwise'` for listwise deletion of missing values in repeated
measures design (= complete-case analysis) or `'pairwise'` for the
more liberal pairwise deletion (= available-case analysis). The former (default) is more
appropriate for post-hoc analysis following an ANOVA, however it can drastically reduce
the power of the test: any subject with one or more missing value(s) will be
completely removed from the analysis.
.. versionadded:: 0.2.9
return_desc : boolean
If True, append group means and std to the output dataframe
interaction : boolean
If there are multiple factors and ``interaction`` is True (default),
Pingouin will also calculate T-tests for the interaction term (see Notes).
.. versionadded:: 0.2.9
within_first : boolean
Determines the order of the interaction in mixed design. Pingouin will
return within * between when this parameter is set to True (default),
and between * within otherwise.
.. versionadded:: 0.3.6
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'Contrast'``: Contrast (= independent variable or interaction)
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'Paired'``: indicates whether the two measurements are paired or
independent
* ``'Parametric'``: indicates if (non)-parametric tests were used
* ``'T'``: T statistic (only if parametric=True)
* ``'U-val'``: Mann-Whitney U stat (if parametric=False and unpaired
data)
* ``'W-val'``: Wilcoxon W stat (if parametric=False and paired data)
* ``'dof'``: degrees of freedom (only if parametric=True)
* ``'alternative'``: tail of the test
* ``'p-unc'``: Uncorrected p-values
* ``'p-corr'``: Corrected p-values
* ``'p-adjust'``: p-values correction method
* ``'BF10'``: Bayes Factor
* ``'hedges'``: effect size (or any effect size defined in
``effsize``)
See also
--------
ttest, mwu, wilcoxon, compute_effsize, multicomp
Notes
-----
Data are expected to be in long-format. If your data is in wide-format,
you can use the :py:func:`pandas.melt` function to convert from wide to
long format.
If ``between`` or ``within`` is a list (e.g. ['col1', 'col2']),
the function returns 1) the pairwise T-tests between each values of the
first column, 2) the pairwise T-tests between each values of the second
column and 3) the interaction between col1 and col2. The interaction is
dependent of the order of the list, so ['col1', 'col2'] will not yield the
same results as ['col2', 'col1']. Furthermore, the interaction will only be
calculated if ``interaction=True``.
If ``between`` is a list with two elements, the output
model is between1 + between2 + between1 * between2.
Similarly, if ``within`` is a list with two elements, the output model is
within1 + within2 + within1 * within2.
If both ``between`` and ``within`` are specified, the output model is
within + between + within * between (= mixed design), unless
``within_first=False`` in which case the model becomes between + within +
between * within.
Missing values in repeated measurements are automatically removed using a
listwise (default) or pairwise deletion strategy. The former is more conservative, as any
subject with one or more missing value(s) will be completely removed from the dataframe prior
to calculating the T-tests. The ``nan_policy`` parameter can therefore have a huge impact
on the results.
Examples
--------
For more examples, please refer to the `Jupyter notebooks
<https://github.com/raphaelvallat/pingouin/blob/master/notebooks/01_ANOVA.ipynb>`_
1. One between-subject factor
>>> import pandas as pd
>>> import pingouin as pg
>>> pd.set_option('display.expand_frame_repr', False)
>>> pd.set_option('display.max_columns', 20)
>>> df = pg.read_dataset('mixed_anova.csv')
>>> pg.pairwise_tests(dv='Scores', between='Group', data=df).round(3)
Contrast A B Paired Parametric T dof alternative p-unc BF10 hedges
0 Group Control Meditation False True -2.29 178.0 two-sided 0.023 1.813 -0.34
2. One within-subject factor
>>> post_hocs = pg.pairwise_tests(dv='Scores', within='Time', subject='Subject', data=df)
>>> post_hocs.round(3)
Contrast A B Paired Parametric T dof alternative p-unc BF10 hedges
0 Time August January True True -1.740 59.0 two-sided 0.087 0.582 -0.328
1 Time August June True True -2.743 59.0 two-sided 0.008 4.232 -0.483
2 Time | (data=None, dv=None, between=None, within=None, subject=None, parametric=True, marginal=True, alpha=0.05, alternative='two-sided', padjust='none', effsize='hedges', correction='auto', nan_policy='listwise', return_desc=False, interaction=True, within_first=True) | [
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|
32,033 | pingouin.pairwise | pairwise_ttests | This function has been deprecated . Use :py:func:`pingouin.pairwise_tests` instead. | @pf.register_dataframe_method
def pairwise_ttests(*args, **kwargs):
"""This function has been deprecated . Use :py:func:`pingouin.pairwise_tests` instead."""
warnings.warn("pairwise_ttests is deprecated, use pairwise_tests instead.", UserWarning)
return pairwise_tests(*args, **kwargs)
| (*args, **kwargs) | [
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|
32,034 | pingouin.pairwise | pairwise_tukey | Pairwise Tukey-HSD post-hoc test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a Pandas method, in which
case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
between: string
Name of column containing the between factor.
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'mean(A)'``: Mean of first measurement
* ``'mean(B)'``: Mean of second measurement
* ``'diff'``: Mean difference (= mean(A) - mean(B))
* ``'se'``: Standard error
* ``'T'``: T-values
* ``'p-tukey'``: Tukey-HSD corrected p-values
* ``'hedges'``: Hedges effect size (or any effect size defined in
``effsize``)
See also
--------
pairwise_tests, pairwise_gameshowell
Notes
-----
Tukey HSD post-hoc [1]_ is best for balanced one-way ANOVA.
It has been proven to be conservative for one-way ANOVA with unequal sample sizes. However, it
is not robust if the groups have unequal variances, in which case the Games-Howell test is
more adequate. Tukey HSD is not valid for repeated measures ANOVA. Only one-way ANOVA design
are supported.
The T-values are defined as:
.. math::
t = \frac{\overline{x}_i - \overline{x}_j}
{\sqrt{2 \cdot \text{MS}_w / n}}
where :math:`\overline{x}_i` and :math:`\overline{x}_j` are the means of the first and
second group, respectively, :math:`\text{MS}_w` the mean squares of the error (computed using
ANOVA) and :math:`n` the sample size.
If the sample sizes are unequal, the Tukey-Kramer procedure is automatically used:
.. math::
t = \frac{\overline{x}_i - \overline{x}_j}{\sqrt{\frac{MS_w}{n_i}
+ \frac{\text{MS}_w}{n_j}}}
where :math:`n_i` and :math:`n_j` are the sample sizes of the first and second group,
respectively.
The p-values are then approximated using the Studentized range distribution
:math:`Q(\sqrt2|t_i|, r, N - r)` where :math:`r` is the total number of groups and
:math:`N` is the total sample size.
References
----------
.. [1] Tukey, John W. "Comparing individual means in the analysis of
variance." Biometrics (1949): 99-114.
.. [2] Gleason, John R. "An accurate, non-iterative approximation for
studentized range quantiles." Computational statistics & data
analysis 31.2 (1999): 147-158.
Examples
--------
Pairwise Tukey post-hocs on the Penguins dataset.
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> df.pairwise_tukey(dv='body_mass_g', between='species').round(3)
A B mean(A) mean(B) diff se T p-tukey hedges
0 Adelie Chinstrap 3700.662 3733.088 -32.426 67.512 -0.480 0.881 -0.074
1 Adelie Gentoo 3700.662 5076.016 -1375.354 56.148 -24.495 0.000 -2.860
2 Chinstrap Gentoo 3733.088 5076.016 -1342.928 69.857 -19.224 0.000 -2.875
| @pf.register_dataframe_method
def pairwise_tukey(data=None, dv=None, between=None, effsize="hedges"):
"""Pairwise Tukey-HSD post-hoc test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a Pandas method, in which
case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
between: string
Name of column containing the between factor.
effsize : string or None
Effect size type. Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'A'``: Name of first measurement
* ``'B'``: Name of second measurement
* ``'mean(A)'``: Mean of first measurement
* ``'mean(B)'``: Mean of second measurement
* ``'diff'``: Mean difference (= mean(A) - mean(B))
* ``'se'``: Standard error
* ``'T'``: T-values
* ``'p-tukey'``: Tukey-HSD corrected p-values
* ``'hedges'``: Hedges effect size (or any effect size defined in
``effsize``)
See also
--------
pairwise_tests, pairwise_gameshowell
Notes
-----
Tukey HSD post-hoc [1]_ is best for balanced one-way ANOVA.
It has been proven to be conservative for one-way ANOVA with unequal sample sizes. However, it
is not robust if the groups have unequal variances, in which case the Games-Howell test is
more adequate. Tukey HSD is not valid for repeated measures ANOVA. Only one-way ANOVA design
are supported.
The T-values are defined as:
.. math::
t = \\frac{\\overline{x}_i - \\overline{x}_j}
{\\sqrt{2 \\cdot \\text{MS}_w / n}}
where :math:`\\overline{x}_i` and :math:`\\overline{x}_j` are the means of the first and
second group, respectively, :math:`\\text{MS}_w` the mean squares of the error (computed using
ANOVA) and :math:`n` the sample size.
If the sample sizes are unequal, the Tukey-Kramer procedure is automatically used:
.. math::
t = \\frac{\\overline{x}_i - \\overline{x}_j}{\\sqrt{\\frac{MS_w}{n_i}
+ \\frac{\\text{MS}_w}{n_j}}}
where :math:`n_i` and :math:`n_j` are the sample sizes of the first and second group,
respectively.
The p-values are then approximated using the Studentized range distribution
:math:`Q(\\sqrt2|t_i|, r, N - r)` where :math:`r` is the total number of groups and
:math:`N` is the total sample size.
References
----------
.. [1] Tukey, John W. "Comparing individual means in the analysis of
variance." Biometrics (1949): 99-114.
.. [2] Gleason, John R. "An accurate, non-iterative approximation for
studentized range quantiles." Computational statistics & data
analysis 31.2 (1999): 147-158.
Examples
--------
Pairwise Tukey post-hocs on the Penguins dataset.
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> df.pairwise_tukey(dv='body_mass_g', between='species').round(3)
A B mean(A) mean(B) diff se T p-tukey hedges
0 Adelie Chinstrap 3700.662 3733.088 -32.426 67.512 -0.480 0.881 -0.074
1 Adelie Gentoo 3700.662 5076.016 -1375.354 56.148 -24.495 0.000 -2.860
2 Chinstrap Gentoo 3733.088 5076.016 -1342.928 69.857 -19.224 0.000 -2.875
"""
# First compute the ANOVA
# For max precision, make sure rounding is disabled
old_options = options.copy()
options["round"] = None
aov = anova(dv=dv, data=data, between=between, detailed=True)
options.update(old_options) # Restore original options
df = aov.at[1, "DF"]
ng = aov.at[0, "DF"] + 1
grp = data.groupby(between, observed=True)[dv] # default is sort=True
# Careful: pd.unique does NOT sort whereas numpy does
# The line below should be equal to labels = np.unique(data[between])
# However, this does not work if between is a Categorical column, because
# Pandas applies a custom, not alphabetical, sorting.
# See https://github.com/raphaelvallat/pingouin/issues/111
labels = np.array(list(grp.groups.keys()))
n = grp.count().to_numpy()
gmeans = grp.mean(numeric_only=True).to_numpy()
gvar = aov.at[1, "MS"] / n
# Pairwise combinations
g1, g2 = np.array(list(combinations(np.arange(ng), 2))).T
mn = gmeans[g1] - gmeans[g2]
se = np.sqrt(gvar[g1] + gvar[g2])
tval = mn / se
# Critical values and p-values
# crit = studentized_range.ppf(1 - alpha, ng, df) / np.sqrt(2)
pval = studentized_range.sf(np.sqrt(2) * np.abs(tval), ng, df)
pval = np.clip(pval, 0, 1)
# Uncorrected p-values
# from scipy.stats import t
# punc = t.sf(np.abs(tval), n[g1].size + n[g2].size - 2) * 2
# Effect size
# Method 1: Approximation
# d = tval * np.sqrt(1 / n[g1] + 1 / n[g2])
# ef = convert_effsize(d, "cohen", effsize, n[g1], n[g2])
# Method 2: Exact
ef = []
for idx_a, idx_b in zip(g1, g2):
ef.append(
compute_effsize(
grp.get_group(labels[idx_a]),
grp.get_group(labels[idx_b]),
paired=False,
eftype=effsize,
)
)
# Create dataframe
stats = pd.DataFrame(
{
"A": labels[g1],
"B": labels[g2],
"mean(A)": gmeans[g1],
"mean(B)": gmeans[g2],
"diff": mn,
"se": se,
"T": tval,
"p-tukey": pval,
effsize: ef,
}
)
return _postprocess_dataframe(stats)
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|
32,036 | pingouin.correlation | partial_corr | Partial and semi-partial correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Pandas Dataframe. Note that this function can also directly be used
as a :py:class:`pandas.DataFrame` method, in which case this argument
is no longer needed.
x, y : string
x and y. Must be names of columns in ``data``.
covar : string or list
Covariate(s). Must be a names of columns in ``data``. Use a list if
there are two or more covariates.
x_covar : string or list
Covariate(s) for the ``x`` variable. This is used to compute
semi-partial correlation (i.e. the effect of ``x_covar`` is removed
from ``x`` but not from ``y``). Only one of ``covar``, ``x_covar`` and
``y_covar`` can be specified.
y_covar : string or list
Covariate(s) for the ``y`` variable. This is used to compute
semi-partial correlation (i.e. the effect of ``y_covar`` is removed
from ``y`` but not from ``x``). Only one of ``covar``, ``x_covar`` and
``y_covar`` can be specified.
alternative : string
Defines the alternative hypothesis, or tail of the partial correlation. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return a one-sided
p-value. "greater" tests against the alternative hypothesis that the partial correlation is
positive (greater than zero), "less" tests against the hypothesis that the partial
correlation is negative.
method : string
Correlation type:
* ``'pearson'``: Pearson :math:`r` product-moment correlation
* ``'spearman'``: Spearman :math:`\rho` rank-order correlation
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'n'``: Sample size (after removal of missing values)
* ``'r'``: Partial correlation coefficient
* ``'CI95'``: 95% parametric confidence intervals around :math:`r`
* ``'p-val'``: p-value
See also
--------
corr, pcorr, pairwise_corr, rm_corr
Notes
-----
Partial correlation [1]_ measures the degree of association between ``x``
and ``y``, after removing the effect of one or more controlling variables
(``covar``, or :math:`Z`). Practically, this is achieved by calculating the
correlation coefficient between the residuals of two linear regressions:
.. math:: x \sim Z, y \sim Z
Like the correlation coefficient, the partial correlation
coefficient takes on a value in the range from –1 to 1, where 1 indicates a
perfect positive association.
The semipartial correlation is similar to the partial correlation,
with the exception that the set of controlling variables is only
removed for either ``x`` or ``y``, but not both.
Pingouin uses the method described in [2]_ to calculate the (semi)partial
correlation coefficients and associated p-values. This method is based on
the inverse covariance matrix and is significantly faster than the
traditional regression-based method. Results have been tested against the
`ppcor <https://cran.r-project.org/web/packages/ppcor/index.html>`_
R package.
.. important:: Rows with missing values are automatically removed from
data.
References
----------
.. [1] https://en.wikipedia.org/wiki/Partial_correlation
.. [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4681537/
Examples
--------
1. Partial correlation with one covariate
>>> import pingouin as pg
>>> df = pg.read_dataset('partial_corr')
>>> pg.partial_corr(data=df, x='x', y='y', covar='cv1').round(3)
n r CI95% p-val
pearson 30 0.568 [0.25, 0.77] 0.001
2. Spearman partial correlation with several covariates
>>> # Partial correlation of x and y controlling for cv1, cv2 and cv3
>>> pg.partial_corr(data=df, x='x', y='y', covar=['cv1', 'cv2', 'cv3'],
... method='spearman').round(3)
n r CI95% p-val
spearman 30 0.521 [0.18, 0.75] 0.005
3. Same but one-sided test
>>> pg.partial_corr(data=df, x='x', y='y', covar=['cv1', 'cv2', 'cv3'],
... alternative="greater", method='spearman').round(3)
n r CI95% p-val
spearman 30 0.521 [0.24, 1.0] 0.003
>>> pg.partial_corr(data=df, x='x', y='y', covar=['cv1', 'cv2', 'cv3'],
... alternative="less", method='spearman').round(3)
n r CI95% p-val
spearman 30 0.521 [-1.0, 0.72] 0.997
4. As a pandas method
>>> df.partial_corr(x='x', y='y', covar=['cv1'], method='spearman').round(3)
n r CI95% p-val
spearman 30 0.578 [0.27, 0.78] 0.001
5. Partial correlation matrix (returns only the correlation coefficients)
>>> df.pcorr().round(3)
x y cv1 cv2 cv3
x 1.000 0.493 -0.095 0.130 -0.385
y 0.493 1.000 -0.007 0.104 -0.002
cv1 -0.095 -0.007 1.000 -0.241 -0.470
cv2 0.130 0.104 -0.241 1.000 -0.118
cv3 -0.385 -0.002 -0.470 -0.118 1.000
6. Semi-partial correlation on x
>>> pg.partial_corr(data=df, x='x', y='y', x_covar=['cv1', 'cv2', 'cv3']).round(3)
n r CI95% p-val
pearson 30 0.463 [0.1, 0.72] 0.015
| @pf.register_dataframe_method
def partial_corr(
data=None,
x=None,
y=None,
covar=None,
x_covar=None,
y_covar=None,
alternative="two-sided",
method="pearson",
):
"""Partial and semi-partial correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Pandas Dataframe. Note that this function can also directly be used
as a :py:class:`pandas.DataFrame` method, in which case this argument
is no longer needed.
x, y : string
x and y. Must be names of columns in ``data``.
covar : string or list
Covariate(s). Must be a names of columns in ``data``. Use a list if
there are two or more covariates.
x_covar : string or list
Covariate(s) for the ``x`` variable. This is used to compute
semi-partial correlation (i.e. the effect of ``x_covar`` is removed
from ``x`` but not from ``y``). Only one of ``covar``, ``x_covar`` and
``y_covar`` can be specified.
y_covar : string or list
Covariate(s) for the ``y`` variable. This is used to compute
semi-partial correlation (i.e. the effect of ``y_covar`` is removed
from ``y`` but not from ``x``). Only one of ``covar``, ``x_covar`` and
``y_covar`` can be specified.
alternative : string
Defines the alternative hypothesis, or tail of the partial correlation. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return a one-sided
p-value. "greater" tests against the alternative hypothesis that the partial correlation is
positive (greater than zero), "less" tests against the hypothesis that the partial
correlation is negative.
method : string
Correlation type:
* ``'pearson'``: Pearson :math:`r` product-moment correlation
* ``'spearman'``: Spearman :math:`\\rho` rank-order correlation
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'n'``: Sample size (after removal of missing values)
* ``'r'``: Partial correlation coefficient
* ``'CI95'``: 95% parametric confidence intervals around :math:`r`
* ``'p-val'``: p-value
See also
--------
corr, pcorr, pairwise_corr, rm_corr
Notes
-----
Partial correlation [1]_ measures the degree of association between ``x``
and ``y``, after removing the effect of one or more controlling variables
(``covar``, or :math:`Z`). Practically, this is achieved by calculating the
correlation coefficient between the residuals of two linear regressions:
.. math:: x \\sim Z, y \\sim Z
Like the correlation coefficient, the partial correlation
coefficient takes on a value in the range from –1 to 1, where 1 indicates a
perfect positive association.
The semipartial correlation is similar to the partial correlation,
with the exception that the set of controlling variables is only
removed for either ``x`` or ``y``, but not both.
Pingouin uses the method described in [2]_ to calculate the (semi)partial
correlation coefficients and associated p-values. This method is based on
the inverse covariance matrix and is significantly faster than the
traditional regression-based method. Results have been tested against the
`ppcor <https://cran.r-project.org/web/packages/ppcor/index.html>`_
R package.
.. important:: Rows with missing values are automatically removed from
data.
References
----------
.. [1] https://en.wikipedia.org/wiki/Partial_correlation
.. [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4681537/
Examples
--------
1. Partial correlation with one covariate
>>> import pingouin as pg
>>> df = pg.read_dataset('partial_corr')
>>> pg.partial_corr(data=df, x='x', y='y', covar='cv1').round(3)
n r CI95% p-val
pearson 30 0.568 [0.25, 0.77] 0.001
2. Spearman partial correlation with several covariates
>>> # Partial correlation of x and y controlling for cv1, cv2 and cv3
>>> pg.partial_corr(data=df, x='x', y='y', covar=['cv1', 'cv2', 'cv3'],
... method='spearman').round(3)
n r CI95% p-val
spearman 30 0.521 [0.18, 0.75] 0.005
3. Same but one-sided test
>>> pg.partial_corr(data=df, x='x', y='y', covar=['cv1', 'cv2', 'cv3'],
... alternative="greater", method='spearman').round(3)
n r CI95% p-val
spearman 30 0.521 [0.24, 1.0] 0.003
>>> pg.partial_corr(data=df, x='x', y='y', covar=['cv1', 'cv2', 'cv3'],
... alternative="less", method='spearman').round(3)
n r CI95% p-val
spearman 30 0.521 [-1.0, 0.72] 0.997
4. As a pandas method
>>> df.partial_corr(x='x', y='y', covar=['cv1'], method='spearman').round(3)
n r CI95% p-val
spearman 30 0.578 [0.27, 0.78] 0.001
5. Partial correlation matrix (returns only the correlation coefficients)
>>> df.pcorr().round(3)
x y cv1 cv2 cv3
x 1.000 0.493 -0.095 0.130 -0.385
y 0.493 1.000 -0.007 0.104 -0.002
cv1 -0.095 -0.007 1.000 -0.241 -0.470
cv2 0.130 0.104 -0.241 1.000 -0.118
cv3 -0.385 -0.002 -0.470 -0.118 1.000
6. Semi-partial correlation on x
>>> pg.partial_corr(data=df, x='x', y='y', x_covar=['cv1', 'cv2', 'cv3']).round(3)
n r CI95% p-val
pearson 30 0.463 [0.1, 0.72] 0.015
"""
from pingouin.utils import _flatten_list
# Safety check
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
assert method in [
"pearson",
"spearman",
], 'only "pearson" and "spearman" are supported for partial correlation.'
assert isinstance(data, pd.DataFrame), "data must be a pandas DataFrame."
assert data.shape[0] > 2, "Data must have at least 3 samples."
if covar is not None and (x_covar is not None or y_covar is not None):
raise ValueError("Cannot specify both covar and {x,y}_covar.")
if x_covar is not None and y_covar is not None:
raise ValueError("Cannot specify both x_covar and y_covar.")
assert x != y, "x and y must be independent"
if isinstance(covar, list):
assert x not in covar, "x and covar must be independent"
assert y not in covar, "y and covar must be independent"
else:
assert x != covar, "x and covar must be independent"
assert y != covar, "y and covar must be independent"
# Check that columns exist
col = _flatten_list([x, y, covar, x_covar, y_covar])
assert all([c in data for c in col]), "columns are not in dataframe."
# Check that columns are numeric
assert all([data[c].dtype.kind in "bfiu" for c in col])
# Drop rows with NaN
data = data[col].dropna()
n = data.shape[0] # Number of samples
k = data.shape[1] - 2 # Number of covariates
assert n > 2, "Data must have at least 3 non-NAN samples."
# Calculate the partial corrrelation matrix - similar to pingouin.pcorr()
if method == "spearman":
# Convert the data to rank, similar to R cov()
V = data.rank(na_option="keep").cov(numeric_only=True)
else:
V = data.cov(numeric_only=True)
Vi = np.linalg.pinv(V, hermitian=True) # Inverse covariance matrix
Vi_diag = Vi.diagonal()
D = np.diag(np.sqrt(1 / Vi_diag))
pcor = -1 * (D @ Vi @ D) # Partial correlation matrix
if covar is not None:
r = pcor[0, 1]
else:
# Semi-partial correlation matrix
with np.errstate(divide="ignore"):
spcor = (
pcor
/ np.sqrt(np.diag(V))[..., None]
/ np.sqrt(np.abs(Vi_diag - Vi**2 / Vi_diag[..., None])).T
)
if y_covar is not None:
r = spcor[0, 1] # y_covar is removed from y
else:
r = spcor[1, 0] # x_covar is removed from x
if np.isnan(r):
| (data=None, x=None, y=None, covar=None, x_covar=None, y_covar=None, alternative='two-sided', method='pearson') | [
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|
32,037 | pingouin.correlation | pcorr | Partial correlation matrix (:py:class:`pandas.DataFrame` method).
Returns
-------
pcormat : :py:class:`pandas.DataFrame`
Partial correlation matrix.
Notes
-----
This function calculates the pairwise partial correlations for each pair of
variables in a :py:class:`pandas.DataFrame` given all the others. It has
the same behavior as the pcor function in the
`ppcor <https://cran.r-project.org/web/packages/ppcor/index.html>`_
R package.
Note that this function only returns the raw Pearson correlation
coefficient. If you want to calculate the test statistic and p-values, or
use more robust estimates of the correlation coefficient, please refer to
the :py:func:`pingouin.pairwise_corr` or :py:func:`pingouin.partial_corr`
functions.
Examples
--------
>>> import pingouin as pg
>>> data = pg.read_dataset('mediation')
>>> data.pcorr().round(3)
X M Y Mbin Ybin W1 W2
X 1.000 0.359 0.074 -0.019 -0.147 -0.148 -0.067
M 0.359 1.000 0.555 -0.024 -0.112 -0.138 -0.176
Y 0.074 0.555 1.000 -0.001 0.169 0.101 0.108
Mbin -0.019 -0.024 -0.001 1.000 -0.080 -0.032 -0.040
Ybin -0.147 -0.112 0.169 -0.080 1.000 -0.000 -0.140
W1 -0.148 -0.138 0.101 -0.032 -0.000 1.000 -0.394
W2 -0.067 -0.176 0.108 -0.040 -0.140 -0.394 1.000
On a subset of columns
>>> data[['X', 'Y', 'M']].pcorr()
X Y M
X 1.000000 0.036649 0.412804
Y 0.036649 1.000000 0.540140
M 0.412804 0.540140 1.000000
| @pf.register_dataframe_method
def pcorr(self):
"""Partial correlation matrix (:py:class:`pandas.DataFrame` method).
Returns
-------
pcormat : :py:class:`pandas.DataFrame`
Partial correlation matrix.
Notes
-----
This function calculates the pairwise partial correlations for each pair of
variables in a :py:class:`pandas.DataFrame` given all the others. It has
the same behavior as the pcor function in the
`ppcor <https://cran.r-project.org/web/packages/ppcor/index.html>`_
R package.
Note that this function only returns the raw Pearson correlation
coefficient. If you want to calculate the test statistic and p-values, or
use more robust estimates of the correlation coefficient, please refer to
the :py:func:`pingouin.pairwise_corr` or :py:func:`pingouin.partial_corr`
functions.
Examples
--------
>>> import pingouin as pg
>>> data = pg.read_dataset('mediation')
>>> data.pcorr().round(3)
X M Y Mbin Ybin W1 W2
X 1.000 0.359 0.074 -0.019 -0.147 -0.148 -0.067
M 0.359 1.000 0.555 -0.024 -0.112 -0.138 -0.176
Y 0.074 0.555 1.000 -0.001 0.169 0.101 0.108
Mbin -0.019 -0.024 -0.001 1.000 -0.080 -0.032 -0.040
Ybin -0.147 -0.112 0.169 -0.080 1.000 -0.000 -0.140
W1 -0.148 -0.138 0.101 -0.032 -0.000 1.000 -0.394
W2 -0.067 -0.176 0.108 -0.040 -0.140 -0.394 1.000
On a subset of columns
>>> data[['X', 'Y', 'M']].pcorr()
X Y M
X 1.000000 0.036649 0.412804
Y 0.036649 1.000000 0.540140
M 0.412804 0.540140 1.000000
"""
V = self.cov(numeric_only=True) # Covariance matrix
Vi = np.linalg.pinv(V, hermitian=True) # Inverse covariance matrix
D = np.diag(np.sqrt(1 / np.diag(Vi)))
pcor = -1 * (D @ Vi @ D) # Partial correlation matrix
pcor[np.diag_indices_from(pcor)] = 1
return pd.DataFrame(pcor, index=V.index, columns=V.columns)
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|
32,038 | pingouin.plotting | plot_blandaltman |
Generate a Bland-Altman plot to compare two sets of measurements.
Parameters
----------
x, y : pd.Series, np.array, or list
First and second measurements.
agreement : float
Multiple of the standard deviation to plot agreement limits.
The defaults is 1.96, which corresponds to 95% confidence interval if
the differences are normally distributed.
xaxis : str
Define which measurements should be used as the reference (x-axis).
Default is to use the average of x and y ("mean"). Accepted values are
"mean", "x" or "y".
confidence : float
If not None, plot the specified percentage confidence interval of
the mean and limits of agreement. The CIs of the mean difference and
agreement limits describe a possible error in the
estimate due to a sampling error. The greater the sample size,
the narrower the CIs will be.
annotate : bool
If True (default), annotate the values for the mean difference
and agreement limits.
ax : matplotlib axes
Axis on which to draw the plot.
**kwargs : optional
Optional argument(s) passed to :py:func:`matplotlib.pyplot.scatter`.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Notes
-----
Bland-Altman plots [1]_ are extensively used to evaluate the agreement
among two different instruments or two measurements techniques.
They allow identification of any systematic difference between the
measurements (i.e., fixed bias) or possible outliers.
The mean difference (= x - y) is the estimated bias, and the SD of the
differences measures the random fluctuations around this mean.
If the mean value of the difference differs significantly from 0 on the
basis of a 1-sample t-test, this indicates the presence of fixed bias.
If there is a consistent bias, it can be adjusted for by subtracting the
mean difference from the new method.
It is common to compute 95% limits of agreement for each comparison
(average difference ± 1.96 standard deviation of the difference), which
tells us how far apart measurements by 2 methods were more likely to be
for most individuals. If the differences within mean ± 1.96 SD are not
clinically important, the two methods may be used interchangeably.
The 95% limits of agreement can be unreliable estimates of the population
parameters especially for small sample sizes so, when comparing methods
or assessing repeatability, it is important to calculate confidence
intervals for the 95% limits of agreement.
The code is an adaptation of the
`PyCompare <https://github.com/jaketmp/pyCompare>`_ package. The present
implementation is a simplified version; please refer to the original
package for more advanced functionalities.
References
----------
.. [1] Bland, J. M., & Altman, D. (1986). Statistical methods for assessing
agreement between two methods of clinical measurement. The lancet,
327(8476), 307-310.
.. [2] Giavarina, D. (2015). Understanding bland altman analysis.
Biochemia medica, 25(2), 141-151.
Examples
--------
Bland-Altman plot (example data from [2]_)
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset("blandaltman")
>>> ax = pg.plot_blandaltman(df['A'], df['B'])
>>> plt.tight_layout()
| def plot_blandaltman(
x, y, agreement=1.96, xaxis="mean", confidence=0.95, annotate=True, ax=None, **kwargs
):
"""
Generate a Bland-Altman plot to compare two sets of measurements.
Parameters
----------
x, y : pd.Series, np.array, or list
First and second measurements.
agreement : float
Multiple of the standard deviation to plot agreement limits.
The defaults is 1.96, which corresponds to 95% confidence interval if
the differences are normally distributed.
xaxis : str
Define which measurements should be used as the reference (x-axis).
Default is to use the average of x and y ("mean"). Accepted values are
"mean", "x" or "y".
confidence : float
If not None, plot the specified percentage confidence interval of
the mean and limits of agreement. The CIs of the mean difference and
agreement limits describe a possible error in the
estimate due to a sampling error. The greater the sample size,
the narrower the CIs will be.
annotate : bool
If True (default), annotate the values for the mean difference
and agreement limits.
ax : matplotlib axes
Axis on which to draw the plot.
**kwargs : optional
Optional argument(s) passed to :py:func:`matplotlib.pyplot.scatter`.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Notes
-----
Bland-Altman plots [1]_ are extensively used to evaluate the agreement
among two different instruments or two measurements techniques.
They allow identification of any systematic difference between the
measurements (i.e., fixed bias) or possible outliers.
The mean difference (= x - y) is the estimated bias, and the SD of the
differences measures the random fluctuations around this mean.
If the mean value of the difference differs significantly from 0 on the
basis of a 1-sample t-test, this indicates the presence of fixed bias.
If there is a consistent bias, it can be adjusted for by subtracting the
mean difference from the new method.
It is common to compute 95% limits of agreement for each comparison
(average difference ± 1.96 standard deviation of the difference), which
tells us how far apart measurements by 2 methods were more likely to be
for most individuals. If the differences within mean ± 1.96 SD are not
clinically important, the two methods may be used interchangeably.
The 95% limits of agreement can be unreliable estimates of the population
parameters especially for small sample sizes so, when comparing methods
or assessing repeatability, it is important to calculate confidence
intervals for the 95% limits of agreement.
The code is an adaptation of the
`PyCompare <https://github.com/jaketmp/pyCompare>`_ package. The present
implementation is a simplified version; please refer to the original
package for more advanced functionalities.
References
----------
.. [1] Bland, J. M., & Altman, D. (1986). Statistical methods for assessing
agreement between two methods of clinical measurement. The lancet,
327(8476), 307-310.
.. [2] Giavarina, D. (2015). Understanding bland altman analysis.
Biochemia medica, 25(2), 141-151.
Examples
--------
Bland-Altman plot (example data from [2]_)
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset("blandaltman")
>>> ax = pg.plot_blandaltman(df['A'], df['B'])
>>> plt.tight_layout()
"""
# Safety check
assert xaxis in ["mean", "x", "y"]
# Get names before converting to NumPy array
xname = x.name if isinstance(x, pd.Series) else "x"
yname = y.name if isinstance(y, pd.Series) else "y"
x = np.asarray(x)
y = np.asarray(y)
assert x.ndim == 1 and y.ndim == 1
assert x.size == y.size
assert not np.isnan(x).any(), "Missing values in x or y are not supported."
assert not np.isnan(y).any(), "Missing values in x or y are not supported."
# Update default kwargs with specified inputs
_scatter_kwargs = {"color": "tab:blue", "alpha": 0.8}
_scatter_kwargs.update(kwargs)
# Calculate mean, STD and SEM of x - y
n = x.size
dof = n - 1
diff = x - y
mean_diff = np.mean(diff)
std_diff = np.std(diff, ddof=1)
mean_diff_se = np.sqrt(std_diff**2 / n)
# Limits of agreements
high = mean_diff + agreement * std_diff
low = mean_diff - agreement * std_diff
high_low_se = np.sqrt(3 * std_diff**2 / n)
# Define x-axis
if xaxis == "mean":
xval = np.vstack((x, y)).mean(0)
xlabel = f"Mean of {xname} and {yname}"
elif xaxis == "x":
xval = x
xlabel = xname
else:
xval = y
xlabel = yname
# Start the plot
if ax is None:
ax = plt.gca()
# Plot the mean diff, limits of agreement and scatter
ax.scatter(xval, diff, **_scatter_kwargs)
ax.axhline(mean_diff, color="k", linestyle="-", lw=2)
ax.axhline(high, color="k", linestyle=":", lw=1.5)
ax.axhline(low, color="k", linestyle=":", lw=1.5)
# Annotate values
if annotate:
loa_range = high - low
offset = (loa_range / 100.0) * 1.5
trans = transforms.blended_transform_factory(ax.transAxes, ax.transData)
xloc = 0.98
ax.text(xloc, mean_diff + offset, "Mean", ha="right", va="bottom", transform=trans)
ax.text(xloc, mean_diff - offset, "%.2f" % mean_diff, ha="right", va="top", transform=trans)
ax.text(
xloc, high + offset, "+%.2f SD" % agreement, ha="right", va="bottom", transform=trans
)
ax.text(xloc, high - offset, "%.2f" % high, ha="right", va="top", transform=trans)
ax.text(xloc, low - offset, "-%.2f SD" % agreement, ha="right", va="top", transform=trans)
ax.text(xloc, low + offset, "%.2f" % low, ha="right", va="bottom", transform=trans)
# Add 95% confidence intervals for mean bias and limits of agreement
if confidence is not None:
assert 0 < confidence < 1
ci = dict()
ci["mean"] = stats.t.interval(confidence, dof, loc=mean_diff, scale=mean_diff_se)
ci["high"] = stats.t.interval(confidence, dof, loc=high, scale=high_low_se)
ci["low"] = stats.t.interval(confidence, dof, loc=low, scale=high_low_se)
ax.axhspan(ci["mean"][0], ci["mean"][1], facecolor="tab:grey", alpha=0.2)
ax.axhspan(ci["high"][0], ci["high"][1], facecolor=_scatter_kwargs["color"], alpha=0.2)
ax.axhspan(ci["low"][0], ci["low"][1], facecolor=_scatter_kwargs["color"], alpha=0.2)
# Labels
ax.set_ylabel(f"{xname} - {yname}")
ax.set_xlabel(xlabel)
sns.despine(ax=ax)
return ax
| (x, y, agreement=1.96, xaxis='mean', confidence=0.95, annotate=True, ax=None, **kwargs) | [
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|
32,039 | pingouin.plotting | plot_circmean | Plot the circular mean and vector length of a set of angles
on the unit circle.
.. versionadded:: 0.3.3
Parameters
----------
angles : array or list
Angles (expressed in radians). Only 1D array are supported here.
square: bool
If True (default), ensure equal aspect ratio between X and Y axes.
ax : matplotlib axes
Axis on which to draw the plot.
kwargs_markers : dict
Optional keywords arguments that are passed to
:obj:`matplotlib.axes.Axes.plot`
to control the markers aesthetics.
kwargs_arrow : dict
Optional keywords arguments that are passed to
:obj:`matplotlib.axes.Axes.arrow`
to control the arrow aesthetics.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Examples
--------
Default plot
.. plot::
>>> import pingouin as pg
>>> ax = pg.plot_circmean([0.05, -0.8, 1.2, 0.8, 0.5, -0.3, 0.3, 0.7])
Changing some aesthetics parameters
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> _, ax = plt.subplots(1, 1, figsize=(3, 3))
>>> ax = pg.plot_circmean([0.05, -0.8, 1.2, 0.8, 0.5, -0.3, 0.3, 0.7],
... kwargs_markers=dict(color='k', mfc='k'),
... kwargs_arrow=dict(ec='k', fc='k'), ax=ax)
.. plot::
>>> import pingouin as pg
>>> import seaborn as sns
>>> sns.set(font_scale=1.5, style='white')
>>> ax = pg.plot_circmean([0.8, 1.5, 3.14, 5.2, 6.1, 2.8, 2.6, 3.2],
... kwargs_markers=dict(marker="None"))
| def plot_circmean(
angles,
square=True,
ax=None,
kwargs_markers=dict(color="tab:blue", marker="o", mfc="none", ms=10),
kwargs_arrow=dict(width=0.01, head_width=0.1, head_length=0.1, fc="tab:red", ec="tab:red"),
):
"""Plot the circular mean and vector length of a set of angles
on the unit circle.
.. versionadded:: 0.3.3
Parameters
----------
angles : array or list
Angles (expressed in radians). Only 1D array are supported here.
square: bool
If True (default), ensure equal aspect ratio between X and Y axes.
ax : matplotlib axes
Axis on which to draw the plot.
kwargs_markers : dict
Optional keywords arguments that are passed to
:obj:`matplotlib.axes.Axes.plot`
to control the markers aesthetics.
kwargs_arrow : dict
Optional keywords arguments that are passed to
:obj:`matplotlib.axes.Axes.arrow`
to control the arrow aesthetics.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Examples
--------
Default plot
.. plot::
>>> import pingouin as pg
>>> ax = pg.plot_circmean([0.05, -0.8, 1.2, 0.8, 0.5, -0.3, 0.3, 0.7])
Changing some aesthetics parameters
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> _, ax = plt.subplots(1, 1, figsize=(3, 3))
>>> ax = pg.plot_circmean([0.05, -0.8, 1.2, 0.8, 0.5, -0.3, 0.3, 0.7],
... kwargs_markers=dict(color='k', mfc='k'),
... kwargs_arrow=dict(ec='k', fc='k'), ax=ax)
.. plot::
>>> import pingouin as pg
>>> import seaborn as sns
>>> sns.set(font_scale=1.5, style='white')
>>> ax = pg.plot_circmean([0.8, 1.5, 3.14, 5.2, 6.1, 2.8, 2.6, 3.2],
... kwargs_markers=dict(marker="None"))
"""
from matplotlib.patches import Circle
from .circular import circ_r, circ_mean
# Sanity checks
angles = np.asarray(angles)
assert angles.ndim == 1, "angles must be a one-dimensional array."
assert angles.size > 1, "angles must have at least 2 values."
assert isinstance(kwargs_markers, dict), "kwargs_markers must be a dict."
assert isinstance(kwargs_arrow, dict), "kwargs_arrow must be a dict."
# Fill missing values in dict
if "color" not in kwargs_markers.keys():
kwargs_markers["color"] = "tab:blue"
if "marker" not in kwargs_markers.keys():
kwargs_markers["marker"] = "o"
if "mfc" not in kwargs_markers.keys():
kwargs_markers["mfc"] = "none"
if "ms" not in kwargs_markers.keys():
kwargs_markers["ms"] = 10
if "width" not in kwargs_arrow.keys():
kwargs_arrow["width"] = 0.01
if "head_width" not in kwargs_arrow.keys():
kwargs_arrow["head_width"] = 0.1
if "head_length" not in kwargs_arrow.keys():
kwargs_arrow["head_length"] = 0.1
if "fc" not in kwargs_arrow.keys():
kwargs_arrow["fc"] = "tab:red"
if "ec" not in kwargs_arrow.keys():
kwargs_arrow["ec"] = "tab:red"
# Convert angles to unit vector
z = np.exp(1j * angles)
r = circ_r(angles) # Resulting vector length
phi = circ_mean(angles) # Circular mean
zm = r * np.exp(1j * phi)
# Plot unit circle
if ax is None:
ax = plt.gca()
circle = Circle((0, 0), 1, edgecolor="k", facecolor="none", linewidth=2)
ax.add_patch(circle)
ax.axvline(0, lw=1, ls=":", color="slategrey")
ax.axhline(0, lw=1, ls=":", color="slategrey")
ax.plot(np.real(z), np.imag(z), ls="None", **kwargs_markers)
# Plot mean resultant vector
ax.arrow(0, 0, np.real(zm), np.imag(zm), **kwargs_arrow)
# X and Y ticks in radians
ax.set_xticks([])
ax.set_yticks([])
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["left"].set_visible(False)
ax.spines["bottom"].set_visible(False)
ax.text(1.2, 0, "0", verticalalignment="center")
ax.text(-1.3, 0, r"$\pi$", verticalalignment="center")
ax.text(0, 1.2, r"$+\pi/2$", horizontalalignment="center")
ax.text(0, -1.3, r"$-\pi/2$", horizontalalignment="center")
# Make square
if square:
ax.set_aspect("equal")
return ax
| (angles, square=True, ax=None, kwargs_markers={'color': 'tab:blue', 'marker': 'o', 'mfc': 'none', 'ms': 10}, kwargs_arrow={'width': 0.01, 'head_width': 0.1, 'head_length': 0.1, 'fc': 'tab:red', 'ec': 'tab:red'}) | [
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|
32,040 | pingouin.plotting | plot_paired |
Paired plot.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Long-format dataFrame.
dv : string
Name of column containing the dependent variable.
within : string
Name of column containing the within-subject factor.
subject : string
Name of column containing the subject identifier.
order : list of str
List of values in ``within`` that define the order of elements on the
x-axis of the plot. If None, uses alphabetical order.
boxplot : boolean
If True, add a boxplot to the paired lines using the
:py:func:`seaborn.boxplot` function.
boxplot_in_front : boolean
If True, the boxplot is plotted on the foreground (i.e. above the
individual lines) and with a slight transparency. This makes the
overall plot more readable when plotting a large numbers of subjects.
.. versionadded:: 0.3.8
orient : string
Plot the boxplots vertically and the subjects on the x-axis if
``orient='v'`` (default). Set to ``orient='h'`` to rotate the plot by
by 90 degrees.
.. versionadded:: 0.3.9
ax : matplotlib axes
Axis on which to draw the plot.
colors : list of str
Line colors names. Default is green when value increases from A to B,
indianred when value decreases from A to B and grey when the value is
the same in both measurements.
pointplot_kwargs : dict
Dictionnary of optional arguments that are passed to the
:py:func:`seaborn.pointplot` function.
boxplot_kwargs : dict
Dictionnary of optional arguments that are passed to the
:py:func:`seaborn.boxplot` function.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Notes
-----
Data must be a long-format pandas DataFrame. Missing values are automatically removed using a
strict listwise approach (= complete-case analysis).
Examples
--------
Default paired plot:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('mixed_anova').query("Time != 'January'")
>>> df = df.query("Group == 'Meditation' and Subject > 40")
>>> ax = pg.plot_paired(data=df, dv='Scores', within='Time', subject='Subject')
Paired plot on an existing axis (no boxplot and uniform color):
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> df = pg.read_dataset('mixed_anova').query("Time != 'January'")
>>> df = df.query("Group == 'Meditation' and Subject > 40")
>>> fig, ax1 = plt.subplots(1, 1, figsize=(5, 4))
>>> pg.plot_paired(data=df, dv='Scores', within='Time',
... subject='Subject', ax=ax1, boxplot=False,
... colors=['grey', 'grey', 'grey']) # doctest: +SKIP
Horizontal paired plot with three unique within-levels:
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> df = pg.read_dataset('mixed_anova').query("Group == 'Meditation'")
>>> # df = df.query("Group == 'Meditation' and Subject > 40")
>>> pg.plot_paired(data=df, dv='Scores', within='Time',
... subject='Subject', orient='h') # doctest: +SKIP
With the boxplot on the foreground:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('mixed_anova').query("Time != 'January'")
>>> df = df.query("Group == 'Control'")
>>> ax = pg.plot_paired(data=df, dv='Scores', within='Time',
... subject='Subject', boxplot_in_front=True)
| def plot_paired(
data=None,
dv=None,
within=None,
subject=None,
order=None,
boxplot=True,
boxplot_in_front=False,
orient="v",
ax=None,
colors=["green", "grey", "indianred"],
pointplot_kwargs={"scale": 0.6, "marker": "."},
boxplot_kwargs={"color": "lightslategrey", "width": 0.2},
):
"""
Paired plot.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Long-format dataFrame.
dv : string
Name of column containing the dependent variable.
within : string
Name of column containing the within-subject factor.
subject : string
Name of column containing the subject identifier.
order : list of str
List of values in ``within`` that define the order of elements on the
x-axis of the plot. If None, uses alphabetical order.
boxplot : boolean
If True, add a boxplot to the paired lines using the
:py:func:`seaborn.boxplot` function.
boxplot_in_front : boolean
If True, the boxplot is plotted on the foreground (i.e. above the
individual lines) and with a slight transparency. This makes the
overall plot more readable when plotting a large numbers of subjects.
.. versionadded:: 0.3.8
orient : string
Plot the boxplots vertically and the subjects on the x-axis if
``orient='v'`` (default). Set to ``orient='h'`` to rotate the plot by
by 90 degrees.
.. versionadded:: 0.3.9
ax : matplotlib axes
Axis on which to draw the plot.
colors : list of str
Line colors names. Default is green when value increases from A to B,
indianred when value decreases from A to B and grey when the value is
the same in both measurements.
pointplot_kwargs : dict
Dictionnary of optional arguments that are passed to the
:py:func:`seaborn.pointplot` function.
boxplot_kwargs : dict
Dictionnary of optional arguments that are passed to the
:py:func:`seaborn.boxplot` function.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Notes
-----
Data must be a long-format pandas DataFrame. Missing values are automatically removed using a
strict listwise approach (= complete-case analysis).
Examples
--------
Default paired plot:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('mixed_anova').query("Time != 'January'")
>>> df = df.query("Group == 'Meditation' and Subject > 40")
>>> ax = pg.plot_paired(data=df, dv='Scores', within='Time', subject='Subject')
Paired plot on an existing axis (no boxplot and uniform color):
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> df = pg.read_dataset('mixed_anova').query("Time != 'January'")
>>> df = df.query("Group == 'Meditation' and Subject > 40")
>>> fig, ax1 = plt.subplots(1, 1, figsize=(5, 4))
>>> pg.plot_paired(data=df, dv='Scores', within='Time',
... subject='Subject', ax=ax1, boxplot=False,
... colors=['grey', 'grey', 'grey']) # doctest: +SKIP
Horizontal paired plot with three unique within-levels:
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> df = pg.read_dataset('mixed_anova').query("Group == 'Meditation'")
>>> # df = df.query("Group == 'Meditation' and Subject > 40")
>>> pg.plot_paired(data=df, dv='Scores', within='Time',
... subject='Subject', orient='h') # doctest: +SKIP
With the boxplot on the foreground:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('mixed_anova').query("Time != 'January'")
>>> df = df.query("Group == 'Control'")
>>> ax = pg.plot_paired(data=df, dv='Scores', within='Time',
... subject='Subject', boxplot_in_front=True)
"""
from pingouin.utils import _check_dataframe
# Update default kwargs with specified inputs
_pointplot_kwargs = {"scale": 0.6, "marker": "."}
_pointplot_kwargs.update(pointplot_kwargs)
_boxplot_kwargs = {"color": "lightslategrey", "width": 0.2}
_boxplot_kwargs.update(boxplot_kwargs)
# Extract pointplot alpha, if set
pp_alpha = _pointplot_kwargs.pop("alpha", 1.0)
# Calculate size of the plot elements by scale as in Seaborn pointplot
scale = _pointplot_kwargs.pop("scale")
lw = plt.rcParams["lines.linewidth"] * 1.8 * scale # get the linewidth
mew = lw * 0.75 # get the markeredgewidth
markersize = np.pi * np.square(lw) * 2 # get the markersize
# Set boxplot in front of Line2D plot (zorder=2 for both) and add alpha
if boxplot_in_front:
_boxplot_kwargs.update(
{
"boxprops": {"zorder": 2},
"whiskerprops": {"zorder": 2},
"zorder": 2,
}
)
# Validate args
data = _check_dataframe(data=data, dv=dv, within=within, subject=subject, effects="within")
# Pivot and melt the table. This has several effects:
# 1) Force missing values to be explicit (a NaN cell is created)
# 2) Automatic collapsing to the mean if multiple within factors are present
# 3) If using dropna, remove rows with missing values (listwise deletion).
# The latter is the same behavior as JASP (= strict complete-case analysis).
data_piv = data.pivot_table(index=subject, columns=within, values=dv, observed=True)
data_piv = data_piv.dropna()
data = data_piv.melt(ignore_index=False, value_name=dv).reset_index()
# Extract within-subject level (alphabetical order)
x_cat = np.unique(data[within])
if order is None:
order = x_cat
else:
assert len(order) == len(
x_cat
), "Order must have the same number of elements as the number of levels in `within`."
# Substitue within by integer order of the ordered columns to allow for
# changing the order of numeric withins.
data["wthn"] = data[within].replace({_ordr: i for i, _ordr in enumerate(order)})
order_num = range(len(order)) # Make numeric order
# Start the plot
if ax is None:
ax = plt.gca()
# Set x and y depending on orientation using the num. replacement within
_x = "wthn" if orient == "v" else dv
_y = dv if orient == "v" else "wthn"
for cat in range(len(x_cat) - 1):
_order = (order_num[cat], order_num[cat + 1])
# Extract data of the current subject-combination
data_now = data.loc[data["wthn"].isin(_order), [dv, "wthn", subject]]
# Select colors for all lines between the current subjects
y1 = data_now.loc[data_now["wthn"] == _order[0], dv].to_numpy()
y2 = data_now.loc[data_now["wthn"] == _order[1], dv].to_numpy()
# Line and scatter colors depending on subject dv trend
_colors = np.where(y1 < y2, colors[0], np.where(y1 > y2, colors[2], colors[1]))
# Line and scatter colors as hue-indexed dictionary
_colors = {subj: clr for subj, clr in zip(data_now[subject].unique(), _colors)}
# Plot individual lines using Seaborn
sns.lineplot(
data=data_now,
x=_x,
y=_y,
hue=subject,
palette=_colors,
ls="-",
lw=lw,
legend=False,
ax=ax,
)
# Plot individual markers using Seaborn
sns.scatterplot(
data=data_now,
x=_x,
y=_y,
hue=subject,
palette=_colors,
edgecolor="face",
lw=mew,
sizes=[markersize] * data_now.shape[0],
legend=False,
ax=ax,
**_pointplot_kwargs,
)
# Set zorder and alpha of pointplot markers and lines
_ = plt.setp(ax.collections, alpha=pp_alpha, zorder=2) # Set marker alpha
_ = plt.setp(ax.lines, alpha=pp_alpha, zorder=2) # Set line alpha
if boxplot:
# Set boxplot x and y d | (data=None, dv=None, within=None, subject=None, order=None, boxplot=True, boxplot_in_front=False, orient='v', ax=None, colors=['green', 'grey', 'indianred'], pointplot_kwargs={'scale': 0.6, 'marker': '.'}, boxplot_kwargs={'color': 'lightslategrey', 'width': 0.2}) | [
0.042630720883607864,
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|
32,041 | pingouin.plotting | plot_rm_corr | Plot a repeated measures correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x, y : string
Name of columns in ``data`` containing the two dependent variables.
subject : string
Name of column in ``data`` containing the subject indicator.
legend : boolean
If True, add legend to plot. Legend will show all the unique values in
``subject``.
kwargs_facetgrid : dict
Optional keyword arguments passed to :py:class:`seaborn.FacetGrid`
kwargs_line : dict
Optional keyword arguments passed to :py:class:`matplotlib.pyplot.plot`
kwargs_scatter : dict
Optional keyword arguments passed to :py:class:`matplotlib.pyplot.scatter`
Returns
-------
g : :py:class:`seaborn.FacetGrid`
Seaborn FacetGrid.
See also
--------
rm_corr
Notes
-----
Repeated measures correlation [1]_ (rmcorr) is a statistical technique
for determining the common within-individual association for paired
measures assessed on two or more occasions for multiple individuals.
Results have been tested against the
`rmcorr <https://github.com/cran/rmcorr>` R package. Note that this
function requires `statsmodels
<https://www.statsmodels.org/stable/index.html>`_.
Missing values are automatically removed from the ``data``
(listwise deletion).
References
----------
.. [1] Bakdash, J.Z., Marusich, L.R., 2017. Repeated Measures Correlation.
Front. Psychol. 8, 456. https://doi.org/10.3389/fpsyg.2017.00456
Examples
--------
Default repeated mesures correlation plot
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
With some tweakings
.. plot::
>>> import pingouin as pg
>>> import seaborn as sns
>>> df = pg.read_dataset('rm_corr')
>>> sns.set(style='darkgrid', font_scale=1.2)
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2',
... subject='Subject', legend=True,
... kwargs_facetgrid=dict(height=4.5, aspect=1.5,
... palette='Spectral'))
| def plot_rm_corr(
data=None,
x=None,
y=None,
subject=None,
legend=False,
kwargs_facetgrid=dict(height=4, aspect=1),
kwargs_line=dict(ls="solid"),
kwargs_scatter=dict(marker="o"),
):
"""Plot a repeated measures correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x, y : string
Name of columns in ``data`` containing the two dependent variables.
subject : string
Name of column in ``data`` containing the subject indicator.
legend : boolean
If True, add legend to plot. Legend will show all the unique values in
``subject``.
kwargs_facetgrid : dict
Optional keyword arguments passed to :py:class:`seaborn.FacetGrid`
kwargs_line : dict
Optional keyword arguments passed to :py:class:`matplotlib.pyplot.plot`
kwargs_scatter : dict
Optional keyword arguments passed to :py:class:`matplotlib.pyplot.scatter`
Returns
-------
g : :py:class:`seaborn.FacetGrid`
Seaborn FacetGrid.
See also
--------
rm_corr
Notes
-----
Repeated measures correlation [1]_ (rmcorr) is a statistical technique
for determining the common within-individual association for paired
measures assessed on two or more occasions for multiple individuals.
Results have been tested against the
`rmcorr <https://github.com/cran/rmcorr>` R package. Note that this
function requires `statsmodels
<https://www.statsmodels.org/stable/index.html>`_.
Missing values are automatically removed from the ``data``
(listwise deletion).
References
----------
.. [1] Bakdash, J.Z., Marusich, L.R., 2017. Repeated Measures Correlation.
Front. Psychol. 8, 456. https://doi.org/10.3389/fpsyg.2017.00456
Examples
--------
Default repeated mesures correlation plot
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
With some tweakings
.. plot::
>>> import pingouin as pg
>>> import seaborn as sns
>>> df = pg.read_dataset('rm_corr')
>>> sns.set(style='darkgrid', font_scale=1.2)
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2',
... subject='Subject', legend=True,
... kwargs_facetgrid=dict(height=4.5, aspect=1.5,
... palette='Spectral'))
"""
# Check that stasmodels is installed
from pingouin.utils import _is_statsmodels_installed
_is_statsmodels_installed(raise_error=True)
from statsmodels.formula.api import ols
# Safety check (duplicated from pingouin.rm_corr)
assert isinstance(data, pd.DataFrame), "Data must be a DataFrame"
assert x in data.columns, "The %s column is not in data." % x
assert y in data.columns, "The %s column is not in data." % y
assert data[x].dtype.kind in "bfiu", "%s must be numeric." % x
assert data[y].dtype.kind in "bfiu", "%s must be numeric." % y
assert subject in data.columns, "The %s column is not in data." % subject
if data[subject].nunique() < 3:
raise ValueError("rm_corr requires at least 3 unique subjects.")
# Remove missing values
data = data[[x, y, subject]].dropna(axis=0)
# Calculate rm_corr
# rmc = pg.rm_corr(data=data, x=x, y=y, subject=subject)
# Fit ANCOVA model
# https://patsy.readthedocs.io/en/latest/builtins-reference.html
# C marks the data as categorical
# Q allows to quote variable that do not meet Python variable name rule
# e.g. if variable is "weight.in.kg" or "2A"
assert x not in ["C", "Q"], "`x` must not be 'C' or 'Q'."
assert y not in ["C", "Q"], "`y` must not be 'C' or 'Q'."
assert subject not in ["C", "Q"], "`subject` must not be 'C' or 'Q'."
formula = f"Q('{y}') ~ C(Q('{subject}')) + Q('{x}')"
model = ols(formula, data=data).fit()
# Fitted values
data["pred"] = model.fittedvalues
# Define color palette
if "palette" not in kwargs_facetgrid:
kwargs_facetgrid["palette"] = sns.hls_palette(data[subject].nunique())
# Start plot
g = sns.FacetGrid(data, hue=subject, **kwargs_facetgrid)
g = g.map(sns.regplot, x, "pred", scatter=False, ci=None, truncate=True, line_kws=kwargs_line)
g = g.map(sns.scatterplot, x, y, **kwargs_scatter)
if legend:
g.add_legend()
return g
| (data=None, x=None, y=None, subject=None, legend=False, kwargs_facetgrid={'height': 4, 'aspect': 1}, kwargs_line={'ls': 'solid'}, kwargs_scatter={'marker': 'o'}) | [
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|
32,042 | pingouin.plotting | plot_shift | Shift plot.
Parameters
----------
x, y : array_like
First and second set of observations.
paired : bool
Specify whether ``x`` and ``y`` are related (i.e. repeated measures) or independent.
.. versionadded:: 0.3.0
n_boot : int
Number of bootstrap iterations. The higher, the better, the slower.
percentiles: array_like
Sequence of percentiles to compute, which must be between 0 and 100 inclusive.
Default set to [10, 20, 30, 40, 50, 60, 70, 80, 90].
confidence : float
Confidence level (0.95 = 95%) for the confidence intervals.
seed : int or None
Random seed for generating bootstrap samples, can be integer or None for no seed (default).
show_median: boolean
If True (default), show the median with black lines.
violin: boolean
If True (default), plot the density of X and Y distributions. Defaut set to True.
Returns
-------
fig : matplotlib Figure instance
Matplotlib Figure. To get the individual axes, use fig.axes.
See also
--------
harrelldavis
Notes
-----
The shift plot is described in [1]_. It computes a shift function [2]_ for two (in)dependent
groups using the robust Harrell-Davis quantile estimator in conjunction with bias-corrected
bootstrap confidence intervals.
References
----------
.. [1] Rousselet, G. A., Pernet, C. R. and Wilcox, R. R. (2017). Beyond
differences in means: robust graphical methods to compare two groups
in neuroscience. Eur J Neurosci, 46: 1738-1748.
doi:10.1111/ejn.13610
.. [2] https://garstats.wordpress.com/2016/07/12/shift-function/
Examples
--------
Default shift plot
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(42)
>>> x = np.random.normal(5.5, 2, 50)
>>> y = np.random.normal(6, 1.5, 50)
>>> fig = pg.plot_shift(x, y)
With different options, and custom axes labels
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> data = pg.read_dataset("pairwise_corr")
>>> fig = pg.plot_shift(data["Neuroticism"], data["Conscientiousness"], paired=True,
... n_boot=2000, percentiles=[25, 50, 75], show_median=False, seed=456,
... violin=False)
>>> fig.axes[0].set_xlabel("Groups")
>>> fig.axes[0].set_ylabel("Values", size=15)
>>> fig.axes[0].set_title("Comparing Neuroticism and Conscientiousness", size=15)
>>> fig.axes[1].set_xlabel("Neuroticism quantiles", size=12)
>>> plt.tight_layout()
| def plot_shift(
x,
y,
paired=False,
n_boot=1000,
percentiles=np.arange(10, 100, 10),
confidence=0.95,
seed=None,
show_median=True,
violin=True,
):
"""Shift plot.
Parameters
----------
x, y : array_like
First and second set of observations.
paired : bool
Specify whether ``x`` and ``y`` are related (i.e. repeated measures) or independent.
.. versionadded:: 0.3.0
n_boot : int
Number of bootstrap iterations. The higher, the better, the slower.
percentiles: array_like
Sequence of percentiles to compute, which must be between 0 and 100 inclusive.
Default set to [10, 20, 30, 40, 50, 60, 70, 80, 90].
confidence : float
Confidence level (0.95 = 95%) for the confidence intervals.
seed : int or None
Random seed for generating bootstrap samples, can be integer or None for no seed (default).
show_median: boolean
If True (default), show the median with black lines.
violin: boolean
If True (default), plot the density of X and Y distributions. Defaut set to True.
Returns
-------
fig : matplotlib Figure instance
Matplotlib Figure. To get the individual axes, use fig.axes.
See also
--------
harrelldavis
Notes
-----
The shift plot is described in [1]_. It computes a shift function [2]_ for two (in)dependent
groups using the robust Harrell-Davis quantile estimator in conjunction with bias-corrected
bootstrap confidence intervals.
References
----------
.. [1] Rousselet, G. A., Pernet, C. R. and Wilcox, R. R. (2017). Beyond
differences in means: robust graphical methods to compare two groups
in neuroscience. Eur J Neurosci, 46: 1738-1748.
doi:10.1111/ejn.13610
.. [2] https://garstats.wordpress.com/2016/07/12/shift-function/
Examples
--------
Default shift plot
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(42)
>>> x = np.random.normal(5.5, 2, 50)
>>> y = np.random.normal(6, 1.5, 50)
>>> fig = pg.plot_shift(x, y)
With different options, and custom axes labels
.. plot::
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> data = pg.read_dataset("pairwise_corr")
>>> fig = pg.plot_shift(data["Neuroticism"], data["Conscientiousness"], paired=True,
... n_boot=2000, percentiles=[25, 50, 75], show_median=False, seed=456,
... violin=False)
>>> fig.axes[0].set_xlabel("Groups")
>>> fig.axes[0].set_ylabel("Values", size=15)
>>> fig.axes[0].set_title("Comparing Neuroticism and Conscientiousness", size=15)
>>> fig.axes[1].set_xlabel("Neuroticism quantiles", size=12)
>>> plt.tight_layout()
"""
from pingouin.regression import _bias_corrected_ci
from pingouin.nonparametric import harrelldavis as hd
# Safety check
x = np.asarray(x)
y = np.asarray(y)
percentiles = np.asarray(percentiles) / 100 # Convert to 0 - 1 range
assert x.ndim == 1, "x must be 1D."
assert y.ndim == 1, "y must be 1D."
nx, ny = x.size, y.size
assert not np.isnan(x).any(), "Missing values are not allowed."
assert not np.isnan(y).any(), "Missing values are not allowed."
assert nx >= 10, "x must have at least 10 samples."
assert ny >= 10, "y must have at least 10 samples."
assert 0 < confidence < 1, "confidence must be between 0 and 1."
if paired:
assert nx == ny, "x and y must have the same size when paired=True."
# Robust percentile
x_per = hd(x, percentiles)
y_per = hd(y, percentiles)
delta = y_per - x_per
# Compute bootstrap distribution of differences
rng = np.random.RandomState(seed)
if paired:
bootsam = rng.choice(np.arange(nx), size=(nx, n_boot), replace=True)
bootstat = hd(y[bootsam], percentiles, axis=0) - hd(x[bootsam], percentiles, axis=0)
else:
x_list = rng.choice(x, size=(nx, n_boot), replace=True)
y_list = rng.choice(y, size=(ny, n_boot), replace=True)
bootstat = hd(y_list, percentiles, axis=0) - hd(x_list, percentiles, axis=0)
# Find upper and lower confidence interval for each quantiles
# Bias-corrected bootstrapped confidence interval
lower, median_per, upper = [], [], []
for i, d in enumerate(delta):
ci = _bias_corrected_ci(bootstat[i, :], d, alpha=(1 - confidence))
median_per.append(_bias_corrected_ci(bootstat[i, :], d, alpha=1)[0])
lower.append(ci[0])
upper.append(ci[1])
lower = np.asarray(lower)
median_per = np.asarray(median_per)
upper = np.asarray(upper)
# Create long-format dataFrame for use with Seaborn
data = pd.DataFrame({"value": np.concatenate([x, y]), "variable": ["X"] * nx + ["Y"] * ny})
#############################
# Plots X and Y distributions
#############################
fig = plt.figure(figsize=(8, 5))
ax1 = plt.subplot2grid((3, 3), (0, 0), rowspan=2, colspan=3)
# Boxplot X & Y
def adjacent_values(vals, q1, q3):
upper_adjacent_value = q3 + (q3 - q1) * 1.5
upper_adjacent_value = np.clip(upper_adjacent_value, q3, vals[-1])
lower_adjacent_value = q1 - (q3 - q1) * 1.5
lower_adjacent_value = np.clip(lower_adjacent_value, vals[0], q1)
return lower_adjacent_value, upper_adjacent_value
for dis, pos in zip([x, y], [1.2, -0.2]):
qrt1, medians, qrt3 = np.percentile(dis, [25, 50, 75])
whiskers = adjacent_values(np.sort(dis), qrt1, qrt3)
ax1.plot(medians, pos, marker="o", color="white", zorder=10)
ax1.hlines(pos, qrt1, qrt3, color="k", linestyle="-", lw=7, zorder=9)
ax1.hlines(pos, whiskers[0], whiskers[1], color="k", linestyle="-", lw=2, zorder=9)
ax1 = sns.stripplot(
data=data,
x="value",
y="variable",
orient="h",
order=["Y", "X"],
palette=["#88bedc", "#cfcfcf"],
)
if violin:
vl = plt.violinplot([y, x], showextrema=False, vert=False, widths=1)
# Upper plot
paths = vl["bodies"][0].get_paths()[0]
paths.vertices[:, 1][paths.vertices[:, 1] >= 1] = 1
paths.vertices[:, 1] = paths.vertices[:, 1] - 1.2
vl["bodies"][0].set_edgecolor("k")
vl["bodies"][0].set_facecolor("#88bedc")
vl["bodies"][0].set_alpha(0.8)
# Lower plot
paths = vl["bodies"][1].get_paths()[0]
paths.vertices[:, 1][paths.vertices[:, 1] <= 2] = 2
paths.vertices[:, 1] = paths.vertices[:, 1] - 0.8
vl["bodies"][1].set_edgecolor("k")
vl["bodies"][1].set_facecolor("#cfcfcf")
vl["bodies"][1].set_alpha(0.8)
# Rescale ylim
ax1.set_ylim(2, -1)
for i in range(len(percentiles)):
# Connection between quantiles
if upper[i] < 0:
col = "#4c72b0"
elif lower[i] > 0:
col = "#c34e52"
else:
col = "darkgray"
plt.plot([y_per[i], x_per[i]], [0.2, 0.8], marker="o", color=col, zorder=10)
# X quantiles
plt.plot([x_per[i], x_per[i]], [0.8, 1.2], "k--", zorder=9)
# Y quantiles
plt.plot([y_per[i], y_per[i]], [-0.2, 0.2], "k--", zorder=9)
if show_median:
x_med, y_med = np.median(x), np.median(y)
plt.plot([x_med, x_med], [0.8, 1.2], "k-")
plt.plot([y_med, y_med], [-0.2, 0.2], "k-")
plt.xlabel("Scores (a.u.)", size=15)
ax1.set_yticklabels(["Y", "X"], size=15)
ax1.set_ylabel("")
#######################
# Plots quantiles shift
#######################
ax2 = plt.subplot2grid((3, 3), (2, 0), rowspan=1, colspan=3)
for i, per in enumerate(x_per):
if upper[i] < 0:
col = "#4c72b0"
elif lower[i] > 0:
col = "#c34e52"
else:
col = "darkgray"
plt.plot([per, per], [upper[i], lower[i]], lw=3, color=col, zorder=10)
plt.plot(per, median_per[i], marker="o", ms=10, color=col, zorder=10)
plt.axh | (x, y, paired=False, n_boot=1000, percentiles=array([10, 20, 30, 40, 50, 60, 70, 80, 90]), confidence=0.95, seed=None, show_median=True, violin=True) | [
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|
32,045 | pingouin.power | power_anova |
Evaluate power, sample size, effect size or significance level of a one-way balanced ANOVA.
Parameters
----------
eta_squared : float
ANOVA effect size (eta-squared, :math:`\eta^2`).
k : int
Number of groups
n : int
Sample size per group. Groups are assumed to be balanced (i.e. same sample size).
power : float
Test power (= 1 - type II error).
alpha : float
Significance level :math:`\alpha` (type I error probability). The default is 0.05.
Notes
-----
Exactly ONE of the parameters ``eta_squared``, ``k``, ``n``, ``power`` and ``alpha``
must be passed as None, and that parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
This function is a Python adaptation of the `pwr.anova.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an
effect there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
For one-way ANOVA, eta-squared is the same as partial eta-squared. It can be evaluated from the
F-value (:math:`F^*`) and the degrees of freedom of the ANOVA (:math:`v_1, v_2`) using the
following formula:
.. math:: \eta^2 = \frac{v_1 F^*}{v_1 F^* + v_2}
GPower uses the :math:`f` effect size instead of the :math:`\eta^2`. The formula to convert
from one to the other are given below:
.. math:: f = \sqrt{\frac{\eta^2}{1 - \eta^2}}
.. math:: \eta^2 = \frac{f^2}{1 + f^2}
Using :math:`\eta^2` and the total sample size :math:`N`, the non-centrality parameter is
defined by:
.. math:: \delta = N * \frac{\eta^2}{1 - \eta^2}
Then the critical value of the non-central F-distribution is computed using the percentile
point function of the F-distribution with:
.. math:: q = 1 - \alpha
.. math:: v_1 = k - 1
.. math:: v_2 = N - k
where :math:`k` is the number of groups.
Finally, the power of the ANOVA is calculated using the survival function of the non-central
F-distribution using the previously computed critical value, non-centrality parameter, and
degrees of freedom.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power
>>> from pingouin import power_anova
>>> print('power: %.4f' % power_anova(eta_squared=0.1, k=3, n=20))
power: 0.6082
2. Compute required number of groups
>>> print('k: %.4f' % power_anova(eta_squared=0.1, n=20, power=0.80))
k: 6.0944
3. Compute required sample size
>>> print('n: %.4f' % power_anova(eta_squared=0.1, k=3, power=0.80))
n: 29.9256
4. Compute achieved effect size
>>> print('eta-squared: %.4f' % power_anova(n=20, k=4, power=0.80, alpha=0.05))
eta-squared: 0.1255
5. Compute achieved alpha (significance)
>>> print('alpha: %.4f' % power_anova(eta_squared=0.1, n=20, k=4, power=0.80, alpha=None))
alpha: 0.1085
| def power_anova(eta_squared=None, k=None, n=None, power=None, alpha=0.05):
"""
Evaluate power, sample size, effect size or significance level of a one-way balanced ANOVA.
Parameters
----------
eta_squared : float
ANOVA effect size (eta-squared, :math:`\\eta^2`).
k : int
Number of groups
n : int
Sample size per group. Groups are assumed to be balanced (i.e. same sample size).
power : float
Test power (= 1 - type II error).
alpha : float
Significance level :math:`\\alpha` (type I error probability). The default is 0.05.
Notes
-----
Exactly ONE of the parameters ``eta_squared``, ``k``, ``n``, ``power`` and ``alpha``
must be passed as None, and that parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
This function is a Python adaptation of the `pwr.anova.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an
effect there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
For one-way ANOVA, eta-squared is the same as partial eta-squared. It can be evaluated from the
F-value (:math:`F^*`) and the degrees of freedom of the ANOVA (:math:`v_1, v_2`) using the
following formula:
.. math:: \\eta^2 = \\frac{v_1 F^*}{v_1 F^* + v_2}
GPower uses the :math:`f` effect size instead of the :math:`\\eta^2`. The formula to convert
from one to the other are given below:
.. math:: f = \\sqrt{\\frac{\\eta^2}{1 - \\eta^2}}
.. math:: \\eta^2 = \\frac{f^2}{1 + f^2}
Using :math:`\\eta^2` and the total sample size :math:`N`, the non-centrality parameter is
defined by:
.. math:: \\delta = N * \\frac{\\eta^2}{1 - \\eta^2}
Then the critical value of the non-central F-distribution is computed using the percentile
point function of the F-distribution with:
.. math:: q = 1 - \\alpha
.. math:: v_1 = k - 1
.. math:: v_2 = N - k
where :math:`k` is the number of groups.
Finally, the power of the ANOVA is calculated using the survival function of the non-central
F-distribution using the previously computed critical value, non-centrality parameter, and
degrees of freedom.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power
>>> from pingouin import power_anova
>>> print('power: %.4f' % power_anova(eta_squared=0.1, k=3, n=20))
power: 0.6082
2. Compute required number of groups
>>> print('k: %.4f' % power_anova(eta_squared=0.1, n=20, power=0.80))
k: 6.0944
3. Compute required sample size
>>> print('n: %.4f' % power_anova(eta_squared=0.1, k=3, power=0.80))
n: 29.9256
4. Compute achieved effect size
>>> print('eta-squared: %.4f' % power_anova(n=20, k=4, power=0.80, alpha=0.05))
eta-squared: 0.1255
5. Compute achieved alpha (significance)
>>> print('alpha: %.4f' % power_anova(eta_squared=0.1, n=20, k=4, power=0.80, alpha=None))
alpha: 0.1085
"""
# Check the number of arguments that are None
n_none = sum([v is None for v in [eta_squared, k, n, power, alpha]])
if n_none != 1:
err = "Exactly one of eta, k, n, power, and alpha must be None."
raise ValueError(err)
# Safety checks
if eta_squared is not None:
eta_squared = abs(eta_squared)
f_sq = eta_squared / (1 - eta_squared)
if alpha is not None:
assert 0 < alpha <= 1
if power is not None:
assert 0 < power <= 1
def func(f_sq, k, n, power, alpha):
nc = (n * k) * f_sq
dof1 = k - 1
dof2 = (n * k) - k
fcrit = stats.f.ppf(1 - alpha, dof1, dof2)
return stats.ncf.sf(fcrit, dof1, dof2, nc)
# Evaluate missing variable
if power is None:
# Compute achieved power
return func(f_sq, k, n, power, alpha)
elif k is None:
# Compute required number of groups
def _eval_k(k, f_sq, n, power, alpha):
return func(f_sq, k, n, power, alpha) - power
try:
return brenth(_eval_k, 2, 100, args=(f_sq, n, power, alpha))
except ValueError: # pragma: no cover
return np.nan
elif n is None:
# Compute required sample size
def _eval_n(n, f_sq, k, power, alpha):
return func(f_sq, k, n, power, alpha) - power
try:
return brenth(_eval_n, 2, 1e07, args=(f_sq, k, power, alpha))
except ValueError: # pragma: no cover
return np.nan
elif eta_squared is None:
# Compute achieved eta-squared
def _eval_eta(f_sq, k, n, power, alpha):
return func(f_sq, k, n, power, alpha) - power
try:
f_sq = brenth(_eval_eta, 1e-10, 1 - 1e-10, args=(k, n, power, alpha))
return f_sq / (f_sq + 1) # Return eta-square
except ValueError: # pragma: no cover
return np.nan
else:
# Compute achieved alpha
def _eval_alpha(alpha, f_sq, k, n, power):
return func(f_sq, k, n, power, alpha) - power
try:
return brenth(_eval_alpha, 1e-10, 1 - 1e-10, args=(f_sq, k, n, power))
except ValueError: # pragma: no cover
return np.nan
| (eta_squared=None, k=None, n=None, power=None, alpha=0.05) | [
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|
32,046 | pingouin.power | power_chi2 |
Evaluate power, sample size, effect size or significance level of chi-squared tests.
Parameters
----------
dof : float
Degree of freedom (depends on the chosen test).
w : float
Cohen's w effect size [1]_.
n : int
Total number of observations.
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability). The default is 0.05.
Notes
-----
Exactly ONE of the parameters ``w``, ``n``, ``power`` and ``alpha`` must be passed as None,
and that parameter is determined from the others. The degrees of freedom ``dof`` must always
be specified.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
This function is a Python adaptation of the `pwr.chisq.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
The non-centrality parameter is defined by:
.. math:: \delta = N * w^2
Then the critical value is computed using the percentile point function of the :math:`\chi^2`
distribution with the alpha level and degrees of freedom.
Finally, the power of the chi-squared test is calculated using the survival function of the
non-central :math:`\chi^2` distribution using the previously computed critical value,
non-centrality parameter, and the degrees of freedom of the test.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
References
----------
.. [1] Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.).
Examples
--------
1. Compute achieved power
>>> from pingouin import power_chi2
>>> print('power: %.4f' % power_chi2(dof=1, w=0.3, n=20))
power: 0.2687
2. Compute required sample size
>>> print('n: %.4f' % power_chi2(dof=3, w=0.3, power=0.80))
n: 121.1396
3. Compute achieved effect size
>>> print('w: %.4f' % power_chi2(dof=2, n=20, power=0.80, alpha=0.05))
w: 0.6941
4. Compute achieved alpha (significance)
>>> print('alpha: %.4f' % power_chi2(dof=1, w=0.5, n=20, power=0.80, alpha=None))
alpha: 0.1630
| def power_chi2(dof, w=None, n=None, power=None, alpha=0.05):
"""
Evaluate power, sample size, effect size or significance level of chi-squared tests.
Parameters
----------
dof : float
Degree of freedom (depends on the chosen test).
w : float
Cohen's w effect size [1]_.
n : int
Total number of observations.
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability). The default is 0.05.
Notes
-----
Exactly ONE of the parameters ``w``, ``n``, ``power`` and ``alpha`` must be passed as None,
and that parameter is determined from the others. The degrees of freedom ``dof`` must always
be specified.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
This function is a Python adaptation of the `pwr.chisq.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
The non-centrality parameter is defined by:
.. math:: \\delta = N * w^2
Then the critical value is computed using the percentile point function of the :math:`\\chi^2`
distribution with the alpha level and degrees of freedom.
Finally, the power of the chi-squared test is calculated using the survival function of the
non-central :math:`\\chi^2` distribution using the previously computed critical value,
non-centrality parameter, and the degrees of freedom of the test.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
References
----------
.. [1] Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.).
Examples
--------
1. Compute achieved power
>>> from pingouin import power_chi2
>>> print('power: %.4f' % power_chi2(dof=1, w=0.3, n=20))
power: 0.2687
2. Compute required sample size
>>> print('n: %.4f' % power_chi2(dof=3, w=0.3, power=0.80))
n: 121.1396
3. Compute achieved effect size
>>> print('w: %.4f' % power_chi2(dof=2, n=20, power=0.80, alpha=0.05))
w: 0.6941
4. Compute achieved alpha (significance)
>>> print('alpha: %.4f' % power_chi2(dof=1, w=0.5, n=20, power=0.80, alpha=None))
alpha: 0.1630
"""
assert isinstance(dof, (int, float))
# Check the number of arguments that are None
n_none = sum([v is None for v in [w, n, power, alpha]])
if n_none != 1:
err = "Exactly one of w, n, power, and alpha must be None."
raise ValueError(err)
# Safety checks
if w is not None:
w = abs(w)
if alpha is not None:
assert 0 < alpha <= 1
if power is not None:
assert 0 < power <= 1
def func(w, n, power, alpha):
k = stats.chi2.ppf(1 - alpha, dof)
nc = n * w**2
return stats.ncx2.sf(k, dof, nc)
# Evaluate missing variable
if power is None:
# Compute achieved power
return func(w, n, power, alpha)
elif n is None:
# Compute required sample size
def _eval_n(n, w, power, alpha):
return func(w, n, power, alpha) - power
try:
return brenth(_eval_n, 1, 1e07, args=(w, power, alpha))
except ValueError: # pragma: no cover
return np.nan
elif w is None:
# Compute achieved effect size
def _eval_w(w, n, power, alpha):
return func(w, n, power, alpha) - power
try:
return brenth(_eval_w, 1e-10, 100, args=(n, power, alpha))
except ValueError: # pragma: no cover
return np.nan
else:
# Compute achieved alpha
def _eval_alpha(alpha, w, n, power):
return func(w, n, power, alpha) - power
try:
return brenth(_eval_alpha, 1e-10, 1 - 1e-10, args=(w, n, power))
except ValueError: # pragma: no cover
return np.nan
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|
32,047 | pingouin.power | power_corr |
Evaluate power, sample size, correlation coefficient or significance level of a correlation
test.
Parameters
----------
r : float
Correlation coefficient.
n : int
Number of observations (sample size).
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability). The default is 0.05.
alternative : string
Defines the alternative hypothesis, or tail of the correlation. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return a one-sided
p-value. "greater" tests against the alternative hypothesis that the correlation is
positive (greater than zero), "less" tests against the hypothesis that the correlation is
negative.
Notes
-----
Exactly ONE of the parameters ``r``, ``n``, ``power`` and ``alpha`` must be passed as None,
and that parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
This function is a Python adaptation of the `pwr.r.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power given ``r``, ``n`` and ``alpha``
>>> from pingouin import power_corr
>>> print('power: %.4f' % power_corr(r=0.5, n=20))
power: 0.6379
2. Same but one-sided test
>>> print('power: %.4f' % power_corr(r=0.5, n=20, alternative="greater"))
power: 0.7510
>>> print('power: %.4f' % power_corr(r=0.5, n=20, alternative="less"))
power: 0.0000
3. Compute required sample size given ``r``, ``power`` and ``alpha``
>>> print('n: %.4f' % power_corr(r=0.5, power=0.80))
n: 28.2484
4. Compute achieved ``r`` given ``n``, ``power`` and ``alpha`` level
>>> print('r: %.4f' % power_corr(n=20, power=0.80, alpha=0.05))
r: 0.5822
5. Compute achieved alpha level given ``r``, ``n`` and ``power``
>>> print('alpha: %.4f' % power_corr(r=0.5, n=20, power=0.80, alpha=None))
alpha: 0.1377
| def power_corr(r=None, n=None, power=None, alpha=0.05, alternative="two-sided"):
"""
Evaluate power, sample size, correlation coefficient or significance level of a correlation
test.
Parameters
----------
r : float
Correlation coefficient.
n : int
Number of observations (sample size).
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability). The default is 0.05.
alternative : string
Defines the alternative hypothesis, or tail of the correlation. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return a one-sided
p-value. "greater" tests against the alternative hypothesis that the correlation is
positive (greater than zero), "less" tests against the hypothesis that the correlation is
negative.
Notes
-----
Exactly ONE of the parameters ``r``, ``n``, ``power`` and ``alpha`` must be passed as None,
and that parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
This function is a Python adaptation of the `pwr.r.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power given ``r``, ``n`` and ``alpha``
>>> from pingouin import power_corr
>>> print('power: %.4f' % power_corr(r=0.5, n=20))
power: 0.6379
2. Same but one-sided test
>>> print('power: %.4f' % power_corr(r=0.5, n=20, alternative="greater"))
power: 0.7510
>>> print('power: %.4f' % power_corr(r=0.5, n=20, alternative="less"))
power: 0.0000
3. Compute required sample size given ``r``, ``power`` and ``alpha``
>>> print('n: %.4f' % power_corr(r=0.5, power=0.80))
n: 28.2484
4. Compute achieved ``r`` given ``n``, ``power`` and ``alpha`` level
>>> print('r: %.4f' % power_corr(n=20, power=0.80, alpha=0.05))
r: 0.5822
5. Compute achieved alpha level given ``r``, ``n`` and ``power``
>>> print('alpha: %.4f' % power_corr(r=0.5, n=20, power=0.80, alpha=None))
alpha: 0.1377
"""
# Check the number of arguments that are None
n_none = sum([v is None for v in [r, n, power, alpha]])
if n_none != 1:
raise ValueError("Exactly one of n, r, power, and alpha must be None")
# Safety checks
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
if r is not None:
assert -1 <= r <= 1
if alternative == "two-sided":
r = abs(r)
if alpha is not None:
assert 0 < alpha <= 1
if power is not None:
assert 0 < power <= 1
if n is not None:
if n <= 4:
warnings.warn("Sample size is too small to estimate power (n <= 4). Returning NaN.")
return np.nan
# Define main function
if alternative == "two-sided":
def func(r, n, power, alpha):
dof = n - 2
ttt = stats.t.ppf(1 - alpha / 2, dof)
rc = np.sqrt(ttt**2 / (ttt**2 + dof))
zr = np.arctanh(r) + r / (2 * (n - 1))
zrc = np.arctanh(rc)
power = stats.norm.cdf((zr - zrc) * np.sqrt(n - 3)) + stats.norm.cdf(
(-zr - zrc) * np.sqrt(n - 3)
)
return power
elif alternative == "greater":
def func(r, n, power, alpha):
dof = n - 2
ttt = stats.t.ppf(1 - alpha, dof)
rc = np.sqrt(ttt**2 / (ttt**2 + dof))
zr = np.arctanh(r) + r / (2 * (n - 1))
zrc = np.arctanh(rc)
power = stats.norm.cdf((zr - zrc) * np.sqrt(n - 3))
return power
else: # alternative == "less":
def func(r, n, power, alpha):
r = -r
dof = n - 2
ttt = stats.t.ppf(1 - alpha, dof)
rc = np.sqrt(ttt**2 / (ttt**2 + dof))
zr = np.arctanh(r) + r / (2 * (n - 1))
zrc = np.arctanh(rc)
power = stats.norm.cdf((zr - zrc) * np.sqrt(n - 3))
return power
# Evaluate missing variable
if power is None and n is not None and r is not None:
# Compute achieved power given r, n and alpha
return func(r, n, power=None, alpha=alpha)
elif n is None and power is not None and r is not None:
# Compute required sample size given r, power and alpha
def _eval_n(n, r, power, alpha):
return func(r, n, power, alpha) - power
try:
return brenth(_eval_n, 4 + 1e-10, 1e09, args=(r, power, alpha))
except ValueError: # pragma: no cover
return np.nan
elif r is None and power is not None and n is not None:
# Compute achieved r given sample size, power and alpha level
def _eval_r(r, n, power, alpha):
return func(r, n, power, alpha) - power
try:
if alternative == "two-sided":
return brenth(_eval_r, 1e-10, 1 - 1e-10, args=(n, power, alpha))
else:
return brenth(_eval_r, -1 + 1e-10, 1 - 1e-10, args=(n, power, alpha))
except ValueError: # pragma: no cover
return np.nan
else:
# Compute achieved alpha (significance) level given r, n and power
def _eval_alpha(alpha, r, n, power):
return func(r, n, power, alpha) - power
try:
return brenth(_eval_alpha, 1e-10, 1 - 1e-10, args=(r, n, power))
except ValueError: # pragma: no cover
return np.nan
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|
32,048 | pingouin.power | power_rm_anova |
Evaluate power, sample size, effect size or significance level of a balanced one-way
repeated measures ANOVA.
Parameters
----------
eta_squared : float
ANOVA effect size (eta-squared, :math:`\eta^2`).
m : int
Number of repeated measurements.
n : int
Sample size per measurement. All measurements must have the same sample size.
power : float
Test power (= 1 - type II error).
alpha : float
Significance level :math:`\alpha` (type I error probability). The default is 0.05.
corr : float
Average correlation coefficient among repeated measurements. The default is :math:`r=0.5`.
epsilon : float
Epsilon adjustement factor for sphericity. This can be calculated using the
:py:func:`pingouin.epsilon` function.
Notes
-----
Exactly ONE of the parameters ``eta_squared``, ``m``, ``n``, ``power`` and ``alpha`` must be
passed as None, and that parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
GPower uses the :math:`f` effect size instead of the :math:`\eta^2`. The formula to convert
from one to the other are given below:
.. math:: f = \sqrt{\frac{\eta^2}{1 - \eta^2}}
.. math:: \eta^2 = \frac{f^2}{1 + f^2}
Using :math:`\eta^2`, the sample size :math:`N`, the number of repeated measurements
:math:`m`, the epsilon correction factor :math:`\epsilon` (see :py:func:`pingouin.epsilon`),
and the average correlation between the repeated measures :math:`c`, one can then calculate the
non-centrality parameter as follow:
.. math:: \delta = \frac{f^2 * N * m * \epsilon}{1 - c}
Then the critical value of the non-central F-distribution is computed using the percentile
point function of the F-distribution with:
.. math:: q = 1 - \alpha
.. math:: v_1 = (m - 1) * \epsilon
.. math:: v_2 = (N - 1) * v_1
Finally, the power of the ANOVA is calculated using the survival function of the non-central
F-distribution using the previously computed critical value, non-centrality parameter,
and degrees of freedom.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables
(i.e. sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power
>>> from pingouin import power_rm_anova
>>> print('power: %.4f' % power_rm_anova(eta_squared=0.1, m=3, n=20))
power: 0.8913
2. Compute required number of groups
>>> print('m: %.4f' % power_rm_anova(eta_squared=0.1, n=20, power=0.90))
m: 3.1347
3. Compute required sample size
>>> print('n: %.4f' % power_rm_anova(eta_squared=0.1, m=3, power=0.80))
n: 15.9979
4. Compute achieved effect size
>>> print('eta-squared: %.4f' % power_rm_anova(n=20, m=4, power=0.80, alpha=0.05))
eta-squared: 0.0680
5. Compute achieved alpha (significance)
>>> print('alpha: %.4f' % power_rm_anova(eta_squared=0.1, n=20, m=4, power=0.80, alpha=None))
alpha: 0.0081
Let's take a more concrete example. First, we'll load a repeated measures
dataset in wide-format. Each row is an observation (e.g. a subject), and
each column a successive repeated measurements (e.g t=0, t=1, ...).
>>> import pingouin as pg
>>> data = pg.read_dataset('rm_anova_wide')
>>> data.head()
Before 1 week 2 week 3 week
0 4.3 5.3 4.8 6.3
1 3.9 2.3 5.6 4.3
2 4.5 2.6 4.1 NaN
3 5.1 4.2 6.0 6.3
4 3.8 3.6 4.8 6.8
Note that this dataset has some missing values. We'll simply delete any row with one or more
missing values, and then compute a repeated measures ANOVA:
>>> data = data.dropna()
>>> pg.rm_anova(data, effsize="n2").round(3)
Source ddof1 ddof2 F p-unc n2 eps
0 Within 3 24 5.201 0.007 0.346 0.694
The repeated measures ANOVA is significant at the 0.05 level. Now, we can
easily compute the power of the ANOVA with the information in the ANOVA table:
>>> # n is the sample size and m is the number of repeated measures
>>> n, m = data.shape
>>> round(pg.power_rm_anova(eta_squared=0.346, m=m, n=n, epsilon=0.694), 3)
0.99
Our ANOVA has a very high statistical power. However, to be even more accurate in our power
calculation, we should also fill in the average correlation among repeated measurements.
Since our dataframe is in wide-format (with each column being a successive measurement), this
can be done by taking the mean of the superdiagonal of the correlation matrix, which is similar
to manually calculating the correlation between each successive pairwise measurements and then
taking the mean. Since correlation coefficients are not normally distributed, we use the
*r-to-z* transform prior to averaging (:py:func:`numpy.arctanh`), and then the *z-to-r*
transform (:py:func:`numpy.tanh`) to convert back to a correlation coefficient. This gives a
more precise estimate of the mean.
>>> import numpy as np
>>> corr = np.diag(data.corr(), k=1)
>>> avgcorr = np.tanh(np.arctanh(corr).mean())
>>> round(avgcorr, 4)
-0.1996
In this example, we're using a fake dataset and the average correlation is negative. However,
it will most likely be positive with real data. Let's now compute the final power of the
repeated measures ANOVA:
>>> round(pg.power_rm_anova(eta_squared=0.346, m=m, n=n, epsilon=0.694, corr=avgcorr), 3)
0.771
| def power_rm_anova(eta_squared=None, m=None, n=None, power=None, alpha=0.05, corr=0.5, epsilon=1):
"""
Evaluate power, sample size, effect size or significance level of a balanced one-way
repeated measures ANOVA.
Parameters
----------
eta_squared : float
ANOVA effect size (eta-squared, :math:`\\eta^2`).
m : int
Number of repeated measurements.
n : int
Sample size per measurement. All measurements must have the same sample size.
power : float
Test power (= 1 - type II error).
alpha : float
Significance level :math:`\\alpha` (type I error probability). The default is 0.05.
corr : float
Average correlation coefficient among repeated measurements. The default is :math:`r=0.5`.
epsilon : float
Epsilon adjustement factor for sphericity. This can be calculated using the
:py:func:`pingouin.epsilon` function.
Notes
-----
Exactly ONE of the parameters ``eta_squared``, ``m``, ``n``, ``power`` and ``alpha`` must be
passed as None, and that parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
GPower uses the :math:`f` effect size instead of the :math:`\\eta^2`. The formula to convert
from one to the other are given below:
.. math:: f = \\sqrt{\\frac{\\eta^2}{1 - \\eta^2}}
.. math:: \\eta^2 = \\frac{f^2}{1 + f^2}
Using :math:`\\eta^2`, the sample size :math:`N`, the number of repeated measurements
:math:`m`, the epsilon correction factor :math:`\\epsilon` (see :py:func:`pingouin.epsilon`),
and the average correlation between the repeated measures :math:`c`, one can then calculate the
non-centrality parameter as follow:
.. math:: \\delta = \\frac{f^2 * N * m * \\epsilon}{1 - c}
Then the critical value of the non-central F-distribution is computed using the percentile
point function of the F-distribution with:
.. math:: q = 1 - \\alpha
.. math:: v_1 = (m - 1) * \\epsilon
.. math:: v_2 = (N - 1) * v_1
Finally, the power of the ANOVA is calculated using the survival function of the non-central
F-distribution using the previously computed critical value, non-centrality parameter,
and degrees of freedom.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables
(i.e. sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power
>>> from pingouin import power_rm_anova
>>> print('power: %.4f' % power_rm_anova(eta_squared=0.1, m=3, n=20))
power: 0.8913
2. Compute required number of groups
>>> print('m: %.4f' % power_rm_anova(eta_squared=0.1, n=20, power=0.90))
m: 3.1347
3. Compute required sample size
>>> print('n: %.4f' % power_rm_anova(eta_squared=0.1, m=3, power=0.80))
n: 15.9979
4. Compute achieved effect size
>>> print('eta-squared: %.4f' % power_rm_anova(n=20, m=4, power=0.80, alpha=0.05))
eta-squared: 0.0680
5. Compute achieved alpha (significance)
>>> print('alpha: %.4f' % power_rm_anova(eta_squared=0.1, n=20, m=4, power=0.80, alpha=None))
alpha: 0.0081
Let's take a more concrete example. First, we'll load a repeated measures
dataset in wide-format. Each row is an observation (e.g. a subject), and
each column a successive repeated measurements (e.g t=0, t=1, ...).
>>> import pingouin as pg
>>> data = pg.read_dataset('rm_anova_wide')
>>> data.head()
Before 1 week 2 week 3 week
0 4.3 5.3 4.8 6.3
1 3.9 2.3 5.6 4.3
2 4.5 2.6 4.1 NaN
3 5.1 4.2 6.0 6.3
4 3.8 3.6 4.8 6.8
Note that this dataset has some missing values. We'll simply delete any row with one or more
missing values, and then compute a repeated measures ANOVA:
>>> data = data.dropna()
>>> pg.rm_anova(data, effsize="n2").round(3)
Source ddof1 ddof2 F p-unc n2 eps
0 Within 3 24 5.201 0.007 0.346 0.694
The repeated measures ANOVA is significant at the 0.05 level. Now, we can
easily compute the power of the ANOVA with the information in the ANOVA table:
>>> # n is the sample size and m is the number of repeated measures
>>> n, m = data.shape
>>> round(pg.power_rm_anova(eta_squared=0.346, m=m, n=n, epsilon=0.694), 3)
0.99
Our ANOVA has a very high statistical power. However, to be even more accurate in our power
calculation, we should also fill in the average correlation among repeated measurements.
Since our dataframe is in wide-format (with each column being a successive measurement), this
can be done by taking the mean of the superdiagonal of the correlation matrix, which is similar
to manually calculating the correlation between each successive pairwise measurements and then
taking the mean. Since correlation coefficients are not normally distributed, we use the
*r-to-z* transform prior to averaging (:py:func:`numpy.arctanh`), and then the *z-to-r*
transform (:py:func:`numpy.tanh`) to convert back to a correlation coefficient. This gives a
more precise estimate of the mean.
>>> import numpy as np
>>> corr = np.diag(data.corr(), k=1)
>>> avgcorr = np.tanh(np.arctanh(corr).mean())
>>> round(avgcorr, 4)
-0.1996
In this example, we're using a fake dataset and the average correlation is negative. However,
it will most likely be positive with real data. Let's now compute the final power of the
repeated measures ANOVA:
>>> round(pg.power_rm_anova(eta_squared=0.346, m=m, n=n, epsilon=0.694, corr=avgcorr), 3)
0.771
"""
# Check the number of arguments that are None
n_none = sum([v is None for v in [eta_squared, m, n, power, alpha]])
if n_none != 1:
msg = "Exactly one of eta, m, n, power, and alpha must be None."
raise ValueError(msg)
# Safety checks
assert 0 < epsilon <= 1, "epsilon must be between 0 and 1."
assert -1 < corr < 1, "corr must be between -1 and 1."
if eta_squared is not None:
eta_squared = abs(eta_squared)
f_sq = eta_squared / (1 - eta_squared)
if alpha is not None:
assert 0 < alpha <= 1, "alpha must be between 0 and 1."
if power is not None:
assert 0 < power <= 1, "power must be between 0 and 1."
if n is not None:
assert n > 1, "The sample size n must be > 1."
if m is not None:
assert m > 1, "The number of repeated measures m must be > 1."
def func(f_sq, m, n, power, alpha, corr):
dof1 = (m - 1) * epsilon
dof2 = (n - 1) * dof1
nc = (f_sq * n * m * epsilon) / (1 - corr)
fcrit = stats.f.ppf(1 - alpha, dof1, dof2)
return stats.ncf.sf(fcrit, dof1, dof2, nc)
# Evaluate missing variable
if power is None:
# Compute achieved power
return func(f_sq, m, n, power, alpha, corr)
elif m is None:
# Compute required number of repeated measures
def _eval_m(m, f_sq, n, power, alpha, corr):
return func(f_sq, m, n, power, alpha, corr) - power
try:
return brenth(_eval_m, 2, 100, args=(f_sq, n, power, alpha, corr))
except ValueError: # pragma: no cover
return np.nan
elif n is None:
# Compute required sample size
def _eval_n(n, f_sq, m, power, alpha, corr):
return func(f_sq, m, n, power, alpha, corr) - power
try:
return brenth(_eval_n, 5, 1e6, args=(f_sq, m, power, alp | (eta_squared=None, m=None, n=None, power=None, alpha=0.05, corr=0.5, epsilon=1) | [
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|
32,049 | pingouin.power | power_ttest |
Evaluate power, sample size, effect size or significance level of a one-sample T-test,
a paired T-test or an independent two-samples T-test with equal sample sizes.
Parameters
----------
d : float
Cohen d effect size
n : int
Sample size
In case of a two-sample T-test, sample sizes are assumed to be equal.
Otherwise, see the :py:func:`power_ttest2n` function.
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability).
The default is 0.05.
contrast : str
Can be `"one-sample"`, `"two-samples"` or `"paired"`.
Note that `"one-sample"` and `"paired"` have the same behavior.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less".
Notes
-----
Exactly ONE of the parameters ``d``, ``n``, ``power`` and ``alpha`` must be passed as None, and
that parameter is determined from the others.
For a paired T-test, the sample size ``n`` corresponds to the number of pairs. For an
independent two-sample T-test with equal sample sizes, ``n`` corresponds to the sample size of
each group (i.e. number of observations in one group). If the sample sizes are unequal, please
use the :py:func:`power_ttest2n` function instead.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
This function is a Python adaptation of the `pwr.t.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
The first step is to use the Cohen's d to calculate the non-centrality parameter
:math:`\delta` and degrees of freedom :math:`v`. In case of paired groups, this is:
.. math:: \delta = d * \sqrt n
.. math:: v = n - 1
and in case of independent groups with equal sample sizes:
.. math:: \delta = d * \sqrt{\frac{n}{2}}
.. math:: v = (n - 1) * 2
where :math:`d` is the Cohen d and :math:`n` the sample size.
The critical value is then found using the percent point function of the T distribution with
:math:`q = 1 - alpha` and :math:`v` degrees of freedom.
Finally, the power of the test is given by the survival function of the non-central
distribution using the previously calculated critical value, degrees of freedom and
non-centrality parameter.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute power of a one-sample T-test given ``d``, ``n`` and ``alpha``
>>> from pingouin import power_ttest
>>> print('power: %.4f' % power_ttest(d=0.5, n=20, contrast='one-sample'))
power: 0.5645
2. Compute required sample size given ``d``, ``power`` and ``alpha``
>>> print('n: %.4f' % power_ttest(d=0.5, power=0.80, alternative='greater'))
n: 50.1508
3. Compute achieved ``d`` given ``n``, ``power`` and ``alpha`` level
>>> print('d: %.4f' % power_ttest(n=20, power=0.80, alpha=0.05, contrast='paired'))
d: 0.6604
4. Compute achieved alpha level given ``d``, ``n`` and ``power``
>>> print('alpha: %.4f' % power_ttest(d=0.5, n=20, power=0.80, alpha=None))
alpha: 0.4430
5. One-sided tests
>>> from pingouin import power_ttest
>>> print('power: %.4f' % power_ttest(d=0.5, n=20, alternative='greater'))
power: 0.4634
>>> print('power: %.4f' % power_ttest(d=0.5, n=20, alternative='less'))
power: 0.0007
| def power_ttest(
d=None, n=None, power=None, alpha=0.05, contrast="two-samples", alternative="two-sided"
):
"""
Evaluate power, sample size, effect size or significance level of a one-sample T-test,
a paired T-test or an independent two-samples T-test with equal sample sizes.
Parameters
----------
d : float
Cohen d effect size
n : int
Sample size
In case of a two-sample T-test, sample sizes are assumed to be equal.
Otherwise, see the :py:func:`power_ttest2n` function.
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability).
The default is 0.05.
contrast : str
Can be `"one-sample"`, `"two-samples"` or `"paired"`.
Note that `"one-sample"` and `"paired"` have the same behavior.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less".
Notes
-----
Exactly ONE of the parameters ``d``, ``n``, ``power`` and ``alpha`` must be passed as None, and
that parameter is determined from the others.
For a paired T-test, the sample size ``n`` corresponds to the number of pairs. For an
independent two-sample T-test with equal sample sizes, ``n`` corresponds to the sample size of
each group (i.e. number of observations in one group). If the sample sizes are unequal, please
use the :py:func:`power_ttest2n` function instead.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to
compute it.
This function is a Python adaptation of the `pwr.t.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
The first step is to use the Cohen's d to calculate the non-centrality parameter
:math:`\\delta` and degrees of freedom :math:`v`. In case of paired groups, this is:
.. math:: \\delta = d * \\sqrt n
.. math:: v = n - 1
and in case of independent groups with equal sample sizes:
.. math:: \\delta = d * \\sqrt{\\frac{n}{2}}
.. math:: v = (n - 1) * 2
where :math:`d` is the Cohen d and :math:`n` the sample size.
The critical value is then found using the percent point function of the T distribution with
:math:`q = 1 - alpha` and :math:`v` degrees of freedom.
Finally, the power of the test is given by the survival function of the non-central
distribution using the previously calculated critical value, degrees of freedom and
non-centrality parameter.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute power of a one-sample T-test given ``d``, ``n`` and ``alpha``
>>> from pingouin import power_ttest
>>> print('power: %.4f' % power_ttest(d=0.5, n=20, contrast='one-sample'))
power: 0.5645
2. Compute required sample size given ``d``, ``power`` and ``alpha``
>>> print('n: %.4f' % power_ttest(d=0.5, power=0.80, alternative='greater'))
n: 50.1508
3. Compute achieved ``d`` given ``n``, ``power`` and ``alpha`` level
>>> print('d: %.4f' % power_ttest(n=20, power=0.80, alpha=0.05, contrast='paired'))
d: 0.6604
4. Compute achieved alpha level given ``d``, ``n`` and ``power``
>>> print('alpha: %.4f' % power_ttest(d=0.5, n=20, power=0.80, alpha=None))
alpha: 0.4430
5. One-sided tests
>>> from pingouin import power_ttest
>>> print('power: %.4f' % power_ttest(d=0.5, n=20, alternative='greater'))
power: 0.4634
>>> print('power: %.4f' % power_ttest(d=0.5, n=20, alternative='less'))
power: 0.0007
"""
# Check the number of arguments that are None
n_none = sum([v is None for v in [d, n, power, alpha]])
if n_none != 1:
raise ValueError("Exactly one of n, d, power, and alpha must be None.")
# Safety checks
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
assert contrast.lower() in ["one-sample", "paired", "two-samples"]
tsample = 2 if contrast.lower() == "two-samples" else 1
tside = 2 if alternative == "two-sided" else 1
if d is not None and tside == 2:
d = abs(d)
if alpha is not None:
assert 0 < alpha <= 1
if power is not None:
assert 0 < power <= 1
if alternative == "less":
def func(d, n, power, alpha):
dof = (n - 1) * tsample
nc = d * np.sqrt(n / tsample)
tcrit = stats.t.ppf(alpha / tside, dof)
return stats.nct.cdf(tcrit, dof, nc)
elif alternative == "two-sided":
def func(d, n, power, alpha):
dof = (n - 1) * tsample
nc = d * np.sqrt(n / tsample)
tcrit = stats.t.ppf(1 - alpha / tside, dof)
return stats.nct.sf(tcrit, dof, nc) + stats.nct.cdf(-tcrit, dof, nc)
else: # Alternative = 'greater'
def func(d, n, power, alpha):
dof = (n - 1) * tsample
nc = d * np.sqrt(n / tsample)
tcrit = stats.t.ppf(1 - alpha / tside, dof)
return stats.nct.sf(tcrit, dof, nc)
# Evaluate missing variable
if power is None:
# Compute achieved power given d, n and alpha
return func(d, n, power=None, alpha=alpha)
elif n is None:
# Compute required sample size given d, power and alpha
def _eval_n(n, d, power, alpha):
return func(d, n, power, alpha) - power
try:
return brenth(_eval_n, 2 + 1e-10, 1e07, args=(d, power, alpha))
except ValueError: # pragma: no cover
return np.nan
elif d is None:
# Compute achieved d given sample size, power and alpha level
if alternative == "two-sided":
b0, b1 = 1e-07, 10
elif alternative == "less":
b0, b1 = -10, 5
else:
b0, b1 = -5, 10
def _eval_d(d, n, power, alpha):
return func(d, n, power, alpha) - power
try:
return brenth(_eval_d, b0, b1, args=(n, power, alpha))
except ValueError: # pragma: no cover
return np.nan
else:
# Compute achieved alpha (significance) level given d, n and power
def _eval_alpha(alpha, d, n, power):
return func(d, n, power, alpha) - power
try:
return brenth(_eval_alpha, 1e-10, 1 - 1e-10, args=(d, n, power))
except ValueError: # pragma: no cover
return np.nan
| (d=None, n=None, power=None, alpha=0.05, contrast='two-samples', alternative='two-sided') | [
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|
32,050 | pingouin.power | power_ttest2n |
Evaluate power, effect size or significance level of an independent two-samples T-test
with unequal sample sizes.
Parameters
----------
nx, ny : int
Sample sizes. Must be specified. If the sample sizes are equal, you should use the
:py:func:`power_ttest` function instead.
d : float
Cohen d effect size
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability). The default is 0.05.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of "two-sided"
(default), "greater" or "less".
Notes
-----
Exactly ONE of the parameters ``d``, ``power`` and ``alpha`` must be passed as None, and that
parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to compute
it.
This function is a Python adaptation of the `pwr.t2n.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
The first step is to use the Cohen's d to calculate the non-centrality parameter
:math:`\delta` and degrees of freedom :math:`v`.cIn case of two independent groups with
unequal sample sizes, this is:
.. math:: \delta = d * \sqrt{\frac{n_i * n_j}{n_i + n_j}}
.. math:: v = n_i + n_j - 2
where :math:`d` is the Cohen d, :math:`n` the sample size,
:math:`n_i` the sample size of the first group and
:math:`n_j` the sample size of the second group,
The critical value is then found using the percent point function of the T distribution with
:math:`q = 1 - alpha` and :math:`v` degrees of freedom.
Finally, the power of the test is given by the survival function of the non-central
distribution using the previously calculated critical value, degrees of freedom and
non-centrality parameter.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power of a T-test given ``d``, ``n`` and ``alpha``
>>> from pingouin import power_ttest2n
>>> print('power: %.4f' % power_ttest2n(nx=20, ny=15, d=0.5, alternative='greater'))
power: 0.4164
2. Compute achieved ``d`` given ``n``, ``power`` and ``alpha`` level
>>> print('d: %.4f' % power_ttest2n(nx=20, ny=15, power=0.80, alpha=0.05))
d: 0.9859
3. Compute achieved alpha level given ``d``, ``n`` and ``power``
>>> print('alpha: %.4f' % power_ttest2n(nx=20, ny=15, d=0.5, power=0.80, alpha=None))
alpha: 0.5000
| def power_ttest2n(nx, ny, d=None, power=None, alpha=0.05, alternative="two-sided"):
"""
Evaluate power, effect size or significance level of an independent two-samples T-test
with unequal sample sizes.
Parameters
----------
nx, ny : int
Sample sizes. Must be specified. If the sample sizes are equal, you should use the
:py:func:`power_ttest` function instead.
d : float
Cohen d effect size
power : float
Test power (= 1 - type II error).
alpha : float
Significance level (type I error probability). The default is 0.05.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of "two-sided"
(default), "greater" or "less".
Notes
-----
Exactly ONE of the parameters ``d``, ``power`` and ``alpha`` must be passed as None, and that
parameter is determined from the others.
``alpha`` has a default value of 0.05 so None must be explicitly passed if you want to compute
it.
This function is a Python adaptation of the `pwr.t2n.test` function implemented in the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Statistical power is the likelihood that a study will detect an effect when there is an effect
there to be detected. A high statistical power means that there is a low probability of
concluding that there is no effect when there is one. Statistical power is mainly affected by
the effect size and the sample size.
The first step is to use the Cohen's d to calculate the non-centrality parameter
:math:`\\delta` and degrees of freedom :math:`v`.cIn case of two independent groups with
unequal sample sizes, this is:
.. math:: \\delta = d * \\sqrt{\\frac{n_i * n_j}{n_i + n_j}}
.. math:: v = n_i + n_j - 2
where :math:`d` is the Cohen d, :math:`n` the sample size,
:math:`n_i` the sample size of the first group and
:math:`n_j` the sample size of the second group,
The critical value is then found using the percent point function of the T distribution with
:math:`q = 1 - alpha` and :math:`v` degrees of freedom.
Finally, the power of the test is given by the survival function of the non-central
distribution using the previously calculated critical value, degrees of freedom and
non-centrality parameter.
:py:func:`scipy.optimize.brenth` is used to solve power equations for other variables (i.e.
sample size, effect size, or significance level). If the solving fails, a nan value is
returned.
Results have been tested against GPower and the
`pwr <https://cran.r-project.org/web/packages/pwr/pwr.pdf>`_ R package.
Examples
--------
1. Compute achieved power of a T-test given ``d``, ``n`` and ``alpha``
>>> from pingouin import power_ttest2n
>>> print('power: %.4f' % power_ttest2n(nx=20, ny=15, d=0.5, alternative='greater'))
power: 0.4164
2. Compute achieved ``d`` given ``n``, ``power`` and ``alpha`` level
>>> print('d: %.4f' % power_ttest2n(nx=20, ny=15, power=0.80, alpha=0.05))
d: 0.9859
3. Compute achieved alpha level given ``d``, ``n`` and ``power``
>>> print('alpha: %.4f' % power_ttest2n(nx=20, ny=15, d=0.5, power=0.80, alpha=None))
alpha: 0.5000
"""
# Check the number of arguments that are None
n_none = sum([v is None for v in [d, power, alpha]])
if n_none != 1:
raise ValueError("Exactly one of d, power, and alpha must be None")
# Safety checks
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
tside = 2 if alternative == "two-sided" else 1
if d is not None and tside == 2:
d = abs(d)
if alpha is not None:
assert 0 < alpha <= 1
if power is not None:
assert 0 < power <= 1
if alternative == "less":
def func(d, nx, ny, power, alpha):
dof = nx + ny - 2
nc = d * (1 / np.sqrt(1 / nx + 1 / ny))
tcrit = stats.t.ppf(alpha / tside, dof)
return stats.nct.cdf(tcrit, dof, nc)
elif alternative == "two-sided":
def func(d, nx, ny, power, alpha):
dof = nx + ny - 2
nc = d * (1 / np.sqrt(1 / nx + 1 / ny))
tcrit = stats.t.ppf(1 - alpha / tside, dof)
return stats.nct.sf(tcrit, dof, nc) + stats.nct.cdf(-tcrit, dof, nc)
else: # Alternative = 'greater'
def func(d, nx, ny, power, alpha):
dof = nx + ny - 2
nc = d * (1 / np.sqrt(1 / nx + 1 / ny))
tcrit = stats.t.ppf(1 - alpha / tside, dof)
return stats.nct.sf(tcrit, dof, nc)
# Evaluate missing variable
if power is None:
# Compute achieved power given d, n and alpha
return func(d, nx, ny, power=None, alpha=alpha)
elif d is None:
# Compute achieved d given sample size, power and alpha level
if alternative == "two-sided":
b0, b1 = 1e-07, 10
elif alternative == "less":
b0, b1 = -10, 5
else:
b0, b1 = -5, 10
def _eval_d(d, nx, ny, power, alpha):
return func(d, nx, ny, power, alpha) - power
try:
return brenth(_eval_d, b0, b1, args=(nx, ny, power, alpha))
except ValueError: # pragma: no cover
return np.nan
else:
# Compute achieved alpha (significance) level given d, n and power
def _eval_alpha(alpha, d, nx, ny, power):
return func(d, nx, ny, power, alpha) - power
try:
return brenth(_eval_alpha, 1e-10, 1 - 1e-10, args=(d, nx, ny, power))
except ValueError: # pragma: no cover
return np.nan
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|
32,051 | pingouin.utils | print_table | Pretty display of table.
Parameters
----------
df : :py:class:`pandas.DataFrame`
Dataframe to print (e.g. ANOVA summary)
floatfmt : string
Decimal number formatting
tablefmt : string
Table format (e.g. 'simple', 'plain', 'html', 'latex', 'grid', 'rst').
For a full list of available formats, please refer to
https://pypi.org/project/tabulate/
| def print_table(df, floatfmt=".3f", tablefmt="simple"):
"""Pretty display of table.
Parameters
----------
df : :py:class:`pandas.DataFrame`
Dataframe to print (e.g. ANOVA summary)
floatfmt : string
Decimal number formatting
tablefmt : string
Table format (e.g. 'simple', 'plain', 'html', 'latex', 'grid', 'rst').
For a full list of available formats, please refer to
https://pypi.org/project/tabulate/
"""
if "F" in df.keys():
print("\n=============\nANOVA SUMMARY\n=============\n")
if "A" in df.keys():
print("\n==============\nPOST HOC TESTS\n==============\n")
print(tabulate(df, headers="keys", showindex=False, floatfmt=floatfmt, tablefmt=tablefmt))
print("")
| (df, floatfmt='.3f', tablefmt='simple') | [
0.020420458167791367,
0.0006551261758431792,
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|
32,052 | pingouin.pairwise | ptests |
Pairwise T-test between columns of a dataframe.
T-values are reported on the lower triangle of the output pairwise matrix and p-values on the
upper triangle. This method is a faster, but less exhaustive, matrix-version of the
:py:func:`pingouin.pairwise_test` function. Missing values are automatically removed from each
pairwise T-test.
.. versionadded:: 0.5.3
Parameters
----------
self : :py:class:`pandas.DataFrame`
Input dataframe.
paired : boolean
Specify whether the two observations are related (i.e. repeated measures) or independent.
decimals : int
Number of decimals to display in the output matrix.
padjust : string or None
P-values adjustment for multiple comparison
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
stars : boolean
If True, only significant p-values are displayed as stars using the pre-defined thresholds
of ``pval_stars``. If False, all the raw p-values are displayed.
pval_stars : dict
Significance thresholds. Default is 3 stars for p-values <0.001, 2 stars for
p-values <0.01 and 1 star for p-values <0.05.
**kwargs : optional
Optional argument(s) passed to the lower-level scipy functions, i.e.
:py:func:`scipy.stats.ttest_ind` for independent T-test and
:py:func:`scipy.stats.ttest_rel` for paired T-test.
Returns
-------
mat : :py:class:`pandas.DataFrame`
Pairwise T-test matrix, of dtype str, with T-values on the lower triangle and p-values on
the upper triangle.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> import pingouin as pg
>>> # Load an example dataset of personality dimensions
>>> df = pg.read_dataset('pairwise_corr').iloc[:30, 1:]
>>> df.columns = ["N", "E", "O", 'A', "C"]
>>> # Add some missing values
>>> df.iloc[[2, 5, 20], 2] = np.nan
>>> df.iloc[[1, 4, 10], 3] = np.nan
>>> df.head().round(2)
N E O A C
0 2.48 4.21 3.94 3.96 3.46
1 2.60 3.19 3.96 NaN 3.23
2 2.81 2.90 NaN 2.75 3.50
3 2.90 3.56 3.52 3.17 2.79
4 3.02 3.33 4.02 NaN 2.85
Independent pairwise T-tests
>>> df.ptests()
N E O A C
N - *** *** *** ***
E -8.397 - ***
O -8.332 -0.596 - ***
A -8.804 0.12 0.72 - ***
C -4.759 3.753 4.074 3.787 -
Let's compare with SciPy
>>> from scipy.stats import ttest_ind
>>> np.round(ttest_ind(df["N"], df["E"]), 3)
array([-8.397, 0. ])
Passing custom parameters to the lower-level :py:func:`scipy.stats.ttest_ind` function
>>> df.ptests(alternative="greater", equal_var=True)
N E O A C
N -
E -8.397 - ***
O -8.332 -0.596 - ***
A -8.804 0.12 0.72 - ***
C -4.759 3.753 4.074 3.787 -
Paired T-test, showing the actual p-values instead of stars
>>> df.ptests(paired=True, stars=False, decimals=4)
N E O A C
N - 0.0000 0.0000 0.0000 0.0002
E -7.0773 - 0.8776 0.7522 0.0012
O -8.0568 -0.1555 - 0.8137 0.0008
A -8.3994 0.3191 0.2383 - 0.0009
C -4.2511 3.5953 3.7849 3.7652 -
Adjusting for multiple comparisons using the Holm-Bonferroni method
>>> df.ptests(paired=True, stars=False, padjust="holm")
N E O A C
N - 0.000 0.000 0.000 0.001
E -7.077 - 1. 1. 0.005
O -8.057 -0.155 - 1. 0.005
A -8.399 0.319 0.238 - 0.005
C -4.251 3.595 3.785 3.765 -
| @pf.register_dataframe_method
def ptests(
self,
paired=False,
decimals=3,
padjust=None,
stars=True,
pval_stars={0.001: "***", 0.01: "**", 0.05: "*"},
**kwargs,
):
"""
Pairwise T-test between columns of a dataframe.
T-values are reported on the lower triangle of the output pairwise matrix and p-values on the
upper triangle. This method is a faster, but less exhaustive, matrix-version of the
:py:func:`pingouin.pairwise_test` function. Missing values are automatically removed from each
pairwise T-test.
.. versionadded:: 0.5.3
Parameters
----------
self : :py:class:`pandas.DataFrame`
Input dataframe.
paired : boolean
Specify whether the two observations are related (i.e. repeated measures) or independent.
decimals : int
Number of decimals to display in the output matrix.
padjust : string or None
P-values adjustment for multiple comparison
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
stars : boolean
If True, only significant p-values are displayed as stars using the pre-defined thresholds
of ``pval_stars``. If False, all the raw p-values are displayed.
pval_stars : dict
Significance thresholds. Default is 3 stars for p-values <0.001, 2 stars for
p-values <0.01 and 1 star for p-values <0.05.
**kwargs : optional
Optional argument(s) passed to the lower-level scipy functions, i.e.
:py:func:`scipy.stats.ttest_ind` for independent T-test and
:py:func:`scipy.stats.ttest_rel` for paired T-test.
Returns
-------
mat : :py:class:`pandas.DataFrame`
Pairwise T-test matrix, of dtype str, with T-values on the lower triangle and p-values on
the upper triangle.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> import pingouin as pg
>>> # Load an example dataset of personality dimensions
>>> df = pg.read_dataset('pairwise_corr').iloc[:30, 1:]
>>> df.columns = ["N", "E", "O", 'A', "C"]
>>> # Add some missing values
>>> df.iloc[[2, 5, 20], 2] = np.nan
>>> df.iloc[[1, 4, 10], 3] = np.nan
>>> df.head().round(2)
N E O A C
0 2.48 4.21 3.94 3.96 3.46
1 2.60 3.19 3.96 NaN 3.23
2 2.81 2.90 NaN 2.75 3.50
3 2.90 3.56 3.52 3.17 2.79
4 3.02 3.33 4.02 NaN 2.85
Independent pairwise T-tests
>>> df.ptests()
N E O A C
N - *** *** *** ***
E -8.397 - ***
O -8.332 -0.596 - ***
A -8.804 0.12 0.72 - ***
C -4.759 3.753 4.074 3.787 -
Let's compare with SciPy
>>> from scipy.stats import ttest_ind
>>> np.round(ttest_ind(df["N"], df["E"]), 3)
array([-8.397, 0. ])
Passing custom parameters to the lower-level :py:func:`scipy.stats.ttest_ind` function
>>> df.ptests(alternative="greater", equal_var=True)
N E O A C
N -
E -8.397 - ***
O -8.332 -0.596 - ***
A -8.804 0.12 0.72 - ***
C -4.759 3.753 4.074 3.787 -
Paired T-test, showing the actual p-values instead of stars
>>> df.ptests(paired=True, stars=False, decimals=4)
N E O A C
N - 0.0000 0.0000 0.0000 0.0002
E -7.0773 - 0.8776 0.7522 0.0012
O -8.0568 -0.1555 - 0.8137 0.0008
A -8.3994 0.3191 0.2383 - 0.0009
C -4.2511 3.5953 3.7849 3.7652 -
Adjusting for multiple comparisons using the Holm-Bonferroni method
>>> df.ptests(paired=True, stars=False, padjust="holm")
N E O A C
N - 0.000 0.000 0.000 0.001
E -7.077 - 1. 1. 0.005
O -8.057 -0.155 - 1. 0.005
A -8.399 0.319 0.238 - 0.005
C -4.251 3.595 3.785 3.765 -
"""
from itertools import combinations
from numpy import triu_indices_from as tif
from numpy import format_float_positional as ffp
from scipy.stats import ttest_ind, ttest_rel
assert isinstance(pval_stars, dict), "pval_stars must be a dictionary."
assert isinstance(decimals, int), "decimals must be an int."
if paired:
func = ttest_rel
else:
func = ttest_ind
# Get T-values and p-values
# We cannot use pandas.DataFrame.corr here because it will incorrectly remove rows missing
# values, even when using an independent T-test!
cols = self.columns
combs = list(combinations(cols, 2))
mat = pd.DataFrame(columns=cols, index=cols, dtype=np.float64)
mat_upper = mat.copy()
for a, b in combs:
t, p = func(self[a], self[b], **kwargs, nan_policy="omit")
mat.loc[b, a] = np.round(t, decimals)
# Do not round p-value here, or we'll lose precision for multicomp
mat_upper.loc[a, b] = p
if padjust is not None:
pvals = mat_upper.to_numpy()[tif(mat, k=1)]
mat_upper.to_numpy()[tif(mat, k=1)] = multicomp(pvals, alpha=0.05, method=padjust)[1]
# Convert T-values to str, and fill the diagonal with "-"
mat = mat.astype(str)
np.fill_diagonal(mat.to_numpy(), "-")
def replace_pval(x):
for key, value in pval_stars.items():
if x < key:
return value
return ""
if stars:
# Replace p-values by stars
mat_upper = mat_upper.applymap(replace_pval)
else:
mat_upper = mat_upper.applymap(lambda x: ffp(x, precision=decimals))
# Replace upper triangle by p-values
mat.to_numpy()[tif(mat, k=1)] = mat_upper.to_numpy()[tif(mat, k=1)]
return mat
| (self, paired=False, decimals=3, padjust=None, stars=True, pval_stars={0.001: '***', 0.01: '**', 0.05: '*'}, **kwargs) | [
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|
32,053 | pingouin.plotting | qqplot | Quantile-Quantile plot.
Parameters
----------
x : array_like
Sample data.
dist : str or stats.distributions instance, optional
Distribution or distribution function name. The default is `'norm'`
for a normal probability plot.
sparams : tuple, optional
Distribution-specific shape parameters (shape parameters, location,
and scale). See :py:func:`scipy.stats.probplot` for more details.
confidence : float
Confidence level (.95 = 95%) for point-wise confidence envelope.
Can be disabled by passing False.
square: bool
If True (default), ensure equal aspect ratio between X and Y axes.
ax : matplotlib axes
Axis on which to draw the plot
**kwargs : optional
Optional argument(s) passed to :py:func:`matplotlib.pyplot.scatter`.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Raises
------
ValueError
If ``sparams`` does not contain the required parameters for ``dist``.
(e.g. :py:class:`scipy.stats.t` has a mandatory degrees of
freedom parameter *df*.)
Notes
-----
This function returns a scatter plot of the quantile of the sample data
``x`` against the theoretical quantiles of the distribution given in
``dist`` (default = *'norm'*).
The points plotted in a Q–Q plot are always non-decreasing when viewed
from left to right. If the two distributions being compared are identical,
the Q–Q plot follows the 45° line y = x. If the two distributions agree
after linearly transforming the values in one of the distributions,
then the Q–Q plot follows some line, but not necessarily the line y = x.
If the general trend of the Q–Q plot is flatter than the line y = x,
the distribution plotted on the horizontal axis is more dispersed than
the distribution plotted on the vertical axis. Conversely, if the general
trend of the Q–Q plot is steeper than the line y = x, the distribution
plotted on the vertical axis is more dispersed than the distribution
plotted on the horizontal axis. Q–Q plots are often arced, or "S" shaped,
indicating that one of the distributions is more skewed than the other,
or that one of the distributions has heavier tails than the other.
In addition, the function also plots a best-fit line (linear regression)
for the data and annotates the plot with the coefficient of
determination :math:`R^2`. Note that the intercept and slope of the
linear regression between the quantiles gives a measure of the relative
location and relative scale of the samples.
.. warning:: Be extra careful when using fancier distributions with several
parameters. Always double-check your results with another
software or package.
References
----------
* https://github.com/cran/car/blob/master/R/qqPlot.R
* Fox, J. (2008), Applied Regression Analysis and Generalized Linear
Models, 2nd Ed., Sage Publications, Inc.
Examples
--------
Q-Q plot using a normal theoretical distribution:
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.normal(size=50)
>>> ax = pg.qqplot(x, dist='norm')
Two Q-Q plots using two separate axes:
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> np.random.seed(123)
>>> x = np.random.normal(size=50)
>>> x_exp = np.random.exponential(size=50)
>>> fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 4))
>>> ax1 = pg.qqplot(x, dist='norm', ax=ax1, confidence=False)
>>> ax2 = pg.qqplot(x_exp, dist='expon', ax=ax2)
Using custom location / scale parameters as well as another Seaborn style
.. plot::
>>> import numpy as np
>>> import seaborn as sns
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> np.random.seed(123)
>>> x = np.random.normal(size=50)
>>> mean, std = 0, 0.8
>>> sns.set_style('darkgrid')
>>> ax = pg.qqplot(x, dist='norm', sparams=(mean, std))
| def qqplot(x, dist="norm", sparams=(), confidence=0.95, square=True, ax=None, **kwargs):
"""Quantile-Quantile plot.
Parameters
----------
x : array_like
Sample data.
dist : str or stats.distributions instance, optional
Distribution or distribution function name. The default is `'norm'`
for a normal probability plot.
sparams : tuple, optional
Distribution-specific shape parameters (shape parameters, location,
and scale). See :py:func:`scipy.stats.probplot` for more details.
confidence : float
Confidence level (.95 = 95%) for point-wise confidence envelope.
Can be disabled by passing False.
square: bool
If True (default), ensure equal aspect ratio between X and Y axes.
ax : matplotlib axes
Axis on which to draw the plot
**kwargs : optional
Optional argument(s) passed to :py:func:`matplotlib.pyplot.scatter`.
Returns
-------
ax : Matplotlib Axes instance
Returns the Axes object with the plot for further tweaking.
Raises
------
ValueError
If ``sparams`` does not contain the required parameters for ``dist``.
(e.g. :py:class:`scipy.stats.t` has a mandatory degrees of
freedom parameter *df*.)
Notes
-----
This function returns a scatter plot of the quantile of the sample data
``x`` against the theoretical quantiles of the distribution given in
``dist`` (default = *'norm'*).
The points plotted in a Q–Q plot are always non-decreasing when viewed
from left to right. If the two distributions being compared are identical,
the Q–Q plot follows the 45° line y = x. If the two distributions agree
after linearly transforming the values in one of the distributions,
then the Q–Q plot follows some line, but not necessarily the line y = x.
If the general trend of the Q–Q plot is flatter than the line y = x,
the distribution plotted on the horizontal axis is more dispersed than
the distribution plotted on the vertical axis. Conversely, if the general
trend of the Q–Q plot is steeper than the line y = x, the distribution
plotted on the vertical axis is more dispersed than the distribution
plotted on the horizontal axis. Q–Q plots are often arced, or "S" shaped,
indicating that one of the distributions is more skewed than the other,
or that one of the distributions has heavier tails than the other.
In addition, the function also plots a best-fit line (linear regression)
for the data and annotates the plot with the coefficient of
determination :math:`R^2`. Note that the intercept and slope of the
linear regression between the quantiles gives a measure of the relative
location and relative scale of the samples.
.. warning:: Be extra careful when using fancier distributions with several
parameters. Always double-check your results with another
software or package.
References
----------
* https://github.com/cran/car/blob/master/R/qqPlot.R
* Fox, J. (2008), Applied Regression Analysis and Generalized Linear
Models, 2nd Ed., Sage Publications, Inc.
Examples
--------
Q-Q plot using a normal theoretical distribution:
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.normal(size=50)
>>> ax = pg.qqplot(x, dist='norm')
Two Q-Q plots using two separate axes:
.. plot::
>>> import numpy as np
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> np.random.seed(123)
>>> x = np.random.normal(size=50)
>>> x_exp = np.random.exponential(size=50)
>>> fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 4))
>>> ax1 = pg.qqplot(x, dist='norm', ax=ax1, confidence=False)
>>> ax2 = pg.qqplot(x_exp, dist='expon', ax=ax2)
Using custom location / scale parameters as well as another Seaborn style
.. plot::
>>> import numpy as np
>>> import seaborn as sns
>>> import pingouin as pg
>>> import matplotlib.pyplot as plt
>>> np.random.seed(123)
>>> x = np.random.normal(size=50)
>>> mean, std = 0, 0.8
>>> sns.set_style('darkgrid')
>>> ax = pg.qqplot(x, dist='norm', sparams=(mean, std))
"""
# Update default kwargs with specified inputs
_scatter_kwargs = {"marker": "o", "color": "blue"}
_scatter_kwargs.update(kwargs)
if isinstance(dist, str):
dist = getattr(stats, dist)
x = np.asarray(x)
x = x[~np.isnan(x)] # NaN are automatically removed
# Check sparams: if single parameter, tuple becomes int
if not isinstance(sparams, (tuple, list)):
sparams = (sparams,)
# For fancier distributions, check that the required parameters are passed
if len(sparams) < dist.numargs:
raise ValueError(
"The following sparams are required for this "
"distribution: %s. See scipy.stats.%s for details." % (dist.shapes, dist.name)
)
# Extract quantiles and regression
quantiles = stats.probplot(x, sparams=sparams, dist=dist, fit=False)
theor, observed = quantiles[0], quantiles[1]
fit_params = dist.fit(x)
loc = fit_params[-2]
scale = fit_params[-1]
shape = fit_params[:-2] if len(fit_params) > 2 else None
# Observed values to observed quantiles
if loc != 0 and scale != 1:
observed = (np.sort(observed) - fit_params[-2]) / fit_params[-1]
# Linear regression
slope, intercept, r, _, _ = stats.linregress(theor, observed)
# Start the plot
if ax is None:
ax = plt.gca()
ax.scatter(theor, observed, **_scatter_kwargs)
ax.set_xlabel("Theoretical quantiles")
ax.set_ylabel("Ordered quantiles")
# Add diagonal line
end_pts = [ax.get_xlim(), ax.get_ylim()]
end_pts[0] = min(end_pts[0])
end_pts[1] = max(end_pts[1])
ax.plot(end_pts, end_pts, color="slategrey", lw=1.5)
ax.set_xlim(end_pts)
ax.set_ylim(end_pts)
# Add regression line and annotate R2
fit_val = slope * theor + intercept
ax.plot(theor, fit_val, "r-", lw=2)
posx = end_pts[0] + 0.60 * (end_pts[1] - end_pts[0])
posy = end_pts[0] + 0.10 * (end_pts[1] - end_pts[0])
ax.text(posx, posy, "$R^2=%.3f$" % r**2)
if confidence is not False:
# Confidence envelope
n = x.size
P = _ppoints(n)
crit = stats.norm.ppf(1 - (1 - confidence) / 2)
pdf = dist.pdf(theor) if shape is None else dist.pdf(theor, *shape)
se = (slope / pdf) * np.sqrt(P * (1 - P) / n)
upper = fit_val + crit * se
lower = fit_val - crit * se
ax.plot(theor, upper, "r--", lw=1.25)
ax.plot(theor, lower, "r--", lw=1.25)
# Make square
if square:
ax.set_aspect("equal")
return ax
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|
32,054 | pingouin.correlation | rcorr |
Correlation matrix of a dataframe with p-values and/or sample size on the
upper triangle (:py:class:`pandas.DataFrame` method).
This method is a faster, but less exhaustive, matrix-version of the
:py:func:`pingouin.pairwise_corr` function. It is based on the
:py:func:`pandas.DataFrame.corr` method. Missing values are automatically
removed from each pairwise correlation.
Parameters
----------
self : :py:class:`pandas.DataFrame`
Input dataframe.
method : str
Correlation method. Can be either 'pearson' or 'spearman'.
upper : str
If 'pval', the upper triangle of the output correlation matrix shows
the p-values. If 'n', the upper triangle is the sample size used in
each pairwise correlation.
decimals : int
Number of decimals to display in the output correlation matrix.
padjust : string or None
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
stars : boolean
If True, only significant p-values are displayed as stars using the
pre-defined thresholds of ``pval_stars``. If False, all the raw
p-values are displayed.
pval_stars : dict
Significance thresholds. Default is 3 stars for p-values < 0.001,
2 stars for p-values < 0.01 and 1 star for p-values < 0.05.
Returns
-------
rcorr : :py:class:`pandas.DataFrame`
Correlation matrix, of type str.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> import pingouin as pg
>>> # Load an example dataset of personality dimensions
>>> df = pg.read_dataset('pairwise_corr').iloc[:, 1:]
>>> # Add some missing values
>>> df.iloc[[2, 5, 20], 2] = np.nan
>>> df.iloc[[1, 4, 10], 3] = np.nan
>>> df.head().round(2)
Neuroticism Extraversion Openness Agreeableness Conscientiousness
0 2.48 4.21 3.94 3.96 3.46
1 2.60 3.19 3.96 NaN 3.23
2 2.81 2.90 NaN 2.75 3.50
3 2.90 3.56 3.52 3.17 2.79
4 3.02 3.33 4.02 NaN 2.85
>>> # Correlation matrix on the four first columns
>>> df.iloc[:, 0:4].rcorr()
Neuroticism Extraversion Openness Agreeableness
Neuroticism - *** **
Extraversion -0.35 - ***
Openness -0.01 0.265 - ***
Agreeableness -0.134 0.054 0.161 -
>>> # Spearman correlation and Holm adjustement for multiple comparisons
>>> df.iloc[:, 0:4].rcorr(method='spearman', padjust='holm')
Neuroticism Extraversion Openness Agreeableness
Neuroticism - *** **
Extraversion -0.325 - ***
Openness -0.027 0.24 - ***
Agreeableness -0.15 0.06 0.173 -
>>> # Compare with the pg.pairwise_corr function
>>> pairwise = df.iloc[:, 0:4].pairwise_corr(method='spearman',
... padjust='holm')
>>> pairwise[['X', 'Y', 'r', 'p-corr']].round(3) # Do not show all columns
X Y r p-corr
0 Neuroticism Extraversion -0.325 0.000
1 Neuroticism Openness -0.027 0.543
2 Neuroticism Agreeableness -0.150 0.002
3 Extraversion Openness 0.240 0.000
4 Extraversion Agreeableness 0.060 0.358
5 Openness Agreeableness 0.173 0.000
>>> # Display the raw p-values with four decimals
>>> df.iloc[:, [0, 1, 3]].rcorr(stars=False, decimals=4)
Neuroticism Extraversion Agreeableness
Neuroticism - 0.0000 0.0028
Extraversion -0.3501 - 0.2305
Agreeableness -0.134 0.0539 -
>>> # With the sample size on the upper triangle instead of the p-values
>>> df.iloc[:, [0, 1, 2]].rcorr(upper='n')
Neuroticism Extraversion Openness
Neuroticism - 500 497
Extraversion -0.35 - 497
Openness -0.01 0.265 -
| @pf.register_dataframe_method
def rcorr(
self,
method="pearson",
upper="pval",
decimals=3,
padjust=None,
stars=True,
pval_stars={0.001: "***", 0.01: "**", 0.05: "*"},
):
"""
Correlation matrix of a dataframe with p-values and/or sample size on the
upper triangle (:py:class:`pandas.DataFrame` method).
This method is a faster, but less exhaustive, matrix-version of the
:py:func:`pingouin.pairwise_corr` function. It is based on the
:py:func:`pandas.DataFrame.corr` method. Missing values are automatically
removed from each pairwise correlation.
Parameters
----------
self : :py:class:`pandas.DataFrame`
Input dataframe.
method : str
Correlation method. Can be either 'pearson' or 'spearman'.
upper : str
If 'pval', the upper triangle of the output correlation matrix shows
the p-values. If 'n', the upper triangle is the sample size used in
each pairwise correlation.
decimals : int
Number of decimals to display in the output correlation matrix.
padjust : string or None
Method used for testing and adjustment of pvalues.
* ``'none'``: no correction
* ``'bonf'``: one-step Bonferroni correction
* ``'sidak'``: one-step Sidak correction
* ``'holm'``: step-down method using Bonferroni adjustments
* ``'fdr_bh'``: Benjamini/Hochberg FDR correction
* ``'fdr_by'``: Benjamini/Yekutieli FDR correction
stars : boolean
If True, only significant p-values are displayed as stars using the
pre-defined thresholds of ``pval_stars``. If False, all the raw
p-values are displayed.
pval_stars : dict
Significance thresholds. Default is 3 stars for p-values < 0.001,
2 stars for p-values < 0.01 and 1 star for p-values < 0.05.
Returns
-------
rcorr : :py:class:`pandas.DataFrame`
Correlation matrix, of type str.
Examples
--------
>>> import numpy as np
>>> import pandas as pd
>>> import pingouin as pg
>>> # Load an example dataset of personality dimensions
>>> df = pg.read_dataset('pairwise_corr').iloc[:, 1:]
>>> # Add some missing values
>>> df.iloc[[2, 5, 20], 2] = np.nan
>>> df.iloc[[1, 4, 10], 3] = np.nan
>>> df.head().round(2)
Neuroticism Extraversion Openness Agreeableness Conscientiousness
0 2.48 4.21 3.94 3.96 3.46
1 2.60 3.19 3.96 NaN 3.23
2 2.81 2.90 NaN 2.75 3.50
3 2.90 3.56 3.52 3.17 2.79
4 3.02 3.33 4.02 NaN 2.85
>>> # Correlation matrix on the four first columns
>>> df.iloc[:, 0:4].rcorr()
Neuroticism Extraversion Openness Agreeableness
Neuroticism - *** **
Extraversion -0.35 - ***
Openness -0.01 0.265 - ***
Agreeableness -0.134 0.054 0.161 -
>>> # Spearman correlation and Holm adjustement for multiple comparisons
>>> df.iloc[:, 0:4].rcorr(method='spearman', padjust='holm')
Neuroticism Extraversion Openness Agreeableness
Neuroticism - *** **
Extraversion -0.325 - ***
Openness -0.027 0.24 - ***
Agreeableness -0.15 0.06 0.173 -
>>> # Compare with the pg.pairwise_corr function
>>> pairwise = df.iloc[:, 0:4].pairwise_corr(method='spearman',
... padjust='holm')
>>> pairwise[['X', 'Y', 'r', 'p-corr']].round(3) # Do not show all columns
X Y r p-corr
0 Neuroticism Extraversion -0.325 0.000
1 Neuroticism Openness -0.027 0.543
2 Neuroticism Agreeableness -0.150 0.002
3 Extraversion Openness 0.240 0.000
4 Extraversion Agreeableness 0.060 0.358
5 Openness Agreeableness 0.173 0.000
>>> # Display the raw p-values with four decimals
>>> df.iloc[:, [0, 1, 3]].rcorr(stars=False, decimals=4)
Neuroticism Extraversion Agreeableness
Neuroticism - 0.0000 0.0028
Extraversion -0.3501 - 0.2305
Agreeableness -0.134 0.0539 -
>>> # With the sample size on the upper triangle instead of the p-values
>>> df.iloc[:, [0, 1, 2]].rcorr(upper='n')
Neuroticism Extraversion Openness
Neuroticism - 500 497
Extraversion -0.35 - 497
Openness -0.01 0.265 -
"""
from numpy import triu_indices_from as tif
from numpy import format_float_positional as ffp
from scipy.stats import pearsonr, spearmanr
# Safety check
assert isinstance(pval_stars, dict), "pval_stars must be a dictionnary."
assert isinstance(decimals, int), "decimals must be an int."
assert method in ["pearson", "spearman"], "Method is not recognized."
assert upper in ["pval", "n"], "upper must be either `pval` or `n`."
mat = self.corr(method=method, numeric_only=True).round(decimals)
if upper == "n":
mat_upper = self.corr(method=lambda x, y: len(x), numeric_only=True).astype(int)
else:
if method == "pearson":
mat_upper = self.corr(method=lambda x, y: pearsonr(x, y)[1], numeric_only=True)
else:
# Method = 'spearman'
mat_upper = self.corr(method=lambda x, y: spearmanr(x, y)[1], numeric_only=True)
if padjust is not None:
pvals = mat_upper.to_numpy()[tif(mat, k=1)]
mat_upper.to_numpy()[tif(mat, k=1)] = multicomp(pvals, alpha=0.05, method=padjust)[1]
# Convert r to text
mat = mat.astype(str)
# Inplace modification of the diagonal
np.fill_diagonal(mat.to_numpy(), "-")
if upper == "pval":
def replace_pval(x):
for key, value in pval_stars.items():
if x < key:
return value
return ""
if stars:
# Replace p-values by stars
mat_upper = mat_upper.applymap(replace_pval)
else:
mat_upper = mat_upper.applymap(lambda x: ffp(x, precision=decimals))
# Replace upper triangle by p-values or n
mat.to_numpy()[tif(mat, k=1)] = mat_upper.to_numpy()[tif(mat, k=1)]
return mat
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|
32,055 | pingouin.datasets | read_dataset | Read example datasets.
Parameters
----------
dname : string
Name of dataset to read (without extension).
Must be a valid dataset present in pingouin.datasets
Returns
-------
data : :py:class:`pandas.DataFrame`
Requested dataset.
Examples
--------
Load the `Penguin <https://github.com/allisonhorst/palmerpenguins>`_
dataset:
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> df # doctest: +SKIP
species island bill_length_mm ... flipper_length_mm body_mass_g sex
0 Adelie Biscoe 37.8 ... 174.0 3400.0 female
1 Adelie Biscoe 37.7 ... 180.0 3600.0 male
2 Adelie Biscoe 35.9 ... 189.0 3800.0 female
3 Adelie Biscoe 38.2 ... 185.0 3950.0 male
4 Adelie Biscoe 38.8 ... 180.0 3800.0 male
.. ... ... ... ... ... ... ...
339 Gentoo Biscoe NaN ... NaN NaN NaN
340 Gentoo Biscoe 46.8 ... 215.0 4850.0 female
341 Gentoo Biscoe 50.4 ... 222.0 5750.0 male
342 Gentoo Biscoe 45.2 ... 212.0 5200.0 female
343 Gentoo Biscoe 49.9 ... 213.0 5400.0 male
| def read_dataset(dname):
"""Read example datasets.
Parameters
----------
dname : string
Name of dataset to read (without extension).
Must be a valid dataset present in pingouin.datasets
Returns
-------
data : :py:class:`pandas.DataFrame`
Requested dataset.
Examples
--------
Load the `Penguin <https://github.com/allisonhorst/palmerpenguins>`_
dataset:
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> df # doctest: +SKIP
species island bill_length_mm ... flipper_length_mm body_mass_g sex
0 Adelie Biscoe 37.8 ... 174.0 3400.0 female
1 Adelie Biscoe 37.7 ... 180.0 3600.0 male
2 Adelie Biscoe 35.9 ... 189.0 3800.0 female
3 Adelie Biscoe 38.2 ... 185.0 3950.0 male
4 Adelie Biscoe 38.8 ... 180.0 3800.0 male
.. ... ... ... ... ... ... ...
339 Gentoo Biscoe NaN ... NaN NaN NaN
340 Gentoo Biscoe 46.8 ... 215.0 4850.0 female
341 Gentoo Biscoe 50.4 ... 222.0 5750.0 male
342 Gentoo Biscoe 45.2 ... 212.0 5200.0 female
343 Gentoo Biscoe 49.9 ... 213.0 5400.0 male
"""
# Check extension
d, ext = op.splitext(dname)
if ext.lower() == ".csv":
dname = d
# Check that dataset exist
if dname not in dts["dataset"].to_numpy():
raise ValueError(
"Dataset does not exist. Valid datasets names are", dts["dataset"].to_numpy()
)
# Load dataset
return pd.read_csv(op.join(ddir, dname + ".csv"), sep=",")
| (dname) | [
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|
32,058 | pingouin.utils | remove_na | Remove missing values along a given axis in one or more (paired) numpy arrays.
Parameters
----------
x, y : 1D or 2D arrays
Data. ``x`` and ``y`` must have the same number of dimensions.
``y`` can be None to only remove missing values in ``x``.
paired : bool
Indicates if the measurements are paired or not.
axis : str
Axis or axes along which missing values are removed.
Can be 'rows' or 'columns'. This has no effect if ``x`` and ``y`` are
one-dimensional arrays.
Returns
-------
x, y : np.ndarray
Data without missing values
Examples
--------
Single 1D array
>>> import numpy as np
>>> from pingouin import remove_na
>>> x = [6.4, 3.2, 4.5, np.nan]
>>> remove_na(x)
array([6.4, 3.2, 4.5])
With two paired 1D arrays
>>> y = [2.3, np.nan, 5.2, 4.6]
>>> remove_na(x, y, paired=True)
(array([6.4, 4.5]), array([2.3, 5.2]))
With two independent 2D arrays
>>> x = np.array([[4, 2], [4, np.nan], [7, 6]])
>>> y = np.array([[6, np.nan], [3, 2], [2, 2]])
>>> x_no_nan, y_no_nan = remove_na(x, y, paired=False)
| def remove_na(x, y=None, paired=False, axis="rows"):
"""Remove missing values along a given axis in one or more (paired) numpy arrays.
Parameters
----------
x, y : 1D or 2D arrays
Data. ``x`` and ``y`` must have the same number of dimensions.
``y`` can be None to only remove missing values in ``x``.
paired : bool
Indicates if the measurements are paired or not.
axis : str
Axis or axes along which missing values are removed.
Can be 'rows' or 'columns'. This has no effect if ``x`` and ``y`` are
one-dimensional arrays.
Returns
-------
x, y : np.ndarray
Data without missing values
Examples
--------
Single 1D array
>>> import numpy as np
>>> from pingouin import remove_na
>>> x = [6.4, 3.2, 4.5, np.nan]
>>> remove_na(x)
array([6.4, 3.2, 4.5])
With two paired 1D arrays
>>> y = [2.3, np.nan, 5.2, 4.6]
>>> remove_na(x, y, paired=True)
(array([6.4, 4.5]), array([2.3, 5.2]))
With two independent 2D arrays
>>> x = np.array([[4, 2], [4, np.nan], [7, 6]])
>>> y = np.array([[6, np.nan], [3, 2], [2, 2]])
>>> x_no_nan, y_no_nan = remove_na(x, y, paired=False)
"""
# Safety checks
x = np.asarray(x)
assert axis in ["rows", "columns"], "axis must be rows or columns."
if y is None:
return _remove_na_single(x, axis=axis)
elif isinstance(y, (int, float, str)):
return _remove_na_single(x, axis=axis), y
else: # y is list, np.array, pd.Series
y = np.asarray(y)
assert y.size != 0, "y cannot be an empty list or array."
# Make sure that we just pass-through if y have only 1 element
if y.size == 1:
return _remove_na_single(x, axis=axis), y
if x.ndim != y.ndim or paired is False:
# x and y do not have the same dimension
x_no_nan = _remove_na_single(x, axis=axis)
y_no_nan = _remove_na_single(y, axis=axis)
return x_no_nan, y_no_nan
# At this point, we assume that x and y are paired and have same dimensions
if x.ndim == 1:
# 1D arrays
x_mask = ~np.isnan(x)
y_mask = ~np.isnan(y)
else:
# 2D arrays
ax = 1 if axis == "rows" else 0
x_mask = ~np.any(np.isnan(x), axis=ax)
y_mask = ~np.any(np.isnan(y), axis=ax)
# Check if missing values are present
if ~x_mask.all() or ~y_mask.all():
ax = 0 if axis == "rows" else 1
ax = 0 if x.ndim == 1 else ax
both = np.logical_and(x_mask, y_mask)
x = x.compress(both, axis=ax)
y = y.compress(both, axis=ax)
return x, y
| (x, y=None, paired=False, axis='rows') | [
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|
32,059 | pingouin.parametric | rm_anova | One-way and two-way repeated measures ANOVA.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
:py:class:`pandas.DataFrame` method, in which case this argument is no
longer needed.
Both wide and long-format dataframe are supported for one-way repeated
measures ANOVA. However, ``data`` must be in long format for two-way
repeated measures.
dv : string
Name of column containing the dependent variable (only required if
``data`` is in long format).
within : string or list of string
Name of column containing the within factor (only required if ``data``
is in long format).
If ``within`` is a single string, then compute a one-way repeated
measures ANOVA, if ``within`` is a list with two strings,
compute a two-way repeated measures ANOVA.
subject : string
Name of column containing the subject identifier (only required if
``data`` is in long format).
correction : string or boolean
If True, also return the Greenhouse-Geisser corrected p-value.
The default for one-way design is to compute Mauchly's test of
sphericity to determine whether the p-values needs to be corrected
(see :py:func:`pingouin.sphericity`).
The default for two-way design is to return both the uncorrected and
Greenhouse-Geisser corrected p-values. Note that sphericity test for
two-way design are not currently implemented in Pingouin.
detailed : boolean
If True, return a full ANOVA table.
effsize : string
Effect size. Must be one of 'np2' (partial eta-squared), 'n2'
(eta-squared) or 'ng2'(generalized eta-squared, default). Note that for
one-way repeated measure ANOVA, eta-squared is the same as the generalized eta-squared.
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Name of the within-group factor
* ``'ddof1'``: Degrees of freedom (numerator)
* ``'ddof2'``: Degrees of freedom (denominator)
* ``'F'``: F-value
* ``'p-unc'``: Uncorrected p-value
* ``'ng2'``: Generalized eta-square effect size
* ``'eps'``: Greenhouse-Geisser epsilon factor (= index of sphericity)
* ``'p-GG-corr'``: Greenhouse-Geisser corrected p-value
* ``'W-spher'``: Sphericity test statistic
* ``'p-spher'``: p-value of the sphericity test
* ``'sphericity'``: sphericity of the data (boolean)
See Also
--------
anova : One-way and N-way ANOVA
mixed_anova : Two way mixed ANOVA
friedman : Non-parametric one-way repeated measures ANOVA
Notes
-----
Data can be in wide or long format for one-way repeated measures ANOVA but
*must* be in long format for two-way repeated measures ANOVA.
In one-way repeated-measures ANOVA, the total variance (sums of squares)
is divided into three components
.. math::
SS_{\text{total}} = SS_{\text{effect}} +
(SS_{\text{subjects}} + SS_{\text{error}})
with
.. math::
SS_{\text{total}} = \sum_i^r \sum_j^n (Y_{ij} - \overline{Y})^2
SS_{\text{effect}} = \sum_i^r n_i(\overline{Y_i} - \overline{Y})^2
SS_{\text{subjects}} = r\sum (\overline{Y}_s - \overline{Y})^2
SS_{\text{error}} = SS_{\text{total}} - SS_{\text{effect}} -
SS_{\text{subjects}}
where :math:`i=1,...,r; j=1,...,n_i`, :math:`r` is the number of
conditions, :math:`n_i` the number of observations for each condition,
:math:`\overline{Y}` the grand mean of the data, :math:`\overline{Y_i}`
the mean of the :math:`i^{th}` condition and :math:`\overline{Y}_{subj}`
the mean of the :math:`s^{th}` subject.
The F-statistics is then defined as:
.. math::
F^* = \frac{MS_{\text{effect}}}{MS_{\text{error}}} =
\frac{\frac{SS_{\text{effect}}}
{r-1}}{\frac{SS_{\text{error}}}{(n - 1)(r - 1)}}
and the p-value can be calculated using a F-distribution with
:math:`v_{\text{effect}} = r - 1` and
:math:`v_{\text{error}} = (n - 1)(r - 1)` degrees of freedom.
The default effect size reported in Pingouin is the generalized eta-squared,
which is equivalent to eta-squared for one-way repeated measures ANOVA.
.. math::
\eta_g^2 = \frac{SS_{\text{effect}}}{SS_{\text{total}}}
The partial eta-squared is defined as:
.. math::
\eta_p^2 = \frac{SS_{\text{effect}}}{SS_{\text{effect}} + SS_{\text{error}}}
Missing values are automatically removed using a strict listwise approach (= complete-case
analysis). In other words, any subject with one or more missing value(s) is completely removed
from the dataframe prior to running the test. This could drastically decrease the power of the
ANOVA if many missing values are present. In that case, we strongly recommend using linear
mixed effect modelling, which can handle missing values in repeated measures.
.. warning:: The epsilon adjustement factor of the interaction in
two-way repeated measures ANOVA where both factors have more than
two levels slightly differs than from R and JASP.
Please always make sure to double-check your results with another
software.
.. warning:: Sphericity tests for the interaction term of a two-way
repeated measures ANOVA are not currently supported in Pingouin.
Instead, please refer to the Greenhouse-Geisser epsilon value
(a value close to 1 indicates that sphericity is met.) For more
details, see :py:func:`pingouin.sphericity`.
Examples
--------
1. One-way repeated measures ANOVA using a wide-format dataset
>>> import pingouin as pg
>>> data = pg.read_dataset('rm_anova_wide')
>>> pg.rm_anova(data)
Source ddof1 ddof2 F p-unc ng2 eps
0 Within 3 24 5.200652 0.006557 0.346392 0.694329
2. One-way repeated-measures ANOVA using a long-format dataset.
We're also specifying two additional options here: ``detailed=True`` means
that we'll get a more detailed ANOVA table, and ``effsize='np2'``
means that we want to get the partial eta-squared effect size instead
of the default (generalized) eta-squared.
>>> df = pg.read_dataset('rm_anova')
>>> aov = pg.rm_anova(dv='DesireToKill', within='Disgustingness',
... subject='Subject', data=df, detailed=True, effsize="np2")
>>> aov.round(3)
Source SS DF MS F p-unc np2 eps
0 Disgustingness 27.485 1 27.485 12.044 0.001 0.116 1.0
1 Error 209.952 92 2.282 NaN NaN NaN NaN
3. Two-way repeated-measures ANOVA
>>> aov = pg.rm_anova(dv='DesireToKill', within=['Disgustingness', 'Frighteningness'],
... subject='Subject', data=df)
4. As a :py:class:`pandas.DataFrame` method
>>> df.rm_anova(dv='DesireToKill', within='Disgustingness', subject='Subject', detailed=False)
Source ddof1 ddof2 F p-unc ng2 eps
0 Disgustingness 1 92 12.043878 0.000793 0.025784 1.0
| @pf.register_dataframe_method
def rm_anova(
data=None, dv=None, within=None, subject=None, correction="auto", detailed=False, effsize="ng2"
):
"""One-way and two-way repeated measures ANOVA.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
:py:class:`pandas.DataFrame` method, in which case this argument is no
longer needed.
Both wide and long-format dataframe are supported for one-way repeated
measures ANOVA. However, ``data`` must be in long format for two-way
repeated measures.
dv : string
Name of column containing the dependent variable (only required if
``data`` is in long format).
within : string or list of string
Name of column containing the within factor (only required if ``data``
is in long format).
If ``within`` is a single string, then compute a one-way repeated
measures ANOVA, if ``within`` is a list with two strings,
compute a two-way repeated measures ANOVA.
subject : string
Name of column containing the subject identifier (only required if
``data`` is in long format).
correction : string or boolean
If True, also return the Greenhouse-Geisser corrected p-value.
The default for one-way design is to compute Mauchly's test of
sphericity to determine whether the p-values needs to be corrected
(see :py:func:`pingouin.sphericity`).
The default for two-way design is to return both the uncorrected and
Greenhouse-Geisser corrected p-values. Note that sphericity test for
two-way design are not currently implemented in Pingouin.
detailed : boolean
If True, return a full ANOVA table.
effsize : string
Effect size. Must be one of 'np2' (partial eta-squared), 'n2'
(eta-squared) or 'ng2'(generalized eta-squared, default). Note that for
one-way repeated measure ANOVA, eta-squared is the same as the generalized eta-squared.
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Name of the within-group factor
* ``'ddof1'``: Degrees of freedom (numerator)
* ``'ddof2'``: Degrees of freedom (denominator)
* ``'F'``: F-value
* ``'p-unc'``: Uncorrected p-value
* ``'ng2'``: Generalized eta-square effect size
* ``'eps'``: Greenhouse-Geisser epsilon factor (= index of sphericity)
* ``'p-GG-corr'``: Greenhouse-Geisser corrected p-value
* ``'W-spher'``: Sphericity test statistic
* ``'p-spher'``: p-value of the sphericity test
* ``'sphericity'``: sphericity of the data (boolean)
See Also
--------
anova : One-way and N-way ANOVA
mixed_anova : Two way mixed ANOVA
friedman : Non-parametric one-way repeated measures ANOVA
Notes
-----
Data can be in wide or long format for one-way repeated measures ANOVA but
*must* be in long format for two-way repeated measures ANOVA.
In one-way repeated-measures ANOVA, the total variance (sums of squares)
is divided into three components
.. math::
SS_{\\text{total}} = SS_{\\text{effect}} +
(SS_{\\text{subjects}} + SS_{\\text{error}})
with
.. math::
SS_{\\text{total}} = \\sum_i^r \\sum_j^n (Y_{ij} - \\overline{Y})^2
SS_{\\text{effect}} = \\sum_i^r n_i(\\overline{Y_i} - \\overline{Y})^2
SS_{\\text{subjects}} = r\\sum (\\overline{Y}_s - \\overline{Y})^2
SS_{\\text{error}} = SS_{\\text{total}} - SS_{\\text{effect}} -
SS_{\\text{subjects}}
where :math:`i=1,...,r; j=1,...,n_i`, :math:`r` is the number of
conditions, :math:`n_i` the number of observations for each condition,
:math:`\\overline{Y}` the grand mean of the data, :math:`\\overline{Y_i}`
the mean of the :math:`i^{th}` condition and :math:`\\overline{Y}_{subj}`
the mean of the :math:`s^{th}` subject.
The F-statistics is then defined as:
.. math::
F^* = \\frac{MS_{\\text{effect}}}{MS_{\\text{error}}} =
\\frac{\\frac{SS_{\\text{effect}}}
{r-1}}{\\frac{SS_{\\text{error}}}{(n - 1)(r - 1)}}
and the p-value can be calculated using a F-distribution with
:math:`v_{\\text{effect}} = r - 1` and
:math:`v_{\\text{error}} = (n - 1)(r - 1)` degrees of freedom.
The default effect size reported in Pingouin is the generalized eta-squared,
which is equivalent to eta-squared for one-way repeated measures ANOVA.
.. math::
\\eta_g^2 = \\frac{SS_{\\text{effect}}}{SS_{\\text{total}}}
The partial eta-squared is defined as:
.. math::
\\eta_p^2 = \\frac{SS_{\\text{effect}}}{SS_{\\text{effect}} + SS_{\\text{error}}}
Missing values are automatically removed using a strict listwise approach (= complete-case
analysis). In other words, any subject with one or more missing value(s) is completely removed
from the dataframe prior to running the test. This could drastically decrease the power of the
ANOVA if many missing values are present. In that case, we strongly recommend using linear
mixed effect modelling, which can handle missing values in repeated measures.
.. warning:: The epsilon adjustement factor of the interaction in
two-way repeated measures ANOVA where both factors have more than
two levels slightly differs than from R and JASP.
Please always make sure to double-check your results with another
software.
.. warning:: Sphericity tests for the interaction term of a two-way
repeated measures ANOVA are not currently supported in Pingouin.
Instead, please refer to the Greenhouse-Geisser epsilon value
(a value close to 1 indicates that sphericity is met.) For more
details, see :py:func:`pingouin.sphericity`.
Examples
--------
1. One-way repeated measures ANOVA using a wide-format dataset
>>> import pingouin as pg
>>> data = pg.read_dataset('rm_anova_wide')
>>> pg.rm_anova(data)
Source ddof1 ddof2 F p-unc ng2 eps
0 Within 3 24 5.200652 0.006557 0.346392 0.694329
2. One-way repeated-measures ANOVA using a long-format dataset.
We're also specifying two additional options here: ``detailed=True`` means
that we'll get a more detailed ANOVA table, and ``effsize='np2'``
means that we want to get the partial eta-squared effect size instead
of the default (generalized) eta-squared.
>>> df = pg.read_dataset('rm_anova')
>>> aov = pg.rm_anova(dv='DesireToKill', within='Disgustingness',
... subject='Subject', data=df, detailed=True, effsize="np2")
>>> aov.round(3)
Source SS DF MS F p-unc np2 eps
0 Disgustingness 27.485 1 27.485 12.044 0.001 0.116 1.0
1 Error 209.952 92 2.282 NaN NaN NaN NaN
3. Two-way repeated-measures ANOVA
>>> aov = pg.rm_anova(dv='DesireToKill', within=['Disgustingness', 'Frighteningness'],
... subject='Subject', data=df)
4. As a :py:class:`pandas.DataFrame` method
>>> df.rm_anova(dv='DesireToKill', within='Disgustingness', subject='Subject', detailed=False)
Source ddof1 ddof2 F p-unc ng2 eps
0 Disgustingness 1 92 12.043878 0.000793 0.025784 1.0
"""
assert effsize in ["n2", "np2", "ng2"], "effsize must be n2, np2 or ng2."
if isinstance(within, list):
assert len(within) > 0, "Within cannot be empty."
if len(within) == 1:
within = within[0]
elif len(within) == 2:
return rm_anova2(dv=dv, within=within, data=data, subject=subject, effsize=effsize)
else:
raise ValueError("Repeated measures ANOVA with three or more factors is not supported.")
# Convert from wide to long-format, if needed
if all([v is None for v in [dv, within, subject]]):
assert isinstance(data, pd.DataFrame)
data = data._get_numeric_data().d | (data=None, dv=None, within=None, subject=None, correction='auto', detailed=False, effsize='ng2') | [
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|
32,060 | pingouin.correlation | rm_corr | Repeated measures correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x, y : string
Name of columns in ``data`` containing the two dependent variables.
subject : string
Name of column in ``data`` containing the subject indicator.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'r'``: Repeated measures correlation coefficient
* ``'dof'``: Degrees of freedom
* ``'pval'``: p-value
* ``'CI95'``: 95% parametric confidence intervals
* ``'power'``: achieved power of the test (= 1 - type II error).
See also
--------
plot_rm_corr
Notes
-----
Repeated measures correlation (rmcorr) is a statistical technique for determining the common
within-individual association for paired measures assessed on two or more occasions for
multiple individuals.
From `Bakdash and Marusich (2017)
<https://doi.org/10.3389/fpsyg.2017.00456>`_:
*Rmcorr accounts for non-independence among observations using analysis
of covariance (ANCOVA) to statistically adjust for inter-individual
variability. By removing measured variance between-participants,
rmcorr provides the best linear fit for each participant using parallel
regression lines (the same slope) with varying intercepts.
Like a Pearson correlation coefficient, the rmcorr coefficient
is bounded by − 1 to 1 and represents the strength of the linear
association between two variables.*
Results have been tested against the `rmcorr <https://github.com/cran/rmcorr>`_ R package.
Missing values are automatically removed from the dataframe (listwise deletion).
Examples
--------
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> pg.rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
r dof pval CI95% power
rm_corr -0.50677 38 0.000847 [-0.71, -0.23] 0.929579
Now plot using the :py:func:`pingouin.plot_rm_corr` function:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
| def rm_corr(data=None, x=None, y=None, subject=None):
"""Repeated measures correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Dataframe.
x, y : string
Name of columns in ``data`` containing the two dependent variables.
subject : string
Name of column in ``data`` containing the subject indicator.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'r'``: Repeated measures correlation coefficient
* ``'dof'``: Degrees of freedom
* ``'pval'``: p-value
* ``'CI95'``: 95% parametric confidence intervals
* ``'power'``: achieved power of the test (= 1 - type II error).
See also
--------
plot_rm_corr
Notes
-----
Repeated measures correlation (rmcorr) is a statistical technique for determining the common
within-individual association for paired measures assessed on two or more occasions for
multiple individuals.
From `Bakdash and Marusich (2017)
<https://doi.org/10.3389/fpsyg.2017.00456>`_:
*Rmcorr accounts for non-independence among observations using analysis
of covariance (ANCOVA) to statistically adjust for inter-individual
variability. By removing measured variance between-participants,
rmcorr provides the best linear fit for each participant using parallel
regression lines (the same slope) with varying intercepts.
Like a Pearson correlation coefficient, the rmcorr coefficient
is bounded by − 1 to 1 and represents the strength of the linear
association between two variables.*
Results have been tested against the `rmcorr <https://github.com/cran/rmcorr>`_ R package.
Missing values are automatically removed from the dataframe (listwise deletion).
Examples
--------
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> pg.rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
r dof pval CI95% power
rm_corr -0.50677 38 0.000847 [-0.71, -0.23] 0.929579
Now plot using the :py:func:`pingouin.plot_rm_corr` function:
.. plot::
>>> import pingouin as pg
>>> df = pg.read_dataset('rm_corr')
>>> g = pg.plot_rm_corr(data=df, x='pH', y='PacO2', subject='Subject')
"""
from pingouin import ancova, power_corr
# Safety checks
assert isinstance(data, pd.DataFrame), "Data must be a DataFrame"
assert x in data.columns, "The %s column is not in data." % x
assert y in data.columns, "The %s column is not in data." % y
assert data[x].dtype.kind in "bfiu", "%s must be numeric." % x
assert data[y].dtype.kind in "bfiu", "%s must be numeric." % y
assert subject in data.columns, "The %s column is not in data." % subject
if data[subject].nunique() < 3:
raise ValueError("rm_corr requires at least 3 unique subjects.")
# Remove missing values
data = data[[x, y, subject]].dropna(axis=0)
# Using PINGOUIN
# For max precision, make sure rounding is disabled
old_options = options.copy()
options["round"] = None
aov = ancova(dv=y, covar=x, between=subject, data=data)
options.update(old_options) # restore options
bw = aov.bw_ # Beta within parameter
sign = np.sign(bw)
dof = int(aov.at[2, "DF"])
n = dof + 2
ssfactor = aov.at[1, "SS"]
sserror = aov.at[2, "SS"]
rm = sign * np.sqrt(ssfactor / (ssfactor + sserror))
pval = aov.at[1, "p-unc"]
ci = compute_esci(stat=rm, nx=n, eftype="pearson").tolist()
pwr = power_corr(r=rm, n=n, alternative="two-sided")
# Convert to Dataframe
stats = pd.DataFrame(
{"r": rm, "dof": int(dof), "pval": pval, "CI95%": [ci], "power": pwr}, index=["rm_corr"]
)
return _postprocess_dataframe(stats)
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|
32,061 | pingouin.config | set_default_options | Reset Pingouin's default global options (e.g. rounding).
.. versionadded:: 0.3.8
| def set_default_options():
"""Reset Pingouin's default global options (e.g. rounding).
.. versionadded:: 0.3.8
"""
options.clear()
# Rounding behavior
options["round"] = None
options["round.column.CI95%"] = 2
# default is to return Bayes factors inside DataFrames as formatted str
options["round.column.BF10"] = _format_bf
| () | [
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|
32,062 | pingouin.distribution | sphericity | Mauchly and JNS test for sphericity.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame containing the repeated measurements.
Both wide and long-format dataframe are supported for this function.
To test for an interaction term between two repeated measures factors
with a wide-format dataframe, ``data`` must have a two-levels
:py:class:`pandas.MultiIndex` columns.
dv : string
Name of column containing the dependent variable (only required if
``data`` is in long format).
within : string
Name of column containing the within factor (only required if ``data``
is in long format).
If ``within`` is a list with two strings, this function computes
the epsilon factor for the interaction between the two within-subject
factor.
subject : string
Name of column containing the subject identifier (only required if
``data`` is in long format).
method : str
Method to compute sphericity:
* `'jns'`: John, Nagao and Sugiura test.
* `'mauchly'`: Mauchly test (default).
alpha : float
Significance level
Returns
-------
spher : boolean
True if data have the sphericity property.
W : float
Test statistic.
chi2 : float
Chi-square statistic.
dof : int
Degrees of freedom.
pval : float
P-value.
Raises
------
ValueError
When testing for an interaction, if both within-subject factors have
more than 2 levels (not yet supported in Pingouin).
See Also
--------
epsilon : Epsilon adjustement factor for repeated measures.
homoscedasticity : Test equality of variance.
normality : Univariate normality test.
Notes
-----
The **Mauchly** :math:`W` statistic [1]_ is defined by:
.. math::
W = \frac{\prod \lambda_j}{(\frac{1}{k-1} \sum \lambda_j)^{k-1}}
where :math:`\lambda_j` are the eigenvalues of the population
covariance matrix (= double-centered sample covariance matrix) and
:math:`k` is the number of conditions.
From then, the :math:`W` statistic is transformed into a chi-square
score using the number of observations per condition :math:`n`
.. math:: f = \frac{2(k-1)^2+k+1}{6(k-1)(n-1)}
.. math:: \chi_w^2 = (f-1)(n-1) \text{log}(W)
The p-value is then approximated using a chi-square distribution:
.. math:: \chi_w^2 \sim \chi^2(\frac{k(k-1)}{2}-1)
The **JNS** :math:`V` statistic ([2]_, [3]_, [4]_) is defined by:
.. math::
V = \frac{(\sum_j^{k-1} \lambda_j)^2}{\sum_j^{k-1} \lambda_j^2}
.. math:: \chi_v^2 = \frac{n}{2} (k-1)^2 (V - \frac{1}{k-1})
and the p-value approximated using a chi-square distribution
.. math:: \chi_v^2 \sim \chi^2(\frac{k(k-1)}{2}-1)
Missing values are automatically removed from ``data`` (listwise deletion).
References
----------
.. [1] Mauchly, J. W. (1940). Significance test for sphericity of a normal
n-variate distribution. The Annals of Mathematical Statistics,
11(2), 204-209.
.. [2] Nagao, H. (1973). On some test criteria for covariance matrix.
The Annals of Statistics, 700-709.
.. [3] Sugiura, N. (1972). Locally best invariant test for sphericity and
the limiting distributions. The Annals of Mathematical Statistics,
1312-1316.
.. [4] John, S. (1972). The distribution of a statistic used for testing
sphericity of normal distributions. Biometrika, 59(1), 169-173.
See also http://www.real-statistics.com/anova-repeated-measures/sphericity/
Examples
--------
Mauchly test for sphericity using a wide-format dataframe
>>> import pandas as pd
>>> import pingouin as pg
>>> data = pd.DataFrame({'A': [2.2, 3.1, 4.3, 4.1, 7.2],
... 'B': [1.1, 2.5, 4.1, 5.2, 6.4],
... 'C': [8.2, 4.5, 3.4, 6.2, 7.2]})
>>> spher, W, chisq, dof, pval = pg.sphericity(data)
>>> print(spher, round(W, 3), round(chisq, 3), dof, round(pval, 3))
True 0.21 4.677 2 0.096
John, Nagao and Sugiura (JNS) test
>>> round(pg.sphericity(data, method='jns')[-1], 3) # P-value only
0.046
Now using a long-format dataframe
>>> data = pg.read_dataset('rm_anova2')
>>> data.head()
Subject Time Metric Performance
0 1 Pre Product 13
1 2 Pre Product 12
2 3 Pre Product 17
3 4 Pre Product 12
4 5 Pre Product 19
Let's first test sphericity for the *Time* within-subject factor
>>> pg.sphericity(data, dv='Performance', subject='Subject',
... within='Time')
(True, nan, nan, 1, 1.0)
Since *Time* has only two levels (Pre and Post), the sphericity assumption
is necessarily met.
The *Metric* factor, however, has three levels:
>>> round(pg.sphericity(data, dv='Performance', subject='Subject',
... within=['Metric'])[-1], 3)
0.878
The p-value value is very large, and the test therefore indicates that
there is no violation of sphericity.
Now, let's calculate the epsilon for the interaction between the two
repeated measures factor. The current implementation in Pingouin only works
if at least one of the two within-subject factors has no more than two
levels.
>>> spher, _, chisq, dof, pval = pg.sphericity(data, dv='Performance',
... subject='Subject',
... within=['Time', 'Metric'])
>>> print(spher, round(chisq, 3), dof, round(pval, 3))
True 3.763 2 0.152
Here again, there is no violation of sphericity acccording to Mauchly's
test.
Alternatively, we could use a wide-format dataframe with two column
levels:
>>> # Pivot from long-format to wide-format
>>> piv = data.pivot(index='Subject', columns=['Time', 'Metric'], values='Performance')
>>> piv.head()
Time Pre Post
Metric Product Client Action Product Client Action
Subject
1 13 12 17 18 30 34
2 12 19 18 6 18 30
3 17 19 24 21 31 32
4 12 25 25 18 39 40
5 19 27 19 18 28 27
>>> spher, _, chisq, dof, pval = pg.sphericity(piv)
>>> print(spher, round(chisq, 3), dof, round(pval, 3))
True 3.763 2 0.152
which gives the same output as the long-format dataframe.
| def sphericity(data, dv=None, within=None, subject=None, method="mauchly", alpha=0.05):
"""Mauchly and JNS test for sphericity.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame containing the repeated measurements.
Both wide and long-format dataframe are supported for this function.
To test for an interaction term between two repeated measures factors
with a wide-format dataframe, ``data`` must have a two-levels
:py:class:`pandas.MultiIndex` columns.
dv : string
Name of column containing the dependent variable (only required if
``data`` is in long format).
within : string
Name of column containing the within factor (only required if ``data``
is in long format).
If ``within`` is a list with two strings, this function computes
the epsilon factor for the interaction between the two within-subject
factor.
subject : string
Name of column containing the subject identifier (only required if
``data`` is in long format).
method : str
Method to compute sphericity:
* `'jns'`: John, Nagao and Sugiura test.
* `'mauchly'`: Mauchly test (default).
alpha : float
Significance level
Returns
-------
spher : boolean
True if data have the sphericity property.
W : float
Test statistic.
chi2 : float
Chi-square statistic.
dof : int
Degrees of freedom.
pval : float
P-value.
Raises
------
ValueError
When testing for an interaction, if both within-subject factors have
more than 2 levels (not yet supported in Pingouin).
See Also
--------
epsilon : Epsilon adjustement factor for repeated measures.
homoscedasticity : Test equality of variance.
normality : Univariate normality test.
Notes
-----
The **Mauchly** :math:`W` statistic [1]_ is defined by:
.. math::
W = \\frac{\\prod \\lambda_j}{(\\frac{1}{k-1} \\sum \\lambda_j)^{k-1}}
where :math:`\\lambda_j` are the eigenvalues of the population
covariance matrix (= double-centered sample covariance matrix) and
:math:`k` is the number of conditions.
From then, the :math:`W` statistic is transformed into a chi-square
score using the number of observations per condition :math:`n`
.. math:: f = \\frac{2(k-1)^2+k+1}{6(k-1)(n-1)}
.. math:: \\chi_w^2 = (f-1)(n-1) \\text{log}(W)
The p-value is then approximated using a chi-square distribution:
.. math:: \\chi_w^2 \\sim \\chi^2(\\frac{k(k-1)}{2}-1)
The **JNS** :math:`V` statistic ([2]_, [3]_, [4]_) is defined by:
.. math::
V = \\frac{(\\sum_j^{k-1} \\lambda_j)^2}{\\sum_j^{k-1} \\lambda_j^2}
.. math:: \\chi_v^2 = \\frac{n}{2} (k-1)^2 (V - \\frac{1}{k-1})
and the p-value approximated using a chi-square distribution
.. math:: \\chi_v^2 \\sim \\chi^2(\\frac{k(k-1)}{2}-1)
Missing values are automatically removed from ``data`` (listwise deletion).
References
----------
.. [1] Mauchly, J. W. (1940). Significance test for sphericity of a normal
n-variate distribution. The Annals of Mathematical Statistics,
11(2), 204-209.
.. [2] Nagao, H. (1973). On some test criteria for covariance matrix.
The Annals of Statistics, 700-709.
.. [3] Sugiura, N. (1972). Locally best invariant test for sphericity and
the limiting distributions. The Annals of Mathematical Statistics,
1312-1316.
.. [4] John, S. (1972). The distribution of a statistic used for testing
sphericity of normal distributions. Biometrika, 59(1), 169-173.
See also http://www.real-statistics.com/anova-repeated-measures/sphericity/
Examples
--------
Mauchly test for sphericity using a wide-format dataframe
>>> import pandas as pd
>>> import pingouin as pg
>>> data = pd.DataFrame({'A': [2.2, 3.1, 4.3, 4.1, 7.2],
... 'B': [1.1, 2.5, 4.1, 5.2, 6.4],
... 'C': [8.2, 4.5, 3.4, 6.2, 7.2]})
>>> spher, W, chisq, dof, pval = pg.sphericity(data)
>>> print(spher, round(W, 3), round(chisq, 3), dof, round(pval, 3))
True 0.21 4.677 2 0.096
John, Nagao and Sugiura (JNS) test
>>> round(pg.sphericity(data, method='jns')[-1], 3) # P-value only
0.046
Now using a long-format dataframe
>>> data = pg.read_dataset('rm_anova2')
>>> data.head()
Subject Time Metric Performance
0 1 Pre Product 13
1 2 Pre Product 12
2 3 Pre Product 17
3 4 Pre Product 12
4 5 Pre Product 19
Let's first test sphericity for the *Time* within-subject factor
>>> pg.sphericity(data, dv='Performance', subject='Subject',
... within='Time')
(True, nan, nan, 1, 1.0)
Since *Time* has only two levels (Pre and Post), the sphericity assumption
is necessarily met.
The *Metric* factor, however, has three levels:
>>> round(pg.sphericity(data, dv='Performance', subject='Subject',
... within=['Metric'])[-1], 3)
0.878
The p-value value is very large, and the test therefore indicates that
there is no violation of sphericity.
Now, let's calculate the epsilon for the interaction between the two
repeated measures factor. The current implementation in Pingouin only works
if at least one of the two within-subject factors has no more than two
levels.
>>> spher, _, chisq, dof, pval = pg.sphericity(data, dv='Performance',
... subject='Subject',
... within=['Time', 'Metric'])
>>> print(spher, round(chisq, 3), dof, round(pval, 3))
True 3.763 2 0.152
Here again, there is no violation of sphericity acccording to Mauchly's
test.
Alternatively, we could use a wide-format dataframe with two column
levels:
>>> # Pivot from long-format to wide-format
>>> piv = data.pivot(index='Subject', columns=['Time', 'Metric'], values='Performance')
>>> piv.head()
Time Pre Post
Metric Product Client Action Product Client Action
Subject
1 13 12 17 18 30 34
2 12 19 18 6 18 30
3 17 19 24 21 31 32
4 12 25 25 18 39 40
5 19 27 19 18 28 27
>>> spher, _, chisq, dof, pval = pg.sphericity(piv)
>>> print(spher, round(chisq, 3), dof, round(pval, 3))
True 3.763 2 0.152
which gives the same output as the long-format dataframe.
"""
assert isinstance(data, pd.DataFrame), "Data must be a pandas Dataframe."
# If data is in long-format, convert to wide-format
if all([v is not None for v in [dv, within, subject]]):
data = _long_to_wide_rm(data, dv=dv, within=within, subject=subject)
# From now on we assume that data is in wide-format and contains only
# the relevant columns.
# Remove rows with missing values in wide-format dataframe
data = data.dropna()
# Support for two-way factor of shape (2, N)
data = _check_multilevel_rm(data, func="mauchly")
# From here, we work only with one-way design
n, k = data.shape
d = k - 1
# Sphericity is always met with only two repeated measures.
if k <= 2:
return True, np.nan, np.nan, 1, 1.0
# Compute dof of the test
ddof = (d * (d + 1)) / 2 - 1
ddof = 1 if ddof == 0 else ddof
if method.lower() == "mauchly":
# Method 1. Contrast matrix. Similar to R & Matlab implementation.
# Only works for one-way design or two-way design with shape (2, N).
# 1 - Compute the successive difference matrix Z.
# (Note that the order of columns does not matter.)
# 2 - Find the contrast matrix that M so that data * M = Z
# 3 - Performs the QR decomposition of this matrix | (data, dv=None, within=None, subject=None, method='mauchly', alpha=0.05) | [
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|
32,063 | pingouin.equivalence | tost | Two One-Sided Test (TOST) for equivalence.
Parameters
----------
x, y : array_like
First and second set of observations. ``x`` and ``y`` should have the
same units. If ``y`` is a single value (e.g. 0), a one-sample test is
performed.
bound : float
Magnitude of region of similarity (a.k.a epsilon). Note that this
should be expressed in the same unit as ``x`` and ``y``.
paired : boolean
Specify whether the two observations are related (i.e. repeated
measures) or independent.
correction : auto or boolean
Specify whether or not to correct for unequal variances using Welch
separate variances T-test. This only applies if ``paired`` is False.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'bound'``: bound (= epsilon, or equivalence margin)
* ``'dof'``: degrees of freedom
* ``'pval'``: TOST p-value
See also
--------
ttest
References
----------
.. [1] Schuirmann, D.L. 1981. On hypothesis testing to determine if the
mean of a normal distribution is contained in a known interval.
Biometrics 37 617.
.. [2] https://cran.r-project.org/web/packages/equivalence/equivalence.pdf
Examples
--------
1. Independent two-sample TOST with a region of similarity of 1 (default)
>>> import pingouin as pg
>>> a = [4, 7, 8, 6, 3, 2]
>>> b = [6, 8, 7, 10, 11, 9]
>>> pg.tost(a, b)
bound dof pval
TOST 1 10 0.965097
2. Paired TOST with a different region of similarity
>>> pg.tost(a, b, bound=0.5, paired=True)
bound dof pval
TOST 0.5 5 0.954854
3. One sample TOST
>>> pg.tost(a, y=0, bound=4)
bound dof pval
TOST 4 5 0.825967
| def tost(x, y, bound=1, paired=False, correction=False):
"""Two One-Sided Test (TOST) for equivalence.
Parameters
----------
x, y : array_like
First and second set of observations. ``x`` and ``y`` should have the
same units. If ``y`` is a single value (e.g. 0), a one-sample test is
performed.
bound : float
Magnitude of region of similarity (a.k.a epsilon). Note that this
should be expressed in the same unit as ``x`` and ``y``.
paired : boolean
Specify whether the two observations are related (i.e. repeated
measures) or independent.
correction : auto or boolean
Specify whether or not to correct for unequal variances using Welch
separate variances T-test. This only applies if ``paired`` is False.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'bound'``: bound (= epsilon, or equivalence margin)
* ``'dof'``: degrees of freedom
* ``'pval'``: TOST p-value
See also
--------
ttest
References
----------
.. [1] Schuirmann, D.L. 1981. On hypothesis testing to determine if the
mean of a normal distribution is contained in a known interval.
Biometrics 37 617.
.. [2] https://cran.r-project.org/web/packages/equivalence/equivalence.pdf
Examples
--------
1. Independent two-sample TOST with a region of similarity of 1 (default)
>>> import pingouin as pg
>>> a = [4, 7, 8, 6, 3, 2]
>>> b = [6, 8, 7, 10, 11, 9]
>>> pg.tost(a, b)
bound dof pval
TOST 1 10 0.965097
2. Paired TOST with a different region of similarity
>>> pg.tost(a, b, bound=0.5, paired=True)
bound dof pval
TOST 0.5 5 0.954854
3. One sample TOST
>>> pg.tost(a, y=0, bound=4)
bound dof pval
TOST 4 5 0.825967
"""
x = np.asarray(x)
y = np.asarray(y)
assert isinstance(bound, (int, float)), "bound must be int or float."
# T-tests
df_a = ttest(x + bound, y, paired=paired, correction=correction, alternative="greater")
df_b = ttest(x - bound, y, paired=paired, correction=correction, alternative="less")
pval = max(df_a.at["T-test", "p-val"], df_b.at["T-test", "p-val"])
# Create output dataframe
stats = pd.DataFrame(
{"bound": bound, "dof": df_a.at["T-test", "dof"], "pval": pval}, index=["TOST"]
)
return _postprocess_dataframe(stats)
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|
32,064 | pingouin.parametric | ttest | T-test.
Parameters
----------
x : array_like
First set of observations.
y : array_like or float
Second set of observations. If ``y`` is a single value, a one-sample
T-test is computed against that value (= "mu" in the t.test R
function).
paired : boolean
Specify whether the two observations are related (i.e. repeated
measures) or independent.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return one-sided
p-values. "greater" tests against the alternative hypothesis that the mean of ``x``
is greater than the mean of ``y``.
correction : string or boolean
For unpaired two sample T-tests, specify whether or not to correct for
unequal variances using Welch separate variances T-test. If 'auto', it
will automatically uses Welch T-test when the sample sizes are unequal,
as recommended by Zimmerman 2004.
r : float
Cauchy scale factor for computing the Bayes Factor.
Smaller values of r (e.g. 0.5), may be appropriate when small effect
sizes are expected a priori; larger values of r are appropriate when
large effect sizes are expected (Rouder et al 2009).
The default is 0.707 (= :math:`\sqrt{2} / 2`).
confidence : float
Confidence level for the confidence intervals (0.95 = 95%)
.. versionadded:: 0.3.9
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'T'``: T-value
* ``'dof'``: degrees of freedom
* ``'alternative'``: alternative of the test
* ``'p-val'``: p-value
* ``'CI95%'``: confidence intervals of the difference in means
* ``'cohen-d'``: Cohen d effect size
* ``'BF10'``: Bayes Factor of the alternative hypothesis
* ``'power'``: achieved power of the test ( = 1 - type II error)
See also
--------
mwu, wilcoxon, anova, rm_anova, pairwise_tests, compute_effsize
Notes
-----
Missing values are automatically removed from the data. If ``x`` and
``y`` are paired, the entire row is removed (= listwise deletion).
The **T-value for unpaired samples** is defined as:
.. math::
t = \frac{\overline{x} - \overline{y}}
{\sqrt{\frac{s^{2}_{x}}{n_{x}} + \frac{s^{2}_{y}}{n_{y}}}}
where :math:`\overline{x}` and :math:`\overline{y}` are the sample means,
:math:`n_{x}` and :math:`n_{y}` are the sample sizes, and
:math:`s^{2}_{x}` and :math:`s^{2}_{y}` are the sample variances.
The degrees of freedom :math:`v` are :math:`n_x + n_y - 2` when the sample
sizes are equal. When the sample sizes are unequal or when
:code:`correction=True`, the Welch–Satterthwaite equation is used to
approximate the adjusted degrees of freedom:
.. math::
v = \frac{(\frac{s^{2}_{x}}{n_{x}} + \frac{s^{2}_{y}}{n_{y}})^{2}}
{\frac{(\frac{s^{2}_{x}}{n_{x}})^{2}}{(n_{x}-1)} +
\frac{(\frac{s^{2}_{y}}{n_{y}})^{2}}{(n_{y}-1)}}
The p-value is then calculated using a T distribution with :math:`v`
degrees of freedom.
The T-value for **paired samples** is defined by:
.. math:: t = \frac{\overline{x}_d}{s_{\overline{x}}}
where
.. math:: s_{\overline{x}} = \frac{s_d}{\sqrt n}
where :math:`\overline{x}_d` is the sample mean of the differences
between the two paired samples, :math:`n` is the number of observations
(sample size), :math:`s_d` is the sample standard deviation of the
differences and :math:`s_{\overline{x}}` is the estimated standard error
of the mean of the differences. The p-value is then calculated using a
T-distribution with :math:`n-1` degrees of freedom.
The scaled Jeffrey-Zellner-Siow (JZS) Bayes Factor is approximated
using the :py:func:`pingouin.bayesfactor_ttest` function.
Results have been tested against JASP and the `t.test` R function.
References
----------
* https://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
* Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should
by default use Welch’s t-test instead of Student’s t-test.
International Review of Social Psychology, 30(1).
* Zimmerman, D. W. (2004). A note on preliminary tests of equality of
variances. British Journal of Mathematical and Statistical
Psychology, 57(1), 173-181.
* Rouder, J.N., Speckman, P.L., Sun, D., Morey, R.D., Iverson, G.,
2009. Bayesian t tests for accepting and rejecting the null
hypothesis. Psychon. Bull. Rev. 16, 225–237.
https://doi.org/10.3758/PBR.16.2.225
Examples
--------
1. One-sample T-test.
>>> from pingouin import ttest
>>> x = [5.5, 2.4, 6.8, 9.6, 4.2]
>>> ttest(x, 4).round(2)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 1.4 4 two-sided 0.23 [2.32, 9.08] 0.62 0.766 0.19
2. One sided paired T-test.
>>> pre = [5.5, 2.4, 6.8, 9.6, 4.2]
>>> post = [6.4, 3.4, 6.4, 11., 4.8]
>>> ttest(pre, post, paired=True, alternative='less').round(2)
T dof alternative p-val CI95% cohen-d BF10 power
T-test -2.31 4 less 0.04 [-inf, -0.05] 0.25 3.122 0.12
Now testing the opposite alternative hypothesis
>>> ttest(pre, post, paired=True, alternative='greater').round(2)
T dof alternative p-val CI95% cohen-d BF10 power
T-test -2.31 4 greater 0.96 [-1.35, inf] 0.25 0.32 0.02
3. Paired T-test with missing values.
>>> import numpy as np
>>> pre = [5.5, 2.4, np.nan, 9.6, 4.2]
>>> post = [6.4, 3.4, 6.4, 11., 4.8]
>>> ttest(pre, post, paired=True).round(3)
T dof alternative p-val CI95% cohen-d BF10 power
T-test -5.902 3 two-sided 0.01 [-1.5, -0.45] 0.306 7.169 0.073
Compare with SciPy
>>> from scipy.stats import ttest_rel
>>> np.round(ttest_rel(pre, post, nan_policy="omit"), 3)
array([-5.902, 0.01 ])
4. Independent two-sample T-test with equal sample size.
>>> np.random.seed(123)
>>> x = np.random.normal(loc=7, size=20)
>>> y = np.random.normal(loc=4, size=20)
>>> ttest(x, y)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 9.106452 38 two-sided 4.306971e-11 [2.64, 4.15] 2.879713 1.366e+08 1.0
5. Independent two-sample T-test with unequal sample size. A Welch's T-test is used.
>>> np.random.seed(123)
>>> y = np.random.normal(loc=6.5, size=15)
>>> ttest(x, y)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 1.996537 31.567592 two-sided 0.054561 [-0.02, 1.65] 0.673518 1.469 0.481867
6. However, the Welch's correction can be disabled:
>>> ttest(x, y, correction=False)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 1.971859 33 two-sided 0.057056 [-0.03, 1.66] 0.673518 1.418 0.481867
Compare with SciPy
>>> from scipy.stats import ttest_ind
>>> np.round(ttest_ind(x, y, equal_var=True), 6) # T value and p-value
array([1.971859, 0.057056])
| def ttest(x, y, paired=False, alternative="two-sided", correction="auto", r=0.707, confidence=0.95):
"""T-test.
Parameters
----------
x : array_like
First set of observations.
y : array_like or float
Second set of observations. If ``y`` is a single value, a one-sample
T-test is computed against that value (= "mu" in the t.test R
function).
paired : boolean
Specify whether the two observations are related (i.e. repeated
measures) or independent.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". Both "greater" and "less" return one-sided
p-values. "greater" tests against the alternative hypothesis that the mean of ``x``
is greater than the mean of ``y``.
correction : string or boolean
For unpaired two sample T-tests, specify whether or not to correct for
unequal variances using Welch separate variances T-test. If 'auto', it
will automatically uses Welch T-test when the sample sizes are unequal,
as recommended by Zimmerman 2004.
r : float
Cauchy scale factor for computing the Bayes Factor.
Smaller values of r (e.g. 0.5), may be appropriate when small effect
sizes are expected a priori; larger values of r are appropriate when
large effect sizes are expected (Rouder et al 2009).
The default is 0.707 (= :math:`\\sqrt{2} / 2`).
confidence : float
Confidence level for the confidence intervals (0.95 = 95%)
.. versionadded:: 0.3.9
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'T'``: T-value
* ``'dof'``: degrees of freedom
* ``'alternative'``: alternative of the test
* ``'p-val'``: p-value
* ``'CI95%'``: confidence intervals of the difference in means
* ``'cohen-d'``: Cohen d effect size
* ``'BF10'``: Bayes Factor of the alternative hypothesis
* ``'power'``: achieved power of the test ( = 1 - type II error)
See also
--------
mwu, wilcoxon, anova, rm_anova, pairwise_tests, compute_effsize
Notes
-----
Missing values are automatically removed from the data. If ``x`` and
``y`` are paired, the entire row is removed (= listwise deletion).
The **T-value for unpaired samples** is defined as:
.. math::
t = \\frac{\\overline{x} - \\overline{y}}
{\\sqrt{\\frac{s^{2}_{x}}{n_{x}} + \\frac{s^{2}_{y}}{n_{y}}}}
where :math:`\\overline{x}` and :math:`\\overline{y}` are the sample means,
:math:`n_{x}` and :math:`n_{y}` are the sample sizes, and
:math:`s^{2}_{x}` and :math:`s^{2}_{y}` are the sample variances.
The degrees of freedom :math:`v` are :math:`n_x + n_y - 2` when the sample
sizes are equal. When the sample sizes are unequal or when
:code:`correction=True`, the Welch–Satterthwaite equation is used to
approximate the adjusted degrees of freedom:
.. math::
v = \\frac{(\\frac{s^{2}_{x}}{n_{x}} + \\frac{s^{2}_{y}}{n_{y}})^{2}}
{\\frac{(\\frac{s^{2}_{x}}{n_{x}})^{2}}{(n_{x}-1)} +
\\frac{(\\frac{s^{2}_{y}}{n_{y}})^{2}}{(n_{y}-1)}}
The p-value is then calculated using a T distribution with :math:`v`
degrees of freedom.
The T-value for **paired samples** is defined by:
.. math:: t = \\frac{\\overline{x}_d}{s_{\\overline{x}}}
where
.. math:: s_{\\overline{x}} = \\frac{s_d}{\\sqrt n}
where :math:`\\overline{x}_d` is the sample mean of the differences
between the two paired samples, :math:`n` is the number of observations
(sample size), :math:`s_d` is the sample standard deviation of the
differences and :math:`s_{\\overline{x}}` is the estimated standard error
of the mean of the differences. The p-value is then calculated using a
T-distribution with :math:`n-1` degrees of freedom.
The scaled Jeffrey-Zellner-Siow (JZS) Bayes Factor is approximated
using the :py:func:`pingouin.bayesfactor_ttest` function.
Results have been tested against JASP and the `t.test` R function.
References
----------
* https://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
* Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should
by default use Welch’s t-test instead of Student’s t-test.
International Review of Social Psychology, 30(1).
* Zimmerman, D. W. (2004). A note on preliminary tests of equality of
variances. British Journal of Mathematical and Statistical
Psychology, 57(1), 173-181.
* Rouder, J.N., Speckman, P.L., Sun, D., Morey, R.D., Iverson, G.,
2009. Bayesian t tests for accepting and rejecting the null
hypothesis. Psychon. Bull. Rev. 16, 225–237.
https://doi.org/10.3758/PBR.16.2.225
Examples
--------
1. One-sample T-test.
>>> from pingouin import ttest
>>> x = [5.5, 2.4, 6.8, 9.6, 4.2]
>>> ttest(x, 4).round(2)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 1.4 4 two-sided 0.23 [2.32, 9.08] 0.62 0.766 0.19
2. One sided paired T-test.
>>> pre = [5.5, 2.4, 6.8, 9.6, 4.2]
>>> post = [6.4, 3.4, 6.4, 11., 4.8]
>>> ttest(pre, post, paired=True, alternative='less').round(2)
T dof alternative p-val CI95% cohen-d BF10 power
T-test -2.31 4 less 0.04 [-inf, -0.05] 0.25 3.122 0.12
Now testing the opposite alternative hypothesis
>>> ttest(pre, post, paired=True, alternative='greater').round(2)
T dof alternative p-val CI95% cohen-d BF10 power
T-test -2.31 4 greater 0.96 [-1.35, inf] 0.25 0.32 0.02
3. Paired T-test with missing values.
>>> import numpy as np
>>> pre = [5.5, 2.4, np.nan, 9.6, 4.2]
>>> post = [6.4, 3.4, 6.4, 11., 4.8]
>>> ttest(pre, post, paired=True).round(3)
T dof alternative p-val CI95% cohen-d BF10 power
T-test -5.902 3 two-sided 0.01 [-1.5, -0.45] 0.306 7.169 0.073
Compare with SciPy
>>> from scipy.stats import ttest_rel
>>> np.round(ttest_rel(pre, post, nan_policy="omit"), 3)
array([-5.902, 0.01 ])
4. Independent two-sample T-test with equal sample size.
>>> np.random.seed(123)
>>> x = np.random.normal(loc=7, size=20)
>>> y = np.random.normal(loc=4, size=20)
>>> ttest(x, y)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 9.106452 38 two-sided 4.306971e-11 [2.64, 4.15] 2.879713 1.366e+08 1.0
5. Independent two-sample T-test with unequal sample size. A Welch's T-test is used.
>>> np.random.seed(123)
>>> y = np.random.normal(loc=6.5, size=15)
>>> ttest(x, y)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 1.996537 31.567592 two-sided 0.054561 [-0.02, 1.65] 0.673518 1.469 0.481867
6. However, the Welch's correction can be disabled:
>>> ttest(x, y, correction=False)
T dof alternative p-val CI95% cohen-d BF10 power
T-test 1.971859 33 two-sided 0.057056 [-0.03, 1.66] 0.673518 1.418 0.481867
Compare with SciPy
>>> from scipy.stats import ttest_ind
>>> np.round(ttest_ind(x, y, equal_var=True), 6) # T value and p-value
array([1.971859, 0.057056])
"""
from scipy.stats import t, ttest_rel, ttest_ind, ttest_1samp
try: # pragma: no cover
from scipy.stats._stats_py import _unequal_var_ttest_denom, _equal_var_ttest_denom
except ImportError: # pragma: no cover
# Fallback for scipy<1.8.0
from scipy.stats.stats import _unequal_var_ttest_denom, _equal_var_ttest_denom
from pingouin import power_ttest, power_ttest2n, compute_effsize
# Check arguments
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
assert 0 < confidence < 1, "c | (x, y, paired=False, alternative='two-sided', correction='auto', r=0.707, confidence=0.95) | [
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|
32,066 | pingouin.parametric | welch_anova | One-way Welch ANOVA.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
between : string
Name of column containing the between factor.
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Factor names
* ``'ddof1'``: Numerator degrees of freedom
* ``'ddof2'``: Denominator degrees of freedom
* ``'F'``: F-values
* ``'p-unc'``: uncorrected p-values
* ``'np2'``: Partial eta-squared
See Also
--------
anova : One-way and N-way ANOVA
rm_anova : One-way and two-way repeated measures ANOVA
mixed_anova : Two way mixed ANOVA
kruskal : Non-parametric one-way ANOVA
Notes
-----
From Wikipedia:
*It is named for its creator, Bernard Lewis Welch, and is an adaptation of
Student's t-test, and is more reliable when the two samples have
unequal variances and/or unequal sample sizes.*
The classic ANOVA is very powerful when the groups are normally distributed
and have equal variances. However, when the groups have unequal variances,
it is best to use the Welch ANOVA that better controls for
type I error (Liu 2015). The homogeneity of variances can be measured with
the `homoscedasticity` function. The two other assumptions of
normality and independance remain.
The main idea of Welch ANOVA is to use a weight :math:`w_i` to reduce
the effect of unequal variances. This weight is calculated using the sample
size :math:`n_i` and variance :math:`s_i^2` of each group
:math:`i=1,...,r`:
.. math:: w_i = \frac{n_i}{s_i^2}
Using these weights, the adjusted grand mean of the data is:
.. math::
\overline{Y}_{\text{welch}} = \frac{\sum_{i=1}^r
w_i\overline{Y}_i}{\sum w}
where :math:`\overline{Y}_i` is the mean of the :math:`i` group.
The effect sums of squares is defined as:
.. math::
SS_{\text{effect}} = \sum_{i=1}^r w_i
(\overline{Y}_i - \overline{Y}_{\text{welch}})^2
We then need to calculate a term lambda:
.. math::
\Lambda = \frac{3\sum_{i=1}^r(\frac{1}{n_i-1})
(1 - \frac{w_i}{\sum w})^2}{r^2 - 1}
from which the F-value can be calculated:
.. math::
F_{\text{welch}} = \frac{SS_{\text{effect}} / (r-1)}
{1 + \frac{2\Lambda(r-2)}{3}}
and the p-value approximated using a F-distribution with
:math:`(r-1, 1 / \Lambda)` degrees of freedom.
When the groups are balanced and have equal variances, the optimal post-hoc
test is the Tukey-HSD test (:py:func:`pingouin.pairwise_tukey`).
If the groups have unequal variances, the Games-Howell test is more
adequate (:py:func:`pingouin.pairwise_gameshowell`).
Results have been tested against R.
References
----------
.. [1] Liu, Hangcheng. "Comparing Welch's ANOVA, a Kruskal-Wallis test and
traditional ANOVA in case of Heterogeneity of Variance." (2015).
.. [2] Welch, Bernard Lewis. "On the comparison of several mean values:
an alternative approach." Biometrika 38.3/4 (1951): 330-336.
Examples
--------
1. One-way Welch ANOVA on the pain threshold dataset.
>>> from pingouin import welch_anova, read_dataset
>>> df = read_dataset('anova')
>>> aov = welch_anova(dv='Pain threshold', between='Hair color', data=df)
>>> aov
Source ddof1 ddof2 F p-unc np2
0 Hair color 3 8.329841 5.890115 0.018813 0.575962
| @pf.register_dataframe_method
def welch_anova(data=None, dv=None, between=None):
"""One-way Welch ANOVA.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Note that this function can also directly be used as a
Pandas method, in which case this argument is no longer needed.
dv : string
Name of column containing the dependent variable.
between : string
Name of column containing the between factor.
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Factor names
* ``'ddof1'``: Numerator degrees of freedom
* ``'ddof2'``: Denominator degrees of freedom
* ``'F'``: F-values
* ``'p-unc'``: uncorrected p-values
* ``'np2'``: Partial eta-squared
See Also
--------
anova : One-way and N-way ANOVA
rm_anova : One-way and two-way repeated measures ANOVA
mixed_anova : Two way mixed ANOVA
kruskal : Non-parametric one-way ANOVA
Notes
-----
From Wikipedia:
*It is named for its creator, Bernard Lewis Welch, and is an adaptation of
Student's t-test, and is more reliable when the two samples have
unequal variances and/or unequal sample sizes.*
The classic ANOVA is very powerful when the groups are normally distributed
and have equal variances. However, when the groups have unequal variances,
it is best to use the Welch ANOVA that better controls for
type I error (Liu 2015). The homogeneity of variances can be measured with
the `homoscedasticity` function. The two other assumptions of
normality and independance remain.
The main idea of Welch ANOVA is to use a weight :math:`w_i` to reduce
the effect of unequal variances. This weight is calculated using the sample
size :math:`n_i` and variance :math:`s_i^2` of each group
:math:`i=1,...,r`:
.. math:: w_i = \\frac{n_i}{s_i^2}
Using these weights, the adjusted grand mean of the data is:
.. math::
\\overline{Y}_{\\text{welch}} = \\frac{\\sum_{i=1}^r
w_i\\overline{Y}_i}{\\sum w}
where :math:`\\overline{Y}_i` is the mean of the :math:`i` group.
The effect sums of squares is defined as:
.. math::
SS_{\\text{effect}} = \\sum_{i=1}^r w_i
(\\overline{Y}_i - \\overline{Y}_{\\text{welch}})^2
We then need to calculate a term lambda:
.. math::
\\Lambda = \\frac{3\\sum_{i=1}^r(\\frac{1}{n_i-1})
(1 - \\frac{w_i}{\\sum w})^2}{r^2 - 1}
from which the F-value can be calculated:
.. math::
F_{\\text{welch}} = \\frac{SS_{\\text{effect}} / (r-1)}
{1 + \\frac{2\\Lambda(r-2)}{3}}
and the p-value approximated using a F-distribution with
:math:`(r-1, 1 / \\Lambda)` degrees of freedom.
When the groups are balanced and have equal variances, the optimal post-hoc
test is the Tukey-HSD test (:py:func:`pingouin.pairwise_tukey`).
If the groups have unequal variances, the Games-Howell test is more
adequate (:py:func:`pingouin.pairwise_gameshowell`).
Results have been tested against R.
References
----------
.. [1] Liu, Hangcheng. "Comparing Welch's ANOVA, a Kruskal-Wallis test and
traditional ANOVA in case of Heterogeneity of Variance." (2015).
.. [2] Welch, Bernard Lewis. "On the comparison of several mean values:
an alternative approach." Biometrika 38.3/4 (1951): 330-336.
Examples
--------
1. One-way Welch ANOVA on the pain threshold dataset.
>>> from pingouin import welch_anova, read_dataset
>>> df = read_dataset('anova')
>>> aov = welch_anova(dv='Pain threshold', between='Hair color', data=df)
>>> aov
Source ddof1 ddof2 F p-unc np2
0 Hair color 3 8.329841 5.890115 0.018813 0.575962
"""
# Check data
data = _check_dataframe(dv=dv, between=between, data=data, effects="between")
# Reset index (avoid duplicate axis error)
data = data.reset_index(drop=True)
# Number of groups
r = data[between].nunique()
ddof1 = r - 1
# Compute weights and ajusted means
grp = data.groupby(between, observed=True, group_keys=False)[dv]
weights = grp.count() / grp.var(numeric_only=True)
adj_grandmean = (weights * grp.mean(numeric_only=True)).sum() / weights.sum()
# Sums of squares (regular and adjusted)
ss_res = grp.apply(lambda x: (x - x.mean()) ** 2).sum()
ss_bet = (
(grp.mean(numeric_only=True) - data[dv].mean(numeric_only=True)) ** 2 * grp.count()
).sum()
ss_betadj = np.sum(weights * np.square(grp.mean(numeric_only=True) - adj_grandmean))
ms_betadj = ss_betadj / ddof1
# Calculate lambda, F-value, p-value and np2
lamb = (3 * np.sum((1 / (grp.count() - 1)) * (1 - (weights / weights.sum())) ** 2)) / (
r**2 - 1
)
ddof2 = 1 / lamb
fval = ms_betadj / (1 + (2 * lamb * (r - 2)) / 3)
pval = f.sf(fval, ddof1, ddof2)
np2 = ss_bet / (ss_bet + ss_res)
# Create output dataframe
aov = pd.DataFrame(
{
"Source": between,
"ddof1": ddof1,
"ddof2": ddof2,
"F": fval,
"p-unc": pval,
"np2": np2,
},
index=[0],
)
return _postprocess_dataframe(aov)
| (data=None, dv=None, between=None) | [
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|
32,067 | pingouin.nonparametric | wilcoxon |
Wilcoxon signed-rank test. It is the non-parametric version of the paired T-test.
Parameters
----------
x : array_like
Either the first set of measurements
(in which case y is the second set of measurements),
or the differences between two sets of measurements
(in which case y is not to be specified.) Must be one-dimensional.
y : array_like
Either the second set of measurements (if x is the first set of
measurements), or not specified (if x is the differences between
two sets of measurements.) Must be one-dimensional.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". See :py:func:`scipy.stats.wilcoxon` for
more details.
**kwargs : dict
Additional keywords arguments that are passed to :py:func:`scipy.stats.wilcoxon`.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W-val'``: W-value
* ``'alternative'``: tail of the test
* ``'p-val'``: p-value
* ``'RBC'`` : matched pairs rank-biserial correlation (effect size)
* ``'CLES'`` : common language effect size
See also
--------
scipy.stats.wilcoxon, mwu
Notes
-----
The Wilcoxon signed-rank test [1]_ tests the null hypothesis that two
related paired samples come from the same distribution. In particular,
it tests whether the distribution of the differences x - y is symmetric
about zero.
.. important:: Pingouin automatically applies a continuity correction.
Therefore, the p-values will be slightly different than
:py:func:`scipy.stats.wilcoxon` unless ``correction=True`` is
explicitly passed to the latter.
In addition to the test statistic and p-values, Pingouin also computes two
measures of effect size. The matched pairs rank biserial correlation [2]_
is the simple difference between the proportion of favorable and
unfavorable evidence; in the case of the Wilcoxon signed-rank test,
the evidence consists of rank sums (Kerby 2014):
.. math:: r = f - u
The common language effect size is the proportion of pairs where ``x`` is
higher than ``y``. It was first introduced by McGraw and Wong (1992) [3]_.
Pingouin uses a brute-force version of the formula given by Vargha and
Delaney 2000 [4]_:
.. math:: \text{CL} = P(X > Y) + .5 \times P(X = Y)
The advantage is of this method are twofold. First, the brute-force
approach pairs each observation of ``x`` to its ``y`` counterpart, and
therefore does not require normally distributed data. Second, the formula
takes ties into account and therefore works with ordinal data.
When tail is ``'less'``, the CLES is then set to :math:`1 - \text{CL}`,
which gives the proportion of pairs where ``x`` is *lower* than ``y``.
References
----------
.. [1] Wilcoxon, F. (1945). Individual comparisons by ranking methods.
Biometrics bulletin, 1(6), 80-83.
.. [2] Kerby, D. S. (2014). The simple difference formula: An approach to
teaching nonparametric correlation. Comprehensive Psychology,
3, 11-IT.
.. [3] McGraw, K. O., & Wong, S. P. (1992). A common language effect size
statistic. Psychological bulletin, 111(2), 361.
.. [4] Vargha, A., & Delaney, H. D. (2000). A Critique and Improvement of
the “CL” Common Language Effect Size Statistics of McGraw and Wong.
Journal of Educational and Behavioral Statistics: A Quarterly
Publication Sponsored by the American Educational Research
Association and the American Statistical Association, 25(2),
101–132. https://doi.org/10.2307/1165329
Examples
--------
Wilcoxon test on two related samples.
>>> import numpy as np
>>> import pingouin as pg
>>> x = np.array([20, 22, 19, 20, 22, 18, 24, 20, 19, 24, 26, 13])
>>> y = np.array([38, 37, 33, 29, 14, 12, 20, 22, 17, 25, 26, 16])
>>> pg.wilcoxon(x, y, alternative='two-sided')
W-val alternative p-val RBC CLES
Wilcoxon 20.5 two-sided 0.285765 -0.378788 0.395833
Same but using pre-computed differences. However, the CLES effect size
cannot be computed as it requires the raw data.
>>> pg.wilcoxon(x - y)
W-val alternative p-val RBC CLES
Wilcoxon 20.5 two-sided 0.285765 -0.378788 NaN
Compare with SciPy
>>> import scipy
>>> scipy.stats.wilcoxon(x, y)
WilcoxonResult(statistic=20.5, pvalue=0.2661660677806492)
The p-value is not exactly similar to Pingouin. This is because Pingouin automatically applies
a continuity correction. Disabling it gives the same p-value as scipy:
>>> pg.wilcoxon(x, y, alternative='two-sided', correction=False)
W-val alternative p-val RBC CLES
Wilcoxon 20.5 two-sided 0.266166 -0.378788 0.395833
One-sided test
>>> pg.wilcoxon(x, y, alternative='greater')
W-val alternative p-val RBC CLES
Wilcoxon 20.5 greater 0.876244 -0.378788 0.395833
>>> pg.wilcoxon(x, y, alternative='less')
W-val alternative p-val RBC CLES
Wilcoxon 20.5 less 0.142883 -0.378788 0.604167
| def wilcoxon(x, y=None, alternative="two-sided", **kwargs):
"""
Wilcoxon signed-rank test. It is the non-parametric version of the paired T-test.
Parameters
----------
x : array_like
Either the first set of measurements
(in which case y is the second set of measurements),
or the differences between two sets of measurements
(in which case y is not to be specified.) Must be one-dimensional.
y : array_like
Either the second set of measurements (if x is the first set of
measurements), or not specified (if x is the differences between
two sets of measurements.) Must be one-dimensional.
alternative : string
Defines the alternative hypothesis, or tail of the test. Must be one of
"two-sided" (default), "greater" or "less". See :py:func:`scipy.stats.wilcoxon` for
more details.
**kwargs : dict
Additional keywords arguments that are passed to :py:func:`scipy.stats.wilcoxon`.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W-val'``: W-value
* ``'alternative'``: tail of the test
* ``'p-val'``: p-value
* ``'RBC'`` : matched pairs rank-biserial correlation (effect size)
* ``'CLES'`` : common language effect size
See also
--------
scipy.stats.wilcoxon, mwu
Notes
-----
The Wilcoxon signed-rank test [1]_ tests the null hypothesis that two
related paired samples come from the same distribution. In particular,
it tests whether the distribution of the differences x - y is symmetric
about zero.
.. important:: Pingouin automatically applies a continuity correction.
Therefore, the p-values will be slightly different than
:py:func:`scipy.stats.wilcoxon` unless ``correction=True`` is
explicitly passed to the latter.
In addition to the test statistic and p-values, Pingouin also computes two
measures of effect size. The matched pairs rank biserial correlation [2]_
is the simple difference between the proportion of favorable and
unfavorable evidence; in the case of the Wilcoxon signed-rank test,
the evidence consists of rank sums (Kerby 2014):
.. math:: r = f - u
The common language effect size is the proportion of pairs where ``x`` is
higher than ``y``. It was first introduced by McGraw and Wong (1992) [3]_.
Pingouin uses a brute-force version of the formula given by Vargha and
Delaney 2000 [4]_:
.. math:: \\text{CL} = P(X > Y) + .5 \\times P(X = Y)
The advantage is of this method are twofold. First, the brute-force
approach pairs each observation of ``x`` to its ``y`` counterpart, and
therefore does not require normally distributed data. Second, the formula
takes ties into account and therefore works with ordinal data.
When tail is ``'less'``, the CLES is then set to :math:`1 - \\text{CL}`,
which gives the proportion of pairs where ``x`` is *lower* than ``y``.
References
----------
.. [1] Wilcoxon, F. (1945). Individual comparisons by ranking methods.
Biometrics bulletin, 1(6), 80-83.
.. [2] Kerby, D. S. (2014). The simple difference formula: An approach to
teaching nonparametric correlation. Comprehensive Psychology,
3, 11-IT.
.. [3] McGraw, K. O., & Wong, S. P. (1992). A common language effect size
statistic. Psychological bulletin, 111(2), 361.
.. [4] Vargha, A., & Delaney, H. D. (2000). A Critique and Improvement of
the “CL” Common Language Effect Size Statistics of McGraw and Wong.
Journal of Educational and Behavioral Statistics: A Quarterly
Publication Sponsored by the American Educational Research
Association and the American Statistical Association, 25(2),
101–132. https://doi.org/10.2307/1165329
Examples
--------
Wilcoxon test on two related samples.
>>> import numpy as np
>>> import pingouin as pg
>>> x = np.array([20, 22, 19, 20, 22, 18, 24, 20, 19, 24, 26, 13])
>>> y = np.array([38, 37, 33, 29, 14, 12, 20, 22, 17, 25, 26, 16])
>>> pg.wilcoxon(x, y, alternative='two-sided')
W-val alternative p-val RBC CLES
Wilcoxon 20.5 two-sided 0.285765 -0.378788 0.395833
Same but using pre-computed differences. However, the CLES effect size
cannot be computed as it requires the raw data.
>>> pg.wilcoxon(x - y)
W-val alternative p-val RBC CLES
Wilcoxon 20.5 two-sided 0.285765 -0.378788 NaN
Compare with SciPy
>>> import scipy
>>> scipy.stats.wilcoxon(x, y)
WilcoxonResult(statistic=20.5, pvalue=0.2661660677806492)
The p-value is not exactly similar to Pingouin. This is because Pingouin automatically applies
a continuity correction. Disabling it gives the same p-value as scipy:
>>> pg.wilcoxon(x, y, alternative='two-sided', correction=False)
W-val alternative p-val RBC CLES
Wilcoxon 20.5 two-sided 0.266166 -0.378788 0.395833
One-sided test
>>> pg.wilcoxon(x, y, alternative='greater')
W-val alternative p-val RBC CLES
Wilcoxon 20.5 greater 0.876244 -0.378788 0.395833
>>> pg.wilcoxon(x, y, alternative='less')
W-val alternative p-val RBC CLES
Wilcoxon 20.5 less 0.142883 -0.378788 0.604167
"""
x = np.asarray(x)
if y is not None:
y = np.asarray(y)
x, y = remove_na(x, y, paired=True) # Remove NA
else:
x = x[~np.isnan(x)]
# Check tails
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
if "tail" in kwargs:
raise ValueError(
"Since Pingouin 0.4.0, the 'tail' argument has been renamed to 'alternative'."
)
# Compute test
if "correction" not in kwargs:
kwargs["correction"] = True
wval, pval = scipy.stats.wilcoxon(x=x, y=y, alternative=alternative, **kwargs)
# Effect size 1: Common Language Effect Size
# Since Pingouin v0.3.5, CLES is tail-specific and calculated
# according to the formula given in Vargha and Delaney 2000 which
# works with ordinal data.
if y is not None:
diff = x[:, None] - y
# cles = max((diff < 0).sum(), (diff > 0).sum()) / diff.size
# alternative = 'greater', with ties set to 0.5
# Note that alternative = 'two-sided' gives same output as alternative = 'greater'
cles = np.where(diff == 0, 0.5, diff > 0).mean()
cles = 1 - cles if alternative == "less" else cles
else:
# CLES cannot be computed if y is None
cles = np.nan
# Effect size 2: matched-pairs rank biserial correlation (Kerby 2014)
if y is not None:
d = x - y
d = d[d != 0]
else:
d = x[x != 0]
r = scipy.stats.rankdata(abs(d))
rsum = r.sum()
r_plus = np.sum((d > 0) * r)
r_minus = np.sum((d < 0) * r)
rbc = r_plus / rsum - r_minus / rsum
# Fill output DataFrame
stats = pd.DataFrame(
{"W-val": wval, "alternative": alternative, "p-val": pval, "RBC": rbc, "CLES": cles},
index=["Wilcoxon"],
)
return _postprocess_dataframe(stats)
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|
32,068 | bqplot.scales | Albers | A geographical scale which is an alias for a conic equal area projection.
The Albers projection is a conic equal area map. It does not preserve scale
or shape, though it is recommended for chloropleths since it preserves the
relative areas of geographic features. Default values are US-centric.
Attributes
----------
scale_factor: float (default: 250)
Specifies the scale value for the projection
rotate: tuple (default: (96, 0))
Degree of rotation in each axis.
parallels: tuple (default: (29.5, 45.5))
Sets the two parallels for the conic projection.
center: tuple (default: (0, 60))
Specifies the longitude and latitude where the map is centered.
precision: float (default: 0.1)
Specifies the threshold for the projections adaptive resampling to the
specified value in pixels.
rtype: (Number, Number) (class-level attribute)
This attribute should not be modified. The range type of a geo
scale is a tuple.
dtype: type (class-level attribute)
the associated data type / domain type
| class Albers(GeoScale):
"""A geographical scale which is an alias for a conic equal area projection.
The Albers projection is a conic equal area map. It does not preserve scale
or shape, though it is recommended for chloropleths since it preserves the
relative areas of geographic features. Default values are US-centric.
Attributes
----------
scale_factor: float (default: 250)
Specifies the scale value for the projection
rotate: tuple (default: (96, 0))
Degree of rotation in each axis.
parallels: tuple (default: (29.5, 45.5))
Sets the two parallels for the conic projection.
center: tuple (default: (0, 60))
Specifies the longitude and latitude where the map is centered.
precision: float (default: 0.1)
Specifies the threshold for the projections adaptive resampling to the
specified value in pixels.
rtype: (Number, Number) (class-level attribute)
This attribute should not be modified. The range type of a geo
scale is a tuple.
dtype: type (class-level attribute)
the associated data type / domain type
"""
scale_factor = Float(250).tag(sync=True)
rotate = Tuple((96, 0)).tag(sync=True)
center = Tuple((0, 60)).tag(sync=True)
parallels = Tuple((29.5, 45.5)).tag(sync=True)
precision = Float(0.1).tag(sync=True)
rtype = '(Number, Number)'
dtype = np.number
_view_name = Unicode('Albers').tag(sync=True)
_model_name = Unicode('AlbersModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,125 | bqplot.scales | AlbersUSA | A composite projection of four Albers projections meant specifically for
the United States.
Attributes
----------
scale_factor: float (default: 1200)
Specifies the scale value for the projection
translate: tuple (default: (600, 490))
rtype: (Number, Number) (class-level attribute)
This attribute should not be modified. The range type of a geo
scale is a tuple.
dtype: type (class-level attribute)
the associated data type / domain type
| class AlbersUSA(GeoScale):
"""A composite projection of four Albers projections meant specifically for
the United States.
Attributes
----------
scale_factor: float (default: 1200)
Specifies the scale value for the projection
translate: tuple (default: (600, 490))
rtype: (Number, Number) (class-level attribute)
This attribute should not be modified. The range type of a geo
scale is a tuple.
dtype: type (class-level attribute)
the associated data type / domain type
"""
scale_factor = Float(1200).tag(sync=True)
translate = Tuple((600, 490)).tag(sync=True)
rtype = '(Number, Number)'
dtype = np.number
_view_name = Unicode('AlbersUSA').tag(sync=True)
_model_name = Unicode('AlbersUSAModel').tag(sync=True)
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|
32,182 | traittypes.traittypes | Array | A numpy array trait type. | class Array(SciType):
"""A numpy array trait type."""
info_text = 'a numpy array'
dtype = None
def validate(self, obj, value):
if value is None and not self.allow_none:
self.error(obj, value)
if value is None or value is Undefined:
return super(Array, self).validate(obj, value)
try:
r = np.asarray(value, dtype=self.dtype)
if isinstance(value, np.ndarray) and r is not value:
warnings.warn(
'Given trait value dtype "%s" does not match required type "%s". '
'A coerced copy has been created.' % (
np.dtype(value.dtype).name,
np.dtype(self.dtype).name))
value = r
except (ValueError, TypeError) as e:
raise TraitError(e)
return super(Array, self).validate(obj, value)
def set(self, obj, value):
new_value = self._validate(obj, value)
old_value = obj._trait_values.get(self.name, self.default_value)
obj._trait_values[self.name] = new_value
if not np.array_equal(old_value, new_value):
obj._notify_trait(self.name, old_value, new_value)
def __init__(self, default_value=Empty, allow_none=False, dtype=None, **kwargs):
self.dtype = dtype
if default_value is Empty:
default_value = np.array(0, dtype=self.dtype)
elif default_value is not None and default_value is not Undefined:
default_value = np.asarray(default_value, dtype=self.dtype)
super(Array, self).__init__(default_value=default_value, allow_none=allow_none, **kwargs)
def make_dynamic_default(self):
if self.default_value is None or self.default_value is Undefined:
return self.default_value
else:
return np.copy(self.default_value)
| (default_value: Any = traittypes.Empty, allow_none: bool = False, dtype=None, **kwargs) | [
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|
32,184 | traittypes.traittypes | __init__ | null | def __init__(self, default_value=Empty, allow_none=False, dtype=None, **kwargs):
self.dtype = dtype
if default_value is Empty:
default_value = np.array(0, dtype=self.dtype)
elif default_value is not None and default_value is not Undefined:
default_value = np.asarray(default_value, dtype=self.dtype)
super(Array, self).__init__(default_value=default_value, allow_none=allow_none, **kwargs)
| (self, default_value=traittypes.Empty, allow_none=False, dtype=None, **kwargs) | [
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|
32,200 | traittypes.traittypes | make_dynamic_default | null | def make_dynamic_default(self):
if self.default_value is None or self.default_value is Undefined:
return self.default_value
else:
return np.copy(self.default_value)
| (self) | [
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|
32,201 | traittypes.traittypes | set | null | def set(self, obj, value):
new_value = self._validate(obj, value)
old_value = obj._trait_values.get(self.name, self.default_value)
obj._trait_values[self.name] = new_value
if not np.array_equal(old_value, new_value):
obj._notify_trait(self.name, old_value, new_value)
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|
32,205 | traittypes.traittypes | valid |
Register new trait validators
Validators are functions that take two arguments.
- The trait instance
- The proposed value
Validators return the (potentially modified) value, which is either
assigned to the HasTraits attribute or input into the next validator.
They are evaluated in the order in which they are provided to the `valid`
function.
Example
-------
.. code:: python
# Test with a shape constraint
def shape(*dimensions):
def validator(trait, value):
if value.shape != dimensions:
raise TraitError('Expected an of shape %s and got and array with shape %s' % (dimensions, value.shape))
else:
return value
return validator
class Foo(HasTraits):
bar = Array(np.identity(2)).valid(shape(2, 2))
foo = Foo()
foo.bar = [1, 2] # Should raise a TraitError
| def valid(self, *validators):
"""
Register new trait validators
Validators are functions that take two arguments.
- The trait instance
- The proposed value
Validators return the (potentially modified) value, which is either
assigned to the HasTraits attribute or input into the next validator.
They are evaluated in the order in which they are provided to the `valid`
function.
Example
-------
.. code:: python
# Test with a shape constraint
def shape(*dimensions):
def validator(trait, value):
if value.shape != dimensions:
raise TraitError('Expected an of shape %s and got and array with shape %s' % (dimensions, value.shape))
else:
return value
return validator
class Foo(HasTraits):
bar = Array(np.identity(2)).valid(shape(2, 2))
foo = Foo()
foo.bar = [1, 2] # Should raise a TraitError
"""
self.validators.extend(validators)
return self
| (self, *validators) | [
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]
|
32,206 | traittypes.traittypes | validate | null | def validate(self, obj, value):
if value is None and not self.allow_none:
self.error(obj, value)
if value is None or value is Undefined:
return super(Array, self).validate(obj, value)
try:
r = np.asarray(value, dtype=self.dtype)
if isinstance(value, np.ndarray) and r is not value:
warnings.warn(
'Given trait value dtype "%s" does not match required type "%s". '
'A coerced copy has been created.' % (
np.dtype(value.dtype).name,
np.dtype(self.dtype).name))
value = r
except (ValueError, TypeError) as e:
raise TraitError(e)
return super(Array, self).validate(obj, value)
| (self, obj, value) | [
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|
32,207 | bqplot.axes | Axis | A line axis.
A line axis is the visual representation of a numerical or date scale.
Attributes
----------
icon: string (class-level attribute)
The font-awesome icon name for this object.
axis_types: dict (class-level attribute)
A registry of existing axis types.
orientation: {'horizontal', 'vertical'}
The orientation of the axis, either vertical or horizontal
side: {'bottom', 'top', 'left', 'right'} or None (default: None)
The side of the axis, either bottom, top, left or right.
label: string (default: '')
The axis label
tick_format: string or None (default: '')
The tick format for the axis, for dates use d3 string formatting.
scale: Scale
The scale represented by the axis
num_ticks: int or None (default: None)
If tick_values is None, number of ticks
tick_values: numpy.ndarray or None (default: None)
Tick values for the axis
tick_labels: dict (default: None)
Override the tick labels with a dictionary of {value: label}.
Entries are optional, and if not provided, the default tick labels
will be used.
offset: dict (default: {})
Contains a scale and a value {'scale': scale or None,
'value': value of the offset}
If offset['scale'] is None, the corresponding figure scale is used
instead.
label_location: {'middle', 'start', 'end'}
The location of the label along the axis, one of 'start', 'end' or
'middle'
label_color: Color or None (default: None)
The color of the axis label
grid_lines: {'none', 'solid', 'dashed'}
The display of the grid lines
grid_color: Color or None (default: None)
The color of the grid lines
color: Color or None (default: None)
The color of the line
label_offset: string or None (default: None)
Label displacement from the axis line. Units allowed are 'em', 'px'
and 'ex'. Positive values are away from the figure and negative
values are towards the figure with respect to the axis line.
visible: bool (default: True)
A visibility toggle for the axis
tick_style: Dict (default: {})
Dictionary containing the CSS-style of the text for the ticks.
For example: font-size of the text can be changed by passing
`{'font-size': 14}`
tick_rotate: int (default: 0)
Degrees to rotate tick labels by.
| class Axis(BaseAxis):
"""A line axis.
A line axis is the visual representation of a numerical or date scale.
Attributes
----------
icon: string (class-level attribute)
The font-awesome icon name for this object.
axis_types: dict (class-level attribute)
A registry of existing axis types.
orientation: {'horizontal', 'vertical'}
The orientation of the axis, either vertical or horizontal
side: {'bottom', 'top', 'left', 'right'} or None (default: None)
The side of the axis, either bottom, top, left or right.
label: string (default: '')
The axis label
tick_format: string or None (default: '')
The tick format for the axis, for dates use d3 string formatting.
scale: Scale
The scale represented by the axis
num_ticks: int or None (default: None)
If tick_values is None, number of ticks
tick_values: numpy.ndarray or None (default: None)
Tick values for the axis
tick_labels: dict (default: None)
Override the tick labels with a dictionary of {value: label}.
Entries are optional, and if not provided, the default tick labels
will be used.
offset: dict (default: {})
Contains a scale and a value {'scale': scale or None,
'value': value of the offset}
If offset['scale'] is None, the corresponding figure scale is used
instead.
label_location: {'middle', 'start', 'end'}
The location of the label along the axis, one of 'start', 'end' or
'middle'
label_color: Color or None (default: None)
The color of the axis label
grid_lines: {'none', 'solid', 'dashed'}
The display of the grid lines
grid_color: Color or None (default: None)
The color of the grid lines
color: Color or None (default: None)
The color of the line
label_offset: string or None (default: None)
Label displacement from the axis line. Units allowed are 'em', 'px'
and 'ex'. Positive values are away from the figure and negative
values are towards the figure with respect to the axis line.
visible: bool (default: True)
A visibility toggle for the axis
tick_style: Dict (default: {})
Dictionary containing the CSS-style of the text for the ticks.
For example: font-size of the text can be changed by passing
`{'font-size': 14}`
tick_rotate: int (default: 0)
Degrees to rotate tick labels by.
"""
icon = 'fa-arrows'
orientation = Enum(['horizontal', 'vertical'], default_value='horizontal')\
.tag(sync=True)
side = Enum(['bottom', 'top', 'left', 'right'],
allow_none=True, default_value=None).tag(sync=True)
label = Unicode().tag(sync=True)
grid_lines = Enum(['none', 'solid', 'dashed'], default_value='solid')\
.tag(sync=True)
tick_format = Unicode(None, allow_none=True).tag(sync=True)
scale = Instance(Scale).tag(sync=True, **widget_serialization)
num_ticks = Int(default_value=None, allow_none=True).tag(sync=True)
tick_values = Array(None, allow_none=True)\
.tag(sync=True, **array_serialization)\
.valid(array_dimension_bounds(1, 1))
tick_labels = Dict(None, allow_none=True).tag(sync=True)
offset = Dict().tag(sync=True, **widget_serialization)
label_location = Enum(['middle', 'start', 'end'],
default_value='middle').tag(sync=True)
label_color = Color(None, allow_none=True).tag(sync=True)
grid_color = Color(None, allow_none=True).tag(sync=True)
color = Color(None, allow_none=True).tag(sync=True)
label_offset = Unicode(default_value=None, allow_none=True).tag(sync=True)
visible = Bool(True).tag(sync=True)
tick_style = Dict().tag(sync=True)
tick_rotate = Int(0).tag(sync=True)
_view_name = Unicode('Axis').tag(sync=True)
_model_name = Unicode('AxisModel').tag(sync=True)
_ipython_display_ = None # We cannot display an axis outside of a figure.
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,264 | bqplot.marks | Bars | Bar mark.
In the case of the Bars mark, scales for 'x' and 'y' MUST be provided.
The scales of other data attributes are optional. In the case where another
data attribute than 'x' or 'y' is provided but the corresponding scale is
missing, the data attribute is ignored.
Attributes
----------
icon: string (class-level attribute)
font-awesome icon for that mark
name: string (class-level attribute)
user-friendly name of the mark
color_mode: {'auto', 'group', 'element', 'no_group'}
Specify how default colors are applied to bars.
The 'group' mode means colors are assigned per group. If the list
of colors is shorter than the number of groups, colors are reused.
The 'element' mode means colors are assigned per group element. If the list
of colors is shorter than the number of bars in a group, colors are reused.
The 'no_group' mode means colors are assigned per bar, discarding the fact
that there are groups or stacks. If the list of colors is shorter than the
total number of bars, colors are reused.
opacity_mode: {'auto', 'group', 'element', 'no_group'}
Same as the `color_mode` attribute, but for the opacity.
type: {'stacked', 'grouped'}
whether 2-dimensional bar charts should appear grouped or stacked.
colors: list of colors (default: ['steelblue'])
list of colors for the bars.
orientation: {'horizontal', 'vertical'}
Specifies whether the bar chart is drawn horizontally or vertically.
If a horizontal bar chart is drawn, the x data is drawn vertically.
padding: float (default: 0.05)
Attribute to control the spacing between the bars value is specified
as a percentage of the width of the bar
fill: Bool (default: True)
Whether to fill the bars or not
stroke: Color or None (default: None)
Stroke color for the bars
stroke_width: Float (default: 0.)
Stroke width of the bars
opacities: list of floats (default: [])
Opacities for the bars. Defaults to 1 when the list is too
short, or the element of the list is set to None.
base: float (default: 0.0)
reference value from which the bars are drawn. defaults to 0.0
align: {'center', 'left', 'right'}
alignment of bars with respect to the tick value
label_display: bool (default: False)
whether or not to display bar data labels
label_display_format: string (default: .2f)
format for displaying values.
label_font_style: dict
CSS style for the text of each cell
label_display_vertical_offset: float
vertical offset value for the label display
label_display_horizontal_offset: float
horizontal offset value for the label display
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the data points (1d array)
y: numpy.ndarray (default: [])
ordinates of the values for the data points
color: numpy.ndarray or None (default: None)
color of the data points (1d array). Defaults to default_color when not
provided or when a value is NaN
Notes
-----
The fields which can be passed to the default tooltip are:
All the data attributes
index: index of the bar being hovered on
sub_index: if data is two dimensional, this is the minor index
| class Bars(Mark):
"""Bar mark.
In the case of the Bars mark, scales for 'x' and 'y' MUST be provided.
The scales of other data attributes are optional. In the case where another
data attribute than 'x' or 'y' is provided but the corresponding scale is
missing, the data attribute is ignored.
Attributes
----------
icon: string (class-level attribute)
font-awesome icon for that mark
name: string (class-level attribute)
user-friendly name of the mark
color_mode: {'auto', 'group', 'element', 'no_group'}
Specify how default colors are applied to bars.
The 'group' mode means colors are assigned per group. If the list
of colors is shorter than the number of groups, colors are reused.
The 'element' mode means colors are assigned per group element. If the list
of colors is shorter than the number of bars in a group, colors are reused.
The 'no_group' mode means colors are assigned per bar, discarding the fact
that there are groups or stacks. If the list of colors is shorter than the
total number of bars, colors are reused.
opacity_mode: {'auto', 'group', 'element', 'no_group'}
Same as the `color_mode` attribute, but for the opacity.
type: {'stacked', 'grouped'}
whether 2-dimensional bar charts should appear grouped or stacked.
colors: list of colors (default: ['steelblue'])
list of colors for the bars.
orientation: {'horizontal', 'vertical'}
Specifies whether the bar chart is drawn horizontally or vertically.
If a horizontal bar chart is drawn, the x data is drawn vertically.
padding: float (default: 0.05)
Attribute to control the spacing between the bars value is specified
as a percentage of the width of the bar
fill: Bool (default: True)
Whether to fill the bars or not
stroke: Color or None (default: None)
Stroke color for the bars
stroke_width: Float (default: 0.)
Stroke width of the bars
opacities: list of floats (default: [])
Opacities for the bars. Defaults to 1 when the list is too
short, or the element of the list is set to None.
base: float (default: 0.0)
reference value from which the bars are drawn. defaults to 0.0
align: {'center', 'left', 'right'}
alignment of bars with respect to the tick value
label_display: bool (default: False)
whether or not to display bar data labels
label_display_format: string (default: .2f)
format for displaying values.
label_font_style: dict
CSS style for the text of each cell
label_display_vertical_offset: float
vertical offset value for the label display
label_display_horizontal_offset: float
horizontal offset value for the label display
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the data points (1d array)
y: numpy.ndarray (default: [])
ordinates of the values for the data points
color: numpy.ndarray or None (default: None)
color of the data points (1d array). Defaults to default_color when not
provided or when a value is NaN
Notes
-----
The fields which can be passed to the default tooltip are:
All the data attributes
index: index of the bar being hovered on
sub_index: if data is two dimensional, this is the minor index
"""
# Mark decoration
icon = 'fa-bar-chart'
name = 'Bar chart'
# Scaled attributes
x = Array([]).tag(sync=True, scaled=True, rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
y = Array([]).tag(sync=True, scaled=True, rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_dimension_bounds(1, 2), array_supported_kinds())
color = Array(None, allow_none=True)\
.tag(sync=True, scaled=True, rtype='Color',
atype='bqplot.ColorAxis', **array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
# Bar text labels attributes -- add default values.
# Add bool for displaying a label or not. Add d3 formatting in docstring
label_display = Bool(default_value=False).tag(sync=True)
label_display_format = Unicode(default_value=".2f",
allow_none=False).tag(sync=True)
label_font_style = Dict().tag(sync=True)
label_display_vertical_offset = Float(default_value=0.0,
allow_none=False).tag(sync=True)
label_display_horizontal_offset = Float(default_value=0.0,
allow_none=False).tag(sync=True)
# Other attributes
scales_metadata = Dict({
'x': {'orientation': 'horizontal', 'dimension': 'x'},
'y': {'orientation': 'vertical', 'dimension': 'y'},
'color': {'dimension': 'color'}
}).tag(sync=True)
color_mode = Enum(['auto', 'group', 'element', 'no_group'], default_value='auto')\
.tag(sync=True)
opacity_mode = Enum(['auto', 'group', 'element', 'no_group'], default_value='auto')\
.tag(sync=True)
type = Enum(['stacked', 'grouped'], default_value='stacked')\
.tag(sync=True, display_name='Type')
colors = List(trait=Color(default_value=None,
allow_none=True),
default_value=['steelblue'])\
.tag(sync=True, display_name='Colors')
padding = Float(0.05).tag(sync=True)
fill = Bool(True).tag(sync=True)
stroke = Color(None, allow_none=True).tag(sync=True)
stroke_width = Float(1.).tag(sync=True, display_name='Stroke width')
base = Float().tag(sync=True)
opacities = List(trait=Float(1.0, min=0, max=1, allow_none=True))\
.tag(sync=True, display_name='Opacities')
align = Enum(['center', 'left', 'right'], default_value='center')\
.tag(sync=True)
orientation = Enum(['vertical', 'horizontal'], default_value='vertical')\
.tag(sync=True)
@validate('orientation')
def _validate_orientation(self, proposal):
value = proposal['value']
x_orient = "horizontal" if value == "vertical" else "vertical"
self.scales_metadata = {'x': {'orientation': x_orient,
'dimension': 'x'},
'y': {'orientation': value, 'dimension': 'y'}}
return value
_view_name = Unicode('Bars').tag(sync=True)
_model_name = Unicode('BarsModel').tag(sync=True)
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|
32,269 | bqplot.marks | __init__ | null | def __init__(self, **kwargs):
super(Mark, self).__init__(**kwargs)
self._hover_handlers = CallbackDispatcher()
self._click_handlers = CallbackDispatcher()
self._legend_click_handlers = CallbackDispatcher()
self._legend_hover_handlers = CallbackDispatcher()
self._element_click_handlers = CallbackDispatcher()
self._bg_click_handlers = CallbackDispatcher()
self._name_to_handler = {
'hover': self._hover_handlers,
'click': self._click_handlers,
'legend_click': self._legend_click_handlers,
'legend_hover': self._legend_hover_handlers,
'element_click': self._element_click_handlers,
'background_click': self._bg_click_handlers
}
self.on_msg(self._handle_custom_msgs)
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|
32,277 | bqplot.marks | _get_dimension_scales |
Return the list of scales corresponding to a given dimension.
The preserve_domain optional argument specifies whether one should
filter out the scales for which preserve_domain is set to True.
| def _get_dimension_scales(self, dimension, preserve_domain=False):
"""
Return the list of scales corresponding to a given dimension.
The preserve_domain optional argument specifies whether one should
filter out the scales for which preserve_domain is set to True.
"""
if preserve_domain:
return [
self.scales[k] for k in self.scales if (
k in self.scales_metadata and
self.scales_metadata[k].get('dimension') == dimension and
not self.preserve_domain.get(k)
)
]
else:
return [
self.scales[k] for k in self.scales if (
k in self.scales_metadata and
self.scales_metadata[k].get('dimension') == dimension
)
]
| (self, dimension, preserve_domain=False) | [
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|
32,281 | bqplot.marks | _handle_custom_msgs | null | def _handle_custom_msgs(self, _, content, buffers=None):
try:
handler = self._name_to_handler[content['event']]
except KeyError:
return
handler(self, content)
| (self, _, content, buffers=None) | [
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|
32,306 | bqplot.marks | on_background_click | null | def on_background_click(self, callback, remove=False):
self._bg_click_handlers.register_callback(callback, remove=remove)
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|
32,307 | bqplot.marks | on_click | null | def on_click(self, callback, remove=False):
self._click_handlers.register_callback(callback, remove=remove)
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|
32,308 | bqplot.marks | on_element_click | null | def on_element_click(self, callback, remove=False):
self._element_click_handlers.register_callback(callback, remove=remove)
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|
32,309 | bqplot.marks | on_hover | null | def on_hover(self, callback, remove=False):
self._hover_handlers.register_callback(callback, remove=remove)
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|
32,310 | bqplot.marks | on_legend_click | null | def on_legend_click(self, callback, remove=False):
self._legend_click_handlers.register_callback(callback, remove=remove)
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|
32,311 | bqplot.marks | on_legend_hover | null | def on_legend_hover(self, callback, remove=False):
self._legend_hover_handlers.register_callback(callback, remove=remove)
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|
32,329 | bqplot.axes | BaseAxis | null | class BaseAxis(Widget):
axis_types = {}
_view_module = Unicode('bqplot').tag(sync=True)
_model_module = Unicode('bqplot').tag(sync=True)
_view_module_version = Unicode(__frontend_version__).tag(sync=True)
_model_module_version = Unicode(__frontend_version__).tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,386 | bqplot.marks | Bins | Backend histogram mark.
A `Bars` instance that bins sample data.
It is very similar in purpose to the `Hist` mark, the difference being that
the binning is done in the backend (python), which avoids large amounts of
data being shipped back and forth to the frontend. It should therefore be
preferred for large data.
The binning method is the numpy `histogram` method.
The following documentation is in part taken from the numpy documentation.
Attributes
----------
icon: string (class-level attribute)
font-awesome icon for that mark
name: string (class-level attribute)
user-friendly name of the mark
bins: nonnegative int (default: 10)
or {'auto', 'fd', 'doane', 'scott', 'rice', 'sturges', 'sqrt'}
If `bins` is an int, it defines the number of equal-width
bins in the given range (10, by default).
If `bins` is a string (method name), `histogram` will use
the method chosen to calculate the optimal bin width and
consequently the number of bins (see `Notes` for more detail on
the estimators) from the data that falls within the requested
range.
density : bool (default: `False`)
If `False`, the height of each bin is the number of samples in it.
If `True`, the height of each bin is the value of the
probability *density* function at the bin, normalized such that
the *integral* over the range is 1. Note that the sum of the
histogram values will not be equal to 1 unless bins of unity
width are chosen; it is not a probability *mass* function.
min : float (default: None)
The lower range of the bins. If not provided, lower range
is simply `x.min()`.
max : float (default: None)
The upper range of the bins. If not provided, lower range
is simply `x.max()`.
Data Attributes
sample: numpy.ndarray (default: [])
sample of which the histogram must be computed.
Notes
-----
The fields which can be passed to the default tooltip are:
All the `Bars` data attributes (`x`, `y`, `color`)
index: index of the bin
| class Bins(Bars):
"""Backend histogram mark.
A `Bars` instance that bins sample data.
It is very similar in purpose to the `Hist` mark, the difference being that
the binning is done in the backend (python), which avoids large amounts of
data being shipped back and forth to the frontend. It should therefore be
preferred for large data.
The binning method is the numpy `histogram` method.
The following documentation is in part taken from the numpy documentation.
Attributes
----------
icon: string (class-level attribute)
font-awesome icon for that mark
name: string (class-level attribute)
user-friendly name of the mark
bins: nonnegative int (default: 10)
or {'auto', 'fd', 'doane', 'scott', 'rice', 'sturges', 'sqrt'}
If `bins` is an int, it defines the number of equal-width
bins in the given range (10, by default).
If `bins` is a string (method name), `histogram` will use
the method chosen to calculate the optimal bin width and
consequently the number of bins (see `Notes` for more detail on
the estimators) from the data that falls within the requested
range.
density : bool (default: `False`)
If `False`, the height of each bin is the number of samples in it.
If `True`, the height of each bin is the value of the
probability *density* function at the bin, normalized such that
the *integral* over the range is 1. Note that the sum of the
histogram values will not be equal to 1 unless bins of unity
width are chosen; it is not a probability *mass* function.
min : float (default: None)
The lower range of the bins. If not provided, lower range
is simply `x.min()`.
max : float (default: None)
The upper range of the bins. If not provided, lower range
is simply `x.max()`.
Data Attributes
sample: numpy.ndarray (default: [])
sample of which the histogram must be computed.
Notes
-----
The fields which can be passed to the default tooltip are:
All the `Bars` data attributes (`x`, `y`, `color`)
index: index of the bin
"""
# Mark decoration
icon = 'fa-signal'
name = 'Backend Histogram'
# Scaled Attributes
sample = Array([]).tag(
sync=False, display_name='Sample', rtype='Number',
atype='bqplot.Axis', **array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
# Binning options
min = Float(None, allow_none=True).tag(sync=True)
max = Float(None, allow_none=True).tag(sync=True)
density = Bool().tag(sync=True)
bins = (Int(10) | List() | Enum(['auto', 'fd', 'doane',
'scott', 'rice', 'sturges', 'sqrt']))\
.tag(sync=True, display_name='Number of bins')
def __init__(self, **kwargs):
'''
Sets listeners on the data and the binning parameters.
Adjusts `Bars` defaults to suit a histogram better.
'''
self.observe(self.bin_data,
names=['sample', 'bins', 'density', 'min', 'max'])
# One unique color by default
kwargs.setdefault('colors', [CATEGORY10[0]])
# No spacing between bars
kwargs.setdefault('padding', 0.)
super(Bins, self).__init__(**kwargs)
def bin_data(self, *args):
'''
Performs the binning of `sample` data, and draws the corresponding bars
'''
# Get range
_min = self.sample.min() if self.min is None else self.min
_max = self.sample.max() if self.max is None else self.max
_range = (min(_min, _max), max(_min, _max))
# Bin the samples
counts, bin_edges = histogram(self.sample, bins=self.bins,
range=_range, density=self.density)
midpoints = (bin_edges[:-1] + bin_edges[1:]) / 2
# Redraw the underlying Bars
with self.hold_sync():
self.x, self.y = midpoints, counts
| (**kwargs) | [
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|
32,391 | bqplot.marks | __init__ |
Sets listeners on the data and the binning parameters.
Adjusts `Bars` defaults to suit a histogram better.
| def __init__(self, **kwargs):
'''
Sets listeners on the data and the binning parameters.
Adjusts `Bars` defaults to suit a histogram better.
'''
self.observe(self.bin_data,
names=['sample', 'bins', 'density', 'min', 'max'])
# One unique color by default
kwargs.setdefault('colors', [CATEGORY10[0]])
# No spacing between bars
kwargs.setdefault('padding', 0.)
super(Bins, self).__init__(**kwargs)
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|
32,418 | bqplot.marks | bin_data |
Performs the binning of `sample` data, and draws the corresponding bars
| def bin_data(self, *args):
'''
Performs the binning of `sample` data, and draws the corresponding bars
'''
# Get range
_min = self.sample.min() if self.min is None else self.min
_max = self.sample.max() if self.max is None else self.max
_range = (min(_min, _max), max(_min, _max))
# Bin the samples
counts, bin_edges = histogram(self.sample, bins=self.bins,
range=_range, density=self.density)
midpoints = (bin_edges[:-1] + bin_edges[1:]) / 2
# Redraw the underlying Bars
with self.hold_sync():
self.x, self.y = midpoints, counts
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|
32,476 | bqplot.marks | Boxplot | Boxplot marks.
Attributes
----------
stroke: Color or None
stroke color of the marker
color: Color
fill color of the box
opacities: list of floats (default: [])
Opacities for the markers of the boxplot. Defaults to 1 when the
list is too short, or the element of the list is set to None.
outlier-color: color
color for the outlier
box_width: int (default: None)
width of the box in pixels. The minimum value is 5.
If set to None, box_with is auto calculated
auto_detect_outliers: bool (default: True)
Flag to toggle outlier auto-detection
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the data points (1d array)
y: numpy.ndarray (default: [[]])
Sample data points (2d array)
| class Boxplot(Mark):
"""Boxplot marks.
Attributes
----------
stroke: Color or None
stroke color of the marker
color: Color
fill color of the box
opacities: list of floats (default: [])
Opacities for the markers of the boxplot. Defaults to 1 when the
list is too short, or the element of the list is set to None.
outlier-color: color
color for the outlier
box_width: int (default: None)
width of the box in pixels. The minimum value is 5.
If set to None, box_with is auto calculated
auto_detect_outliers: bool (default: True)
Flag to toggle outlier auto-detection
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the data points (1d array)
y: numpy.ndarray (default: [[]])
Sample data points (2d array)
"""
# Mark decoration
icon = 'fa-birthday-cake'
name = 'Boxplot chart'
# Scaled attributes
x = Array([]).tag(sync=True, scaled=True, rtype='Number',
atype='bqplot.Axis', **array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
# Second dimension must contain OHLC data, otherwise the behavior
# is undefined.
y = Array([[]]).tag(sync=True, scaled=True, rtype='Number',
atype='bqplot.Axis', **array_serialization)\
.valid(array_dimension_bounds(1, 2), array_supported_kinds())
# Other attributes
scales_metadata = Dict({
'x': {'orientation': 'horizontal', 'dimension': 'x'},
'y': {'orientation': 'vertical', 'dimension': 'y'}
}).tag(sync=True)
stroke = Color(None, allow_none=True)\
.tag(sync=True, display_name='Stroke color')
box_fill_color = Color('steelblue')\
.tag(sync=True, display_name='Fill color for the box')
outlier_fill_color = Color('gray').tag(sync=True,
display_name='Outlier fill color')
opacities = List(trait=Float(1.0, min=0, max=1, allow_none=True))\
.tag(sync=True, display_name='Opacities')
box_width = Int(None, min=5, allow_none=True).tag(sync=True, display_name='Box Width')
auto_detect_outliers = Bool(True).tag(sync=True, display_name='Auto-detect Outliers')
_view_name = Unicode('Boxplot').tag(sync=True)
_model_name = Unicode('BoxplotModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,593 | bqplot.axes | ColorAxis | A colorbar axis.
A color axis is the visual representation of a color scale.
Attributes
----------
scale: ColorScale
The scale represented by the axis
| class ColorAxis(Axis):
"""A colorbar axis.
A color axis is the visual representation of a color scale.
Attributes
----------
scale: ColorScale
The scale represented by the axis
"""
orientation = Enum(['horizontal', 'vertical'],
default_value='horizontal').tag(sync=True)
side = Enum(['bottom', 'top', 'left', 'right'],
default_value='bottom').tag(sync=True)
label = Unicode().tag(sync=True)
scale = Instance(ColorScale).tag(sync=True, **widget_serialization)
_view_name = Unicode('ColorAxis').tag(sync=True)
_model_name = Unicode('ColorAxisModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,650 | bqplot.scales | ColorScale | A color scale.
A mapping from numbers to colors. The relation is affine by part.
Attributes
----------
scale_type: {'linear'}
scale type
colors: list of colors (default: [])
list of colors
min: float or None (default: None)
if not None, min is the minimal value of the domain
max: float or None (default: None)
if not None, max is the maximal value of the domain
mid: float or None (default: None)
if not None, mid is the value corresponding to the mid color.
scheme: string (default: 'RdYlGn')
Colorbrewer color scheme of the color scale.
extrapolation: {'constant', 'linear'} (default: 'constant')
How to extrapolate values outside the [min, max] domain.
rtype: string (class-level attribute)
The range type of a color scale is 'Color'. This should not be modified.
dtype: type (class-level attribute)
the associated data type / domain type
| class ColorScale(Scale):
"""A color scale.
A mapping from numbers to colors. The relation is affine by part.
Attributes
----------
scale_type: {'linear'}
scale type
colors: list of colors (default: [])
list of colors
min: float or None (default: None)
if not None, min is the minimal value of the domain
max: float or None (default: None)
if not None, max is the maximal value of the domain
mid: float or None (default: None)
if not None, mid is the value corresponding to the mid color.
scheme: string (default: 'RdYlGn')
Colorbrewer color scheme of the color scale.
extrapolation: {'constant', 'linear'} (default: 'constant')
How to extrapolate values outside the [min, max] domain.
rtype: string (class-level attribute)
The range type of a color scale is 'Color'. This should not be modified.
dtype: type (class-level attribute)
the associated data type / domain type
"""
rtype = 'Color'
dtype = np.number
scale_type = Enum(['linear'], default_value='linear').tag(sync=True)
colors = List(trait=Color(default_value=None, allow_none=True))\
.tag(sync=True)
min = Float(None, allow_none=True).tag(sync=True)
max = Float(None, allow_none=True).tag(sync=True)
mid = Float(None, allow_none=True).tag(sync=True)
scheme = Unicode('RdYlGn').tag(sync=True)
extrapolation = Enum(['constant', 'linear'], default_value='constant').tag(sync=True)
_view_name = Unicode('ColorScale').tag(sync=True)
_model_name = Unicode('ColorScaleModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,768 | traittypes.traittypes | DataFrame | A pandas dataframe trait type. | class DataFrame(PandasType):
"""A pandas dataframe trait type."""
info_text = 'a pandas dataframe'
def __init__(self, default_value=Empty, allow_none=False, dtype=None, **kwargs):
if 'klass' not in kwargs and self.klass is None:
import pandas as pd
kwargs['klass'] = pd.DataFrame
super(DataFrame, self).__init__(
default_value=default_value, allow_none=allow_none, dtype=dtype, **kwargs)
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|
32,770 | traittypes.traittypes | __init__ | null | def __init__(self, default_value=Empty, allow_none=False, dtype=None, **kwargs):
if 'klass' not in kwargs and self.klass is None:
import pandas as pd
kwargs['klass'] = pd.DataFrame
super(DataFrame, self).__init__(
default_value=default_value, allow_none=allow_none, dtype=dtype, **kwargs)
| (self, default_value=traittypes.Empty, allow_none=False, dtype=None, **kwargs) | [
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|
32,786 | traittypes.traittypes | make_dynamic_default | null | def make_dynamic_default(self):
if self.default_value is None or self.default_value is Undefined:
return self.default_value
else:
return self.default_value.copy()
| (self) | [
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|
32,787 | traittypes.traittypes | set | null | def set(self, obj, value):
new_value = self._validate(obj, value)
old_value = obj._trait_values.get(self.name, self.default_value)
obj._trait_values[self.name] = new_value
if ((old_value is None and new_value is not None) or
(old_value is Undefined and new_value is not Undefined) or
not old_value.equals(new_value)):
obj._notify_trait(self.name, old_value, new_value)
| (self, obj, value) | [
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|
32,792 | traittypes.traittypes | validate | null | def validate(self, obj, value):
if value is None and not self.allow_none:
self.error(obj, value)
if value is None or value is Undefined:
return super(PandasType, self).validate(obj, value)
try:
value = self.klass(value)
except (ValueError, TypeError) as e:
raise TraitError(e)
return super(PandasType, self).validate(obj, value)
| (self, obj, value) | [
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|
32,793 | bqplot.traits | Date |
A datetime trait type.
Converts the passed date into a string format that can be used to
construct a JavaScript datetime.
| class Date(TraitType):
"""
A datetime trait type.
Converts the passed date into a string format that can be used to
construct a JavaScript datetime.
"""
def validate(self, obj, value):
try:
if isinstance(value, dt.datetime):
return value
if isinstance(value, dt.date):
return dt.datetime(value.year, value.month, value.day)
if np.issubdtype(np.dtype(value), np.datetime64):
# TODO: Fix this. Right now, we have to limit the precision
# of time to microseconds because np.datetime64.astype(datetime)
# returns date values only for precision <= 'us'
value_truncated = np.datetime64(value, 'us')
return value_truncated.astype(dt.datetime)
except Exception:
self.error(obj, value)
self.error(obj, value)
def __init__(self, default_value=dt.datetime.today(), **kwargs):
super(Date, self).__init__(default_value=default_value, **kwargs)
self.tag(**date_serialization)
| (default_value: Any = datetime.datetime(2024, 5, 12, 8, 41, 20, 704540), **kwargs) | [
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|
32,795 | bqplot.traits | __init__ | null | def __init__(self, default_value=dt.datetime.today(), **kwargs):
super(Date, self).__init__(default_value=default_value, **kwargs)
self.tag(**date_serialization)
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|
32,815 | bqplot.traits | validate | null | def validate(self, obj, value):
try:
if isinstance(value, dt.datetime):
return value
if isinstance(value, dt.date):
return dt.datetime(value.year, value.month, value.day)
if np.issubdtype(np.dtype(value), np.datetime64):
# TODO: Fix this. Right now, we have to limit the precision
# of time to microseconds because np.datetime64.astype(datetime)
# returns date values only for precision <= 'us'
value_truncated = np.datetime64(value, 'us')
return value_truncated.astype(dt.datetime)
except Exception:
self.error(obj, value)
self.error(obj, value)
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|
32,816 | bqplot.scales | DateColorScale | A date color scale.
A mapping from dates to a numerical domain.
Attributes
----------
min: Date or None (default: None)
if not None, min is the minimal value of the domain
max: Date or None (default: None)
if not None, max is the maximal value of the domain
mid: Date or None (default: None)
if not None, mid is the value corresponding to the mid color.
rtype: string (class-level attribute)
This attribute should not be modified by the user.
The range type of a color scale is 'Color'.
dtype: type (class-level attribute)
the associated data type / domain type
| class DateColorScale(ColorScale):
"""A date color scale.
A mapping from dates to a numerical domain.
Attributes
----------
min: Date or None (default: None)
if not None, min is the minimal value of the domain
max: Date or None (default: None)
if not None, max is the maximal value of the domain
mid: Date or None (default: None)
if not None, mid is the value corresponding to the mid color.
rtype: string (class-level attribute)
This attribute should not be modified by the user.
The range type of a color scale is 'Color'.
dtype: type (class-level attribute)
the associated data type / domain type
"""
dtype = np.datetime64
domain_class = Type(Date)
min = Date(default_value=None, allow_none=True).tag(sync=True)
mid = Date(default_value=None, allow_none=True).tag(sync=True)
max = Date(default_value=None, allow_none=True).tag(sync=True)
_view_name = Unicode('DateColorScale').tag(sync=True)
_model_name = Unicode('DateColorScaleModel').tag(sync=True)
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|
32,873 | bqplot.scales | DateScale | A date scale, with customizable formatting.
An affine mapping from dates to a numerical range.
Attributes
----------
min: Date or None (default: None)
if not None, min is the minimal value of the domain
max: Date (default: None)
if not None, max is the maximal value of the domain
domain_class: type (default: Date)
traitlet type used to validate values in of the domain of the scale.
rtype: string (class-level attribute)
This attribute should not be modified by the user.
The range type of a linear scale is numerical.
dtype: type (class-level attribute)
the associated data type / domain type
| class DateScale(Scale):
"""A date scale, with customizable formatting.
An affine mapping from dates to a numerical range.
Attributes
----------
min: Date or None (default: None)
if not None, min is the minimal value of the domain
max: Date (default: None)
if not None, max is the maximal value of the domain
domain_class: type (default: Date)
traitlet type used to validate values in of the domain of the scale.
rtype: string (class-level attribute)
This attribute should not be modified by the user.
The range type of a linear scale is numerical.
dtype: type (class-level attribute)
the associated data type / domain type
"""
rtype = 'Number'
dtype = np.datetime64
domain_class = Type(Date)
min = Date(default_value=None, allow_none=True).tag(sync=True)
max = Date(default_value=None, allow_none=True).tag(sync=True)
_view_name = Unicode('DateScale').tag(sync=True)
_model_name = Unicode('DateScaleModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
32,987 | bqplot.scales | EquiRectangular | An elementary projection that uses the identity function.
The projection is neither equal-area nor conformal.
Attributes
----------
scale_factor: float (default: 145)
Specifies the scale value for the projection
center: tuple (default: (0, 60))
Specifies the longitude and latitude where the map is centered.
| class EquiRectangular(GeoScale):
"""An elementary projection that uses the identity function.
The projection is neither equal-area nor conformal.
Attributes
----------
scale_factor: float (default: 145)
Specifies the scale value for the projection
center: tuple (default: (0, 60))
Specifies the longitude and latitude where the map is centered.
"""
scale_factor = Float(145.0).tag(sync=True)
center = Tuple((0, 60)).tag(sync=True)
rtype = '(Number, Number)'
dtype = np.number
_view_name = Unicode('EquiRectangular').tag(sync=True)
_model_name = Unicode('EquiRectangularModel').tag(sync=True)
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|
33,044 | bqplot.figure | Figure | Main canvas for drawing a chart.
The Figure object holds the list of Marks and Axes. It also holds an
optional Interaction object that is responsible for figure-level mouse
interactions, the "interaction layer".
Besides, the Figure object has two reference scales, for positioning items
in an absolute fashion in the figure canvas.
Attributes
----------
title: string (default: '')
title of the figure
axes: List of Axes (default: [])
list containing the instances of the axes for the figure
marks: List of Marks (default: [])
list containing the marks which are to be appended to the figure
interaction: Interaction or None (default: None)
optional interaction layer for the figure
scale_x: Scale
Scale representing the x values of the figure
scale_y: Scale
Scale representing the y values of the figure
padding_x: Float (default: 0.0)
Padding to be applied in the horizontal direction of the figure
around the data points, proportion of the horizontal length
padding_y: Float (default: 0.025)
Padding to be applied in the vertical direction of the figure
around the data points, proportion of the vertical length
legend_location: {'top-right', 'top', 'top-left', 'left',
'bottom-left', 'bottom', 'bottom-right', 'right'}
location of the legend relative to the center of the figure
background_style: Dict (default: {})
CSS style to be applied to the background of the figure
legend_style: Dict (default: {})
CSS style to be applied to the SVG legend e.g, {'fill': 'white'}
legend_text: Dict (default: {})
CSS style to be applied to the legend text e.g., {'font-size': 20}
title_style: Dict (default: {})
CSS style to be applied to the title of the figure
animation_duration: nonnegative int (default: 0)
Duration of transition on change of data attributes, in milliseconds.
pixel_ratio:
Pixel ratio of the WebGL canvas (2 on retina screens). Set to 1 for better performance,
but less crisp edges. If set to None it will use the browser's window.devicePixelRatio.
Layout Attributes
fig_margin: dict (default: {top=60, bottom=60, left=60, right=60})
Dictionary containing the top, bottom, left and right margins. The user
is responsible for making sure that the width and height are greater
than the sum of the margins.
min_aspect_ratio: float
minimum width / height ratio of the figure
max_aspect_ratio: float
maximum width / height ratio of the figure
Methods
-------
save_png:
Saves the figure as a PNG file
save_svg:
Saves the figure as an SVG file
Note
----
The aspect ratios stand for width / height ratios.
- If the available space is within bounds in terms of min and max aspect
ratio, we use the entire available space.
- If the available space is too oblong horizontally, we use the client
height and the width that corresponds max_aspect_ratio (maximize width
under the constraints).
- If the available space is too oblong vertically, we use the client width
and the height that corresponds to min_aspect_ratio (maximize height
under the constraint).
This corresponds to maximizing the area under the constraints.
Default min and max aspect ratio are both equal to 16 / 9.
| class Figure(DOMWidget):
"""Main canvas for drawing a chart.
The Figure object holds the list of Marks and Axes. It also holds an
optional Interaction object that is responsible for figure-level mouse
interactions, the "interaction layer".
Besides, the Figure object has two reference scales, for positioning items
in an absolute fashion in the figure canvas.
Attributes
----------
title: string (default: '')
title of the figure
axes: List of Axes (default: [])
list containing the instances of the axes for the figure
marks: List of Marks (default: [])
list containing the marks which are to be appended to the figure
interaction: Interaction or None (default: None)
optional interaction layer for the figure
scale_x: Scale
Scale representing the x values of the figure
scale_y: Scale
Scale representing the y values of the figure
padding_x: Float (default: 0.0)
Padding to be applied in the horizontal direction of the figure
around the data points, proportion of the horizontal length
padding_y: Float (default: 0.025)
Padding to be applied in the vertical direction of the figure
around the data points, proportion of the vertical length
legend_location: {'top-right', 'top', 'top-left', 'left',
'bottom-left', 'bottom', 'bottom-right', 'right'}
location of the legend relative to the center of the figure
background_style: Dict (default: {})
CSS style to be applied to the background of the figure
legend_style: Dict (default: {})
CSS style to be applied to the SVG legend e.g, {'fill': 'white'}
legend_text: Dict (default: {})
CSS style to be applied to the legend text e.g., {'font-size': 20}
title_style: Dict (default: {})
CSS style to be applied to the title of the figure
animation_duration: nonnegative int (default: 0)
Duration of transition on change of data attributes, in milliseconds.
pixel_ratio:
Pixel ratio of the WebGL canvas (2 on retina screens). Set to 1 for better performance,
but less crisp edges. If set to None it will use the browser's window.devicePixelRatio.
Layout Attributes
fig_margin: dict (default: {top=60, bottom=60, left=60, right=60})
Dictionary containing the top, bottom, left and right margins. The user
is responsible for making sure that the width and height are greater
than the sum of the margins.
min_aspect_ratio: float
minimum width / height ratio of the figure
max_aspect_ratio: float
maximum width / height ratio of the figure
Methods
-------
save_png:
Saves the figure as a PNG file
save_svg:
Saves the figure as an SVG file
Note
----
The aspect ratios stand for width / height ratios.
- If the available space is within bounds in terms of min and max aspect
ratio, we use the entire available space.
- If the available space is too oblong horizontally, we use the client
height and the width that corresponds max_aspect_ratio (maximize width
under the constraints).
- If the available space is too oblong vertically, we use the client width
and the height that corresponds to min_aspect_ratio (maximize height
under the constraint).
This corresponds to maximizing the area under the constraints.
Default min and max aspect ratio are both equal to 16 / 9.
"""
title = Unicode().tag(sync=True, display_name='Title')
axes = List(Instance(Axis)).tag(sync=True, **widget_serialization)
marks = List(Instance(Mark)).tag(sync=True, **widget_serialization)
interaction = Instance(Interaction, default_value=None,
allow_none=True).tag(sync=True,
**widget_serialization)
scale_x = Instance(Scale).tag(sync=True, **widget_serialization)
scale_y = Instance(Scale).tag(sync=True, **widget_serialization)
title_style = Dict(value_trait=Unicode()).tag(sync=True)
background_style = Dict().tag(sync=True)
legend_style = Dict().tag(sync=True)
legend_text = Dict().tag(sync=True)
theme = Enum(['classic', 'gg'], default_value='classic').tag(sync=True)
min_aspect_ratio = Float(0.01).tag(sync=True)
max_aspect_ratio = Float(100).tag(sync=True)
pixel_ratio = Float(None, allow_none=True).tag(sync=True)
fig_margin = Dict(dict(top=60, bottom=60, left=60, right=60))\
.tag(sync=True)
padding_x = Float(0.0, min=0.0, max=1.0).tag(sync=True)
padding_y = Float(0.025, min=0.0, max=1.0).tag(sync=True)
legend_location = Enum(['top-right', 'top', 'top-left', 'left',
'bottom-left', 'bottom', 'bottom-right', 'right'],
default_value='top-right')\
.tag(sync=True, display_name='Legend position')
animation_duration = Int().tag(sync=True,
display_name='Animation duration')
def __init__(self, **kwargs):
super(Figure, self).__init__(**kwargs)
self._upload_png_callback = None
self.on_msg(self._handle_custom_msgs)
@default('scale_x')
def _default_scale_x(self):
return LinearScale(min=0, max=1, allow_padding=False)
@default('scale_y')
def _default_scale_y(self):
return LinearScale(min=0, max=1, allow_padding=False)
def save_png(self, filename='bqplot.png', scale=None):
'''
Saves the Figure as a PNG file
Parameters
----------
filename: str (default: 'bqplot.png')
name of the saved file
scale: float (default: None)
Scale up the png resolution when scale > 1, when not given base this on the screen pixel ratio.
'''
self.send({'type': 'save_png', 'filename': filename, 'scale': scale})
def save_svg(self, filename='bqplot.svg'):
'''
Saves the Figure as an SVG file
Parameters
----------
filename: str (default: 'bqplot.svg')
name of the saved file
'''
self.send({"type": "save_svg", "filename": filename})
def get_png_data(self, callback, scale=None):
'''
Gets the Figure as a PNG memory view
Parameters
----------
callback: callable
Called with the PNG data as the only positional argument.
scale: float (default: None)
Scale up the png resolution when scale > 1, when not given base this on the screen pixel ratio.
'''
if self._upload_png_callback:
raise Exception('get_png_data already in progress')
self._upload_png_callback = callback
self.send({'type': 'upload_png', 'scale': scale})
@validate('min_aspect_ratio', 'max_aspect_ratio')
def _validate_aspect_ratio(self, proposal):
value = proposal['value']
if proposal['trait'].name == 'min_aspect_ratio' and \
value > self.max_aspect_ratio:
raise TraitError('setting min_aspect_ratio > max_aspect_ratio')
if proposal['trait'].name == 'max_aspect_ratio' and \
value < self.min_aspect_ratio:
raise TraitError('setting max_aspect_ratio < min_aspect_ratio')
return value
def _handle_custom_msgs(self, _, content, buffers=None):
if content.get('event') == 'upload_png':
try:
self._upload_png_callback(buffers[0])
finally:
self._upload_png_callback = None
_view_name = Unicode('Figure').tag(sync=True)
_model_name = Unicode('FigureModel').tag(sync=True)
_view_module = Unicode('bqplot').tag(sync=True)
_model_module = Unicode('bqplot').tag(sync=True)
_view_module_version = Unicode(__frontend_version__).tag(sync=True)
_model_module_version = Unicode(__frontend_version__).tag(sync=True)
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|
33,049 | bqplot.figure | __init__ | null | def __init__(self, **kwargs):
super(Figure, self).__init__(**kwargs)
self._upload_png_callback = None
self.on_msg(self._handle_custom_msgs)
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|
33,060 | bqplot.figure | _handle_custom_msgs | null | def _handle_custom_msgs(self, _, content, buffers=None):
if content.get('event') == 'upload_png':
try:
self._upload_png_callback(buffers[0])
finally:
self._upload_png_callback = None
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|
33,080 | bqplot.figure | get_png_data |
Gets the Figure as a PNG memory view
Parameters
----------
callback: callable
Called with the PNG data as the only positional argument.
scale: float (default: None)
Scale up the png resolution when scale > 1, when not given base this on the screen pixel ratio.
| def get_png_data(self, callback, scale=None):
'''
Gets the Figure as a PNG memory view
Parameters
----------
callback: callable
Called with the PNG data as the only positional argument.
scale: float (default: None)
Scale up the png resolution when scale > 1, when not given base this on the screen pixel ratio.
'''
if self._upload_png_callback:
raise Exception('get_png_data already in progress')
self._upload_png_callback = callback
self.send({'type': 'upload_png', 'scale': scale})
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|
33,094 | bqplot.figure | save_png |
Saves the Figure as a PNG file
Parameters
----------
filename: str (default: 'bqplot.png')
name of the saved file
scale: float (default: None)
Scale up the png resolution when scale > 1, when not given base this on the screen pixel ratio.
| def save_png(self, filename='bqplot.png', scale=None):
'''
Saves the Figure as a PNG file
Parameters
----------
filename: str (default: 'bqplot.png')
name of the saved file
scale: float (default: None)
Scale up the png resolution when scale > 1, when not given base this on the screen pixel ratio.
'''
self.send({'type': 'save_png', 'filename': filename, 'scale': scale})
| (self, filename='bqplot.png', scale=None) | [
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|
33,095 | bqplot.figure | save_svg |
Saves the Figure as an SVG file
Parameters
----------
filename: str (default: 'bqplot.svg')
name of the saved file
| def save_svg(self, filename='bqplot.svg'):
'''
Saves the Figure as an SVG file
Parameters
----------
filename: str (default: 'bqplot.svg')
name of the saved file
'''
self.send({"type": "save_svg", "filename": filename})
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|
33,109 | bqplot.marks | FlexLine | Flexible Lines mark.
In the case of the FlexLines mark, scales for 'x' and 'y' MUST be provided.
Scales for the color and width data attributes are optional. In the case
where another data attribute than 'x' or 'y' is provided but the
corresponding scale is missing, the data attribute is ignored.
Attributes
----------
name: string (class-level attributes)
user-friendly name of the mark
colors: list of colors (default: CATEGORY10)
List of colors for the Lines
stroke_width: float (default: 1.5)
Default stroke width of the Lines
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the data points (1d array)
y: numpy.ndarray (default: [])
ordinates of the data points (1d array)
color: numpy.ndarray or None (default: None)
Array controlling the color of the data points
width: numpy.ndarray or None (default: None)
Array controlling the widths of the Lines.
| class FlexLine(Mark):
"""Flexible Lines mark.
In the case of the FlexLines mark, scales for 'x' and 'y' MUST be provided.
Scales for the color and width data attributes are optional. In the case
where another data attribute than 'x' or 'y' is provided but the
corresponding scale is missing, the data attribute is ignored.
Attributes
----------
name: string (class-level attributes)
user-friendly name of the mark
colors: list of colors (default: CATEGORY10)
List of colors for the Lines
stroke_width: float (default: 1.5)
Default stroke width of the Lines
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the data points (1d array)
y: numpy.ndarray (default: [])
ordinates of the data points (1d array)
color: numpy.ndarray or None (default: None)
Array controlling the color of the data points
width: numpy.ndarray or None (default: None)
Array controlling the widths of the Lines.
"""
# Mark decoration
icon = 'fa-line-chart'
name = 'Flexible lines'
# Scaled attributes
x = Array([]).tag(sync=True, scaled=True, rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
y = Array([]).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
color = Array(None, allow_none=True)\
.tag(sync=True, scaled=True, rtype='Color',
atype='bqplot.ColorAxis',
**array_serialization).valid(array_squeeze)
width = Array(None, allow_none=True)\
.tag(sync=True, scaled=True, rtype='Number',
**array_serialization).valid(array_squeeze)
# Other attributes
scales_metadata = Dict({
'x': {'orientation': 'horizontal', 'dimension': 'x'},
'y': {'orientation': 'vertical', 'dimension': 'y'},
'color': {'dimension': 'color'}
}).tag(sync=True)
stroke_width = Float(1.5).tag(sync=True, display_name='Stroke width')
colors = List(trait=Color(default_value=None, allow_none=True),
default_value=CATEGORY10).tag(sync=True)
_view_name = Unicode('FlexLine').tag(sync=True)
_model_name = Unicode('FlexLineModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,197 | bqplot.scales | GeoScale | The base projection scale class for Map marks.
The GeoScale represents a mapping between topographic data and a
2d visual representation.
| class GeoScale(Scale):
"""The base projection scale class for Map marks.
The GeoScale represents a mapping between topographic data and a
2d visual representation.
"""
_view_name = Unicode('GeoScale').tag(sync=True)
_model_name = Unicode('GeoScaleModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,254 | bqplot.scales | Gnomonic | A perspective projection which displays great circles as straight lines.
The projection is neither equal-area nor conformal.
Attributes
----------
scale_factor: float (default: 145)
Specifies the scale value for the projection
center: tuple (default: (0, 60))
Specifies the longitude and latitude where the map is centered.
precision: float (default: 0.1)
Specifies the threshold for the projections adaptive resampling to the
specified value in pixels.
clip_angle: float (default: 89.999)
Specifies the clipping circle radius to the specified angle in degrees.
| class Gnomonic(GeoScale):
"""A perspective projection which displays great circles as straight lines.
The projection is neither equal-area nor conformal.
Attributes
----------
scale_factor: float (default: 145)
Specifies the scale value for the projection
center: tuple (default: (0, 60))
Specifies the longitude and latitude where the map is centered.
precision: float (default: 0.1)
Specifies the threshold for the projections adaptive resampling to the
specified value in pixels.
clip_angle: float (default: 89.999)
Specifies the clipping circle radius to the specified angle in degrees.
"""
scale_factor = Float(145.0).tag(sync=True)
center = Tuple((0, 60)).tag(sync=True)
precision = Float(0.1).tag(sync=True)
clip_angle = Float(89.999, min=0.0, max=360.0).tag(sync=True)
rtype = '(Number, Number)'
dtype = np.number
_view_name = Unicode('Gnomonic').tag(sync=True)
_model_name = Unicode('GnomonicModel').tag(sync=True)
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|
33,311 | bqplot.marks | Graph | Graph with nodes and links.
Attributes
----------
node_data: List
list of node attributes for the graph
link_matrix: numpy.ndarray of shape(len(nodes), len(nodes))
link data passed as 2d matrix
link_data: List
list of link attributes for the graph
charge: int (default: -600)
charge of force layout. Will be ignored when x and y data attributes
are set
static: bool (default: False)
whether the graph is static or not
link_distance: float (default: 100)
link distance in pixels between nodes. Will be ignored when x and y
data attributes are set
link_type: {'arc', 'line', 'slant_line'} (default: 'arc')
Enum representing link type
directed: bool (default: True)
directed or undirected graph
highlight_links: bool (default: True)
highlights incoming and outgoing links when hovered on a node
colors: list (default: CATEGORY10)
list of node colors
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the node data points (1d array)
y: numpy.ndarray (default: [])
ordinates of the node data points (1d array)
color: numpy.ndarray or None (default: None)
color of the node data points (1d array).
link_color: numpy.ndarray of shape(len(nodes), len(nodes))
link data passed as 2d matrix
| class Graph(Mark):
"""Graph with nodes and links.
Attributes
----------
node_data: List
list of node attributes for the graph
link_matrix: numpy.ndarray of shape(len(nodes), len(nodes))
link data passed as 2d matrix
link_data: List
list of link attributes for the graph
charge: int (default: -600)
charge of force layout. Will be ignored when x and y data attributes
are set
static: bool (default: False)
whether the graph is static or not
link_distance: float (default: 100)
link distance in pixels between nodes. Will be ignored when x and y
data attributes are set
link_type: {'arc', 'line', 'slant_line'} (default: 'arc')
Enum representing link type
directed: bool (default: True)
directed or undirected graph
highlight_links: bool (default: True)
highlights incoming and outgoing links when hovered on a node
colors: list (default: CATEGORY10)
list of node colors
Data Attributes
x: numpy.ndarray (default: [])
abscissas of the node data points (1d array)
y: numpy.ndarray (default: [])
ordinates of the node data points (1d array)
color: numpy.ndarray or None (default: None)
color of the node data points (1d array).
link_color: numpy.ndarray of shape(len(nodes), len(nodes))
link data passed as 2d matrix
"""
charge = Int(-600).tag(sync=True)
static = Bool(False).tag(sync=True)
link_distance = Float(100).tag(sync=True)
node_data = List().tag(sync=True)
link_data = List().tag(sync=True)
link_matrix = Array([]).tag(sync=True, rtype='Number',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 2))
link_type = Enum(['arc', 'line', 'slant_line'],
default_value='arc').tag(sync=True)
directed = Bool(True).tag(sync=True)
colors = List(trait=Color(default_value=None, allow_none=True),
default_value=CATEGORY10).tag(sync=True,
display_name='Colors')
interactions = Dict({'hover': 'tooltip', 'click': 'select'}).tag(sync=True)
highlight_links = Bool(True).tag(sync=True)
# Scaled attributes
x = Array([], allow_none=True).tag(sync=True,
scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_dimension_bounds(1, 1))
y = Array([], allow_none=True).tag(sync=True,
scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_dimension_bounds(1, 1))
color = Array(None, allow_none=True).tag(sync=True,
scaled=True,
rtype='Color',
atype='bqplot.ColorAxis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
link_color = Array([]).tag(sync=True, rtype='Color',
atype='bqplot.ColorAxis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 2))
hovered_style = Dict().tag(sync=True)
unhovered_style = Dict().tag(sync=True)
hovered_point = Int(None, allow_none=True).tag(sync=True)
# Other attributes
scales_metadata = Dict({
'x': {'orientation': 'horizontal', 'dimension': 'x'},
'y': {'orientation': 'vertical', 'dimension': 'y'},
'color': {'dimension': 'color'},
'link_color': {'dimension': 'link_color'}
}).tag(sync=True)
_model_name = Unicode('GraphModel').tag(sync=True)
_view_name = Unicode('Graph').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,376 | bqplot.marks | GridHeatMap | GridHeatMap mark.
Alignment: The tiles can be aligned so that the data matches either the
start, the end or the midpoints of the tiles. This is controlled by the
align attribute.
Suppose the data passed is a m-by-n matrix. If the scale for the rows is
Ordinal, then alignment is by default the mid points. For a non-ordinal
scale, the data cannot be aligned to the mid points of the rectangles.
If it is not ordinal, then two cases arise. If the number of rows passed
is m, then align attribute can be used. If the number of rows passed
is m+1, then the data are the boundaries of the m rectangles.
If rows and columns are not passed, and scales for them are also
not passed, then ordinal scales are generated for the rows and columns.
Attributes
----------
row_align: Enum(['start', 'end'])
This is only valid if the number of entries in `row` exactly match the
number of rows in `color` and the `row_scale` is not `OrdinalScale`.
`start` aligns the row values passed to be aligned with the start
of the tiles and `end` aligns the row values to the end of the tiles.
column_align: Enum(['start', end'])
This is only valid if the number of entries in `column` exactly
match the number of columns in `color` and the `column_scale` is
not `OrdinalScale`. `start` aligns the column values passed to
be aligned with the start of the tiles and `end` aligns the
column values to the end of the tiles.
anchor_style: dict (default: {})
Controls the style for the element which serves as the anchor during
selection.
display_format: string (default: None)
format for displaying values. If None, then values are not displayed
font_style: dict
CSS style for the text of each cell
Data Attributes
color: numpy.ndarray or None (default: None)
color of the data points (2d array). The number of elements in
this array correspond to the number of cells created in the heatmap.
row: numpy.ndarray or None (default: None)
labels for the rows of the `color` array passed. The length of
this can be no more than 1 away from the number of rows in `color`.
This is a scaled attribute and can be used to affect the height of the
cells as the entries of `row` can indicate the start or the end points
of the cells. Refer to the property `row_align`.
If this property is None, then a uniformly spaced grid is generated in
the row direction.
column: numpy.ndarray or None (default: None)
labels for the columns of the `color` array passed. The length of
this can be no more than 1 away from the number of columns in `color`
This is a scaled attribute and can be used to affect the width of the
cells as the entries of `column` can indicate the start or the
end points of the cells. Refer to the property `column_align`.
If this property is None, then a uniformly spaced grid is generated in
the column direction.
| class GridHeatMap(Mark):
"""GridHeatMap mark.
Alignment: The tiles can be aligned so that the data matches either the
start, the end or the midpoints of the tiles. This is controlled by the
align attribute.
Suppose the data passed is a m-by-n matrix. If the scale for the rows is
Ordinal, then alignment is by default the mid points. For a non-ordinal
scale, the data cannot be aligned to the mid points of the rectangles.
If it is not ordinal, then two cases arise. If the number of rows passed
is m, then align attribute can be used. If the number of rows passed
is m+1, then the data are the boundaries of the m rectangles.
If rows and columns are not passed, and scales for them are also
not passed, then ordinal scales are generated for the rows and columns.
Attributes
----------
row_align: Enum(['start', 'end'])
This is only valid if the number of entries in `row` exactly match the
number of rows in `color` and the `row_scale` is not `OrdinalScale`.
`start` aligns the row values passed to be aligned with the start
of the tiles and `end` aligns the row values to the end of the tiles.
column_align: Enum(['start', end'])
This is only valid if the number of entries in `column` exactly
match the number of columns in `color` and the `column_scale` is
not `OrdinalScale`. `start` aligns the column values passed to
be aligned with the start of the tiles and `end` aligns the
column values to the end of the tiles.
anchor_style: dict (default: {})
Controls the style for the element which serves as the anchor during
selection.
display_format: string (default: None)
format for displaying values. If None, then values are not displayed
font_style: dict
CSS style for the text of each cell
Data Attributes
color: numpy.ndarray or None (default: None)
color of the data points (2d array). The number of elements in
this array correspond to the number of cells created in the heatmap.
row: numpy.ndarray or None (default: None)
labels for the rows of the `color` array passed. The length of
this can be no more than 1 away from the number of rows in `color`.
This is a scaled attribute and can be used to affect the height of the
cells as the entries of `row` can indicate the start or the end points
of the cells. Refer to the property `row_align`.
If this property is None, then a uniformly spaced grid is generated in
the row direction.
column: numpy.ndarray or None (default: None)
labels for the columns of the `color` array passed. The length of
this can be no more than 1 away from the number of columns in `color`
This is a scaled attribute and can be used to affect the width of the
cells as the entries of `column` can indicate the start or the
end points of the cells. Refer to the property `column_align`.
If this property is None, then a uniformly spaced grid is generated in
the column direction.
"""
# Scaled attributes
row = Array(None, allow_none=True).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
column = Array(None, allow_none=True).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
color = Array(None, allow_none=True).tag(sync=True, scaled=True,
rtype='Color',
atype='bqplot.ColorAxis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 2))
# Other attributes
scales_metadata = Dict({
'row': {'orientation': 'vertical', 'dimension': 'y'},
'column': {'orientation': 'horizontal', 'dimension': 'x'},
'color': {'dimension': 'color'}
}).tag(sync=True)
row_align = Enum(['start', 'end'], default_value='start').tag(sync=True)
column_align = Enum(['start', 'end'], default_value='start').tag(sync=True)
null_color = Color('black', allow_none=True).tag(sync=True)
stroke = Color('black', allow_none=True).tag(sync=True)
opacity = Float(1.0, min=0.2, max=1).tag(sync=True, display_name='Opacity')
anchor_style = Dict().tag(sync=True)
display_format = Unicode(default_value=None, allow_none=True)\
.tag(sync=True)
font_style = Dict().tag(sync=True)
def __init__(self, **kwargs):
# Adding scales in case they are not passed too.
scales = kwargs.pop('scales', {})
if scales.get('row', None) is None:
row_scale = OrdinalScale(reverse=True)
scales['row'] = row_scale
if scales.get('column', None) is None:
column_scale = OrdinalScale()
scales['column'] = column_scale
kwargs['scales'] = scales
super(GridHeatMap, self).__init__(**kwargs)
@validate('row')
def _validate_row(self, proposal):
row = proposal.value
if row is None:
return row
color = np.asarray(self.color)
n_rows = color.shape[0]
if len(row) != n_rows and len(row) != n_rows + 1 and len(row) != n_rows - 1:
raise TraitError('row must be an array of size color.shape[0]')
return row
@validate('column')
def _validate_column(self, proposal):
column = proposal.value
if column is None:
return column
color = np.asarray(self.color)
n_columns = color.shape[1]
if len(column) != n_columns and len(column) != n_columns + 1 and len(column) != n_columns - 1:
raise TraitError('column must be an array of size color.shape[1]')
return column
_view_name = Unicode('GridHeatMap').tag(sync=True)
_model_name = Unicode('GridHeatMapModel').tag(sync=True)
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|
33,381 | bqplot.marks | __init__ | null | def __init__(self, **kwargs):
# Adding scales in case they are not passed too.
scales = kwargs.pop('scales', {})
if scales.get('row', None) is None:
row_scale = OrdinalScale(reverse=True)
scales['row'] = row_scale
if scales.get('column', None) is None:
column_scale = OrdinalScale()
scales['column'] = column_scale
kwargs['scales'] = scales
super(GridHeatMap, self).__init__(**kwargs)
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|
33,441 | bqplot.marks | HeatMap | HeatMap mark.
Attributes
----------
Data Attributes
color: numpy.ndarray or None (default: None)
color of the data points (2d array).
x: numpy.ndarray or None (default: None)
labels for the columns of the `color` array passed. The length of
this has to be the number of columns in `color`.
This is a scaled attribute.
y: numpy.ndarray or None (default: None)
labels for the rows of the `color` array passed. The length of this has
to be the number of rows in `color`.
This is a scaled attribute.
| class HeatMap(Mark):
"""HeatMap mark.
Attributes
----------
Data Attributes
color: numpy.ndarray or None (default: None)
color of the data points (2d array).
x: numpy.ndarray or None (default: None)
labels for the columns of the `color` array passed. The length of
this has to be the number of columns in `color`.
This is a scaled attribute.
y: numpy.ndarray or None (default: None)
labels for the rows of the `color` array passed. The length of this has
to be the number of rows in `color`.
This is a scaled attribute.
"""
# Scaled attributes
x = Array(None, allow_none=True).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
y = Array(None, allow_none=True).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
color = Array(None, allow_none=True).tag(sync=True, scaled=True,
rtype='Color',
atype='bqplot.ColorAxis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(2, 2))
# Other attributes
scales_metadata = Dict({
'x': {'orientation': 'horizontal', 'dimension': 'x'},
'y': {'orientation': 'vertical', 'dimension': 'y'},
'color': {'dimension': 'color'}
}).tag(sync=True)
null_color = Color('black', allow_none=True).tag(sync=True)
def __init__(self, **kwargs):
data = kwargs['color']
kwargs.setdefault('x', range(data.shape[1]))
kwargs.setdefault('y', range(data.shape[0]))
scales = kwargs.pop('scales', {})
# Adding default x and y data if they are not passed.
# Adding scales in case they are not passed too.
if scales.get('x', None) is None:
x_scale = LinearScale()
scales['x'] = x_scale
if scales.get('y', None) is None:
y_scale = LinearScale()
scales['y'] = y_scale
kwargs['scales'] = scales
super(HeatMap, self).__init__(**kwargs)
_view_name = Unicode('HeatMap').tag(sync=True)
_model_name = Unicode('HeatMapModel').tag(sync=True)
| (**kwargs) | [
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|
33,446 | bqplot.marks | __init__ | null | def __init__(self, **kwargs):
data = kwargs['color']
kwargs.setdefault('x', range(data.shape[1]))
kwargs.setdefault('y', range(data.shape[0]))
scales = kwargs.pop('scales', {})
# Adding default x and y data if they are not passed.
# Adding scales in case they are not passed too.
if scales.get('x', None) is None:
x_scale = LinearScale()
scales['x'] = x_scale
if scales.get('y', None) is None:
y_scale = LinearScale()
scales['y'] = y_scale
kwargs['scales'] = scales
super(HeatMap, self).__init__(**kwargs)
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|
33,506 | bqplot.marks | Hist | Histogram mark.
In the case of the Hist mark, scales for 'sample' and 'count' MUST be
provided.
Attributes
----------
icon: string (class-level attribute)
font-awesome icon for that mark
name: string (class-level attribute)
user-friendly name of the mark
bins: nonnegative int (default: 10)
number of bins in the histogram
normalized: bool (default: False)
Boolean attribute to return normalized values which
sum to 1 or direct counts for the `count` attribute. The scale of
`count` attribute is determined by the value of this flag.
colors: list of colors (default: ['steelblue'])
List of colors of the Histogram. If the list is shorter than the number
of bins, the colors are reused.
stroke: Color or None (default: None)
Stroke color of the histogram
opacities: list of floats (default: [])
Opacity for the bins of the histogram. Defaults to 1 when the list
is too short, or the element of the list is set to None.
midpoints: list (default: [])
midpoints of the bins of the histogram. It is a read-only attribute.
Data Attributes
sample: numpy.ndarray (default: [])
sample of which the histogram must be computed.
count: numpy.ndarray (read-only)
number of sample points per bin. It is a read-only attribute.
Notes
-----
The fields which can be passed to the default tooltip are:
midpoint: mid-point of the bin related to the rectangle hovered on
count: number of elements in the bin hovered on
bin_start: start point of the bin
bin-end: end point of the bin
index: index of the bin
| class Hist(Mark):
"""Histogram mark.
In the case of the Hist mark, scales for 'sample' and 'count' MUST be
provided.
Attributes
----------
icon: string (class-level attribute)
font-awesome icon for that mark
name: string (class-level attribute)
user-friendly name of the mark
bins: nonnegative int (default: 10)
number of bins in the histogram
normalized: bool (default: False)
Boolean attribute to return normalized values which
sum to 1 or direct counts for the `count` attribute. The scale of
`count` attribute is determined by the value of this flag.
colors: list of colors (default: ['steelblue'])
List of colors of the Histogram. If the list is shorter than the number
of bins, the colors are reused.
stroke: Color or None (default: None)
Stroke color of the histogram
opacities: list of floats (default: [])
Opacity for the bins of the histogram. Defaults to 1 when the list
is too short, or the element of the list is set to None.
midpoints: list (default: [])
midpoints of the bins of the histogram. It is a read-only attribute.
Data Attributes
sample: numpy.ndarray (default: [])
sample of which the histogram must be computed.
count: numpy.ndarray (read-only)
number of sample points per bin. It is a read-only attribute.
Notes
-----
The fields which can be passed to the default tooltip are:
midpoint: mid-point of the bin related to the rectangle hovered on
count: number of elements in the bin hovered on
bin_start: start point of the bin
bin-end: end point of the bin
index: index of the bin
"""
# Mark decoration
icon = 'fa-signal'
name = 'Histogram'
# Scaled attributes
sample = Array([]).tag(sync=True, display_name='Sample',
scaled=True, rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, array_dimension_bounds(1, 1))
count = Array([], read_only=True).tag(sync=True,
display_name='Count',
scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze)
normalized = Bool().tag(sync=True)
# Other attributes
scales_metadata = Dict({
'sample': {'orientation': 'horizontal', 'dimension': 'x'},
'count': {'orientation': 'vertical', 'dimension': 'y'}
}).tag(sync=True)
bins = Int(10).tag(sync=True, display_name='Number of bins')
midpoints = List(read_only=True).tag(sync=True, display_name='Mid points')
# midpoints is a read-only attribute that is set when the mark is drawn
colors = List(trait=Color(default_value=None, allow_none=True),
default_value=['steelblue'])\
.tag(sync=True, display_name='Colors')
stroke = Color(None, allow_none=True).tag(sync=True)
opacities = List(trait=Float(1.0, min=0, max=1, allow_none=True))\
.tag(sync=True, display_name='Opacities')
_view_name = Unicode('Hist').tag(sync=True)
_model_name = Unicode('HistModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,571 | bqplot.marks | Image | Image mark, based on the ipywidgets image
If no scales are passed, uses the parent Figure scales.
Attributes
----------
image: Instance of ipywidgets.Image
Image to be displayed
Data Attributes
x: tuple (default: (0, 1))
abscissas of the left and right-hand side of the image
in the format (x0, x1)
y: tuple (default: (0, 1))
ordinates of the bottom and top side of the image
in the format (y0, y1)
| class Image(Mark):
"""Image mark, based on the ipywidgets image
If no scales are passed, uses the parent Figure scales.
Attributes
----------
image: Instance of ipywidgets.Image
Image to be displayed
Data Attributes
x: tuple (default: (0, 1))
abscissas of the left and right-hand side of the image
in the format (x0, x1)
y: tuple (default: (0, 1))
ordinates of the bottom and top side of the image
in the format (y0, y1)
"""
_view_name = Unicode('Image').tag(sync=True)
_model_name = Unicode('ImageModel').tag(sync=True)
image = Instance(widgets.Image).tag(sync=True, **widget_serialization)
pixelated = Bool(True).tag(sync=True)
x = Array(default_value=(0, 1)).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, shape(2))
y = Array(default_value=(0, 1)).tag(sync=True, scaled=True,
rtype='Number',
atype='bqplot.Axis',
**array_serialization)\
.valid(array_squeeze, shape(2))
scales_metadata = Dict({
'x': {'orientation': 'horizontal', 'dimension': 'x'},
'y': {'orientation': 'vertical', 'dimension': 'y'},
}).tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,685 | bqplot.interacts | Interaction | The base interaction class.
An interaction is a mouse interaction layer for a figure that requires the
capture of all mouse events on the plot area. A consequence is that one can
allow only one interaction at any time on a figure.
An interaction can be associated with features such as selection or
manual change of specific mark. Although, they differ from the so called
'mark interactions' in that they do not rely on knowing whether a specific
element of the mark are hovered by the mouse.
Attributes
----------
types: dict (class-level attribute) representing interaction types
A registry of existing interaction types.
| class Interaction(Widget):
"""The base interaction class.
An interaction is a mouse interaction layer for a figure that requires the
capture of all mouse events on the plot area. A consequence is that one can
allow only one interaction at any time on a figure.
An interaction can be associated with features such as selection or
manual change of specific mark. Although, they differ from the so called
'mark interactions' in that they do not rely on knowing whether a specific
element of the mark are hovered by the mouse.
Attributes
----------
types: dict (class-level attribute) representing interaction types
A registry of existing interaction types.
"""
types = {}
_view_name = Unicode('Interaction').tag(sync=True)
_model_name = Unicode('BaseModel').tag(sync=True)
_view_module = Unicode('bqplot').tag(sync=True)
_model_module = Unicode('bqplot').tag(sync=True)
_view_module_version = Unicode(__frontend_version__).tag(sync=True)
_model_module_version = Unicode(__frontend_version__).tag(sync=True)
# We cannot display an interaction outside of a figure
_ipython_display_ = None
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,742 | bqplot.marks | Label | Label mark.
Attributes
----------
x_offset: int (default: 0)
horizontal offset in pixels from the stated x location
y_offset: int (default: 0)
vertical offset in pixels from the stated y location
text: string (default: '')
text to be displayed
default_size: string (default: '14px')
font size in px, em or ex
font_weight: {'bold', 'normal', 'bolder'}
font weight of the caption
drag_size: nonnegative float (default: 1.)
Ratio of the size of the dragged label font size to the default
label font size.
align: {'start', 'middle', 'end'}
alignment of the text with respect to the provided location
enable_move: Bool (default: False)
Enable the label to be moved by dragging. Refer to restrict_x,
restrict_y for more options.
restrict_x: bool (default: False)
Restricts movement of the label to only along the x axis. This is valid
only when enable_move is set to True. If both restrict_x and restrict_y
are set to True, the label cannot be moved.
restrict_y: bool (default: False)
Restricts movement of the label to only along the y axis. This is valid
only when enable_move is set to True. If both restrict_x and restrict_y
are set to True, the label cannot be moved.
Data Attributes
x: numpy.ndarray (default: [])
horizontal position of the labels, in data coordinates or in
figure coordinates
y: numpy.ndarray (default: [])
vertical position of the labels, in data coordinates or in
figure coordinates
color: numpy.ndarray or None (default: None)
label colors
size: numpy.ndarray or None (default: None)
label sizes
rotation: numpy.ndarray or None (default: None)
label rotations
opacity: numpy.ndarray or None (default: None)
label opacities
| class Label(_ScatterBase):
"""Label mark.
Attributes
----------
x_offset: int (default: 0)
horizontal offset in pixels from the stated x location
y_offset: int (default: 0)
vertical offset in pixels from the stated y location
text: string (default: '')
text to be displayed
default_size: string (default: '14px')
font size in px, em or ex
font_weight: {'bold', 'normal', 'bolder'}
font weight of the caption
drag_size: nonnegative float (default: 1.)
Ratio of the size of the dragged label font size to the default
label font size.
align: {'start', 'middle', 'end'}
alignment of the text with respect to the provided location
enable_move: Bool (default: False)
Enable the label to be moved by dragging. Refer to restrict_x,
restrict_y for more options.
restrict_x: bool (default: False)
Restricts movement of the label to only along the x axis. This is valid
only when enable_move is set to True. If both restrict_x and restrict_y
are set to True, the label cannot be moved.
restrict_y: bool (default: False)
Restricts movement of the label to only along the y axis. This is valid
only when enable_move is set to True. If both restrict_x and restrict_y
are set to True, the label cannot be moved.
Data Attributes
x: numpy.ndarray (default: [])
horizontal position of the labels, in data coordinates or in
figure coordinates
y: numpy.ndarray (default: [])
vertical position of the labels, in data coordinates or in
figure coordinates
color: numpy.ndarray or None (default: None)
label colors
size: numpy.ndarray or None (default: None)
label sizes
rotation: numpy.ndarray or None (default: None)
label rotations
opacity: numpy.ndarray or None (default: None)
label opacities
"""
# Mark decoration
icon = 'fa-font'
name = 'Labels'
# Other attributes
x_offset = Int(0).tag(sync=True)
y_offset = Int(0).tag(sync=True)
colors = List(trait=Color(default_value=None,
allow_none=True),
default_value=CATEGORY10)\
.tag(sync=True, display_name='Colors')
rotate_angle = Float(0.0).tag(sync=True)
text = Array(None, allow_none=True)\
.tag(sync=True, **array_serialization).valid(array_squeeze)
default_size = Float(16.).tag(sync=True)
drag_size = Float(1.).tag(sync=True)
font_unit = Enum(['px', 'em', 'pt', '%'],
default_value='px').tag(sync=True)
font_weight = Enum(['bold', 'normal', 'bolder'],
default_value='bold').tag(sync=True)
align = Enum(['start', 'middle', 'end'],
default_value='start').tag(sync=True)
_view_name = Unicode('Label').tag(sync=True)
_model_name = Unicode('LabelModel').tag(sync=True)
| (*args: 't.Any', **kwargs: 't.Any') -> 't.Any' | [
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|
33,747 | bqplot.marks | __init__ | null | def __init__(self, **kwargs):
self._drag_start_handlers = CallbackDispatcher()
self._drag_handlers = CallbackDispatcher()
self._drag_end_handlers = CallbackDispatcher()
super(_ScatterBase, self).__init__(**kwargs)
self._name_to_handler.update({
'drag_start': self._drag_start_handlers,
'drag_end': self._drag_end_handlers,
'drag': self._drag_handlers
})
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|
33,786 | bqplot.marks | on_drag | null | def on_drag(self, callback, remove=False):
self._drag_handlers.register_callback(callback, remove=remove)
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|
33,787 | bqplot.marks | on_drag_end | null | def on_drag_end(self, callback, remove=False):
self._drag_end_handlers.register_callback(callback, remove=remove)
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|
33,788 | bqplot.marks | on_drag_start | null | def on_drag_start(self, callback, remove=False):
self._drag_start_handlers.register_callback(callback, remove=remove)
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|
33,810 | ipywidgets.widgets.widget_layout | Layout | Layout specification
Defines a layout that can be expressed using CSS. Supports a subset of
https://developer.mozilla.org/en-US/docs/Web/CSS/Reference
When a property is also accessible via a shorthand property, we only
expose the shorthand.
For example:
- ``flex-grow``, ``flex-shrink`` and ``flex-basis`` are bound to ``flex``.
- ``flex-wrap`` and ``flex-direction`` are bound to ``flex-flow``.
- ``margin-[top/bottom/left/right]`` values are bound to ``margin``, etc.
| class Layout(Widget):
"""Layout specification
Defines a layout that can be expressed using CSS. Supports a subset of
https://developer.mozilla.org/en-US/docs/Web/CSS/Reference
When a property is also accessible via a shorthand property, we only
expose the shorthand.
For example:
- ``flex-grow``, ``flex-shrink`` and ``flex-basis`` are bound to ``flex``.
- ``flex-wrap`` and ``flex-direction`` are bound to ``flex-flow``.
- ``margin-[top/bottom/left/right]`` values are bound to ``margin``, etc.
"""
_view_name = Unicode('LayoutView').tag(sync=True)
_view_module = Unicode('@jupyter-widgets/base').tag(sync=True)
_view_module_version = Unicode(__jupyter_widgets_base_version__).tag(sync=True)
_model_name = Unicode('LayoutModel').tag(sync=True)
# Keys
align_content = CaselessStrEnum(['flex-start', 'flex-end', 'center', 'space-between',
'space-around', 'space-evenly', 'stretch'] + CSS_PROPERTIES, allow_none=True, help="The align-content CSS attribute.").tag(sync=True)
align_items = CaselessStrEnum(['flex-start', 'flex-end', 'center',
'baseline', 'stretch'] + CSS_PROPERTIES, allow_none=True, help="The align-items CSS attribute.").tag(sync=True)
align_self = CaselessStrEnum(['auto', 'flex-start', 'flex-end',
'center', 'baseline', 'stretch'] + CSS_PROPERTIES, allow_none=True, help="The align-self CSS attribute.").tag(sync=True)
border_top = Unicode(None, allow_none=True, help="The border top CSS attribute.").tag(sync=True)
border_right = Unicode(None, allow_none=True, help="The border right CSS attribute.").tag(sync=True)
border_bottom = Unicode(None, allow_none=True, help="The border bottom CSS attribute.").tag(sync=True)
border_left = Unicode(None, allow_none=True, help="The border left CSS attribute.").tag(sync=True)
bottom = Unicode(None, allow_none=True, help="The bottom CSS attribute.").tag(sync=True)
display = Unicode(None, allow_none=True, help="The display CSS attribute.").tag(sync=True)
flex = Unicode(None, allow_none=True, help="The flex CSS attribute.").tag(sync=True)
flex_flow = Unicode(None, allow_none=True, help="The flex-flow CSS attribute.").tag(sync=True)
height = Unicode(None, allow_none=True, help="The height CSS attribute.").tag(sync=True)
justify_content = CaselessStrEnum(['flex-start', 'flex-end', 'center',
'space-between', 'space-around'] + CSS_PROPERTIES, allow_none=True, help="The justify-content CSS attribute.").tag(sync=True)
justify_items = CaselessStrEnum(['flex-start', 'flex-end', 'center'] + CSS_PROPERTIES,
allow_none=True, help="The justify-items CSS attribute.").tag(sync=True)
left = Unicode(None, allow_none=True, help="The left CSS attribute.").tag(sync=True)
margin = Unicode(None, allow_none=True, help="The margin CSS attribute.").tag(sync=True)
max_height = Unicode(None, allow_none=True, help="The max-height CSS attribute.").tag(sync=True)
max_width = Unicode(None, allow_none=True, help="The max-width CSS attribute.").tag(sync=True)
min_height = Unicode(None, allow_none=True, help="The min-height CSS attribute.").tag(sync=True)
min_width = Unicode(None, allow_none=True, help="The min-width CSS attribute.").tag(sync=True)
overflow = Unicode(None, allow_none=True, help="The overflow CSS attribute.").tag(sync=True)
order = Unicode(None, allow_none=True, help="The order CSS attribute.").tag(sync=True)
padding = Unicode(None, allow_none=True, help="The padding CSS attribute.").tag(sync=True)
right = Unicode(None, allow_none=True, help="The right CSS attribute.").tag(sync=True)
top = Unicode(None, allow_none=True, help="The top CSS attribute.").tag(sync=True)
visibility = CaselessStrEnum(['visible', 'hidden']+CSS_PROPERTIES, allow_none=True, help="The visibility CSS attribute.").tag(sync=True)
width = Unicode(None, allow_none=True, help="The width CSS attribute.").tag(sync=True)
object_fit = CaselessStrEnum(['contain', 'cover', 'fill', 'scale-down', 'none'], allow_none=True, help="The object-fit CSS attribute.").tag(sync=True)
object_position = Unicode(None, allow_none=True, help="The object-position CSS attribute.").tag(sync=True)
grid_auto_columns = Unicode(None, allow_none=True, help="The grid-auto-columns CSS attribute.").tag(sync=True)
grid_auto_flow = CaselessStrEnum(['column','row','row dense','column dense']+ CSS_PROPERTIES, allow_none=True, help="The grid-auto-flow CSS attribute.").tag(sync=True)
grid_auto_rows = Unicode(None, allow_none=True, help="The grid-auto-rows CSS attribute.").tag(sync=True)
grid_gap = Unicode(None, allow_none=True, help="The grid-gap CSS attribute.").tag(sync=True)
grid_template_rows = Unicode(None, allow_none=True, help="The grid-template-rows CSS attribute.").tag(sync=True)
grid_template_columns = Unicode(None, allow_none=True, help="The grid-template-columns CSS attribute.").tag(sync=True)
grid_template_areas = Unicode(None, allow_none=True, help="The grid-template-areas CSS attribute.").tag(sync=True)
grid_row = Unicode(None, allow_none=True, help="The grid-row CSS attribute.").tag(sync=True)
grid_column = Unicode(None, allow_none=True, help="The grid-column CSS attribute.").tag(sync=True)
grid_area = Unicode(None, allow_none=True, help="The grid-area CSS attribute.").tag(sync=True)
def __init__(self, **kwargs):
if 'border' in kwargs:
border = kwargs.pop('border')
for side in ['top', 'right', 'bottom', 'left']:
kwargs.setdefault(f'border_{side}', border)
super().__init__(**kwargs)
def _get_border(self):
"""
`border` property getter. Return the common value of all side
borders if they are identical. Otherwise return None.
"""
found = None
for side in ['top', 'right', 'bottom', 'left']:
if not hasattr(self, "border_" + side):
return
old, found = found, getattr(self, "border_" + side)
if found is None or (old is not None and found != old):
return
return found
def _set_border(self, border):
"""
`border` property setter. Set all 4 sides to `border` string.
"""
for side in ['top', 'right', 'bottom', 'left']:
setattr(self, "border_" + side, border)
border = property(_get_border, _set_border)
| (**kwargs) | [
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|
33,815 | ipywidgets.widgets.widget_layout | __init__ | null | def __init__(self, **kwargs):
if 'border' in kwargs:
border = kwargs.pop('border')
for side in ['top', 'right', 'bottom', 'left']:
kwargs.setdefault(f'border_{side}', border)
super().__init__(**kwargs)
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|
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