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int64 0
731k
| package
stringlengths 2
98
⌀ | name
stringlengths 1
76
| docstring
stringlengths 0
281k
⌀ | code
stringlengths 4
8.19k
| signature
stringlengths 2
42.8k
⌀ | embed_func_code
listlengths 768
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|---|---|---|---|---|---|---|
31,840 | stevedore.extension | _load_plugins | null | def _load_plugins(self, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
extensions = []
for ep in self.list_entry_points():
LOG.debug('found extension %r', ep)
try:
ext = self._load_one_plugin(ep,
invoke_on_load,
invoke_args,
invoke_kwds,
verify_requirements,
)
if ext:
extensions.append(ext)
except (KeyboardInterrupt, AssertionError):
raise
except Exception as err:
if self._on_load_failure_callback is not None:
self._on_load_failure_callback(self, ep, err)
else:
# Log the reason we couldn't import the module,
# usually without a traceback. The most common
# reason is an ImportError due to a missing
# dependency, and the error message should be
# enough to debug that. If debug logging is
# enabled for our logger, provide the full
# traceback.
LOG.error('Could not load %r: %s', ep.name, err,
exc_info=LOG.isEnabledFor(logging.DEBUG))
return extensions
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|
31,841 | stevedore.extension | entry_points_names | Return the list of entry points names for this namespace. | def entry_points_names(self):
"""Return the list of entry points names for this namespace."""
return list(map(operator.attrgetter("name"), self.list_entry_points()))
| (self) | [
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|
31,842 | stevedore.extension | items | Return an iterator of tuples of the form (name, extension).
This is analogous to the Mapping.items() method.
| def items(self):
"""Return an iterator of tuples of the form (name, extension).
This is analogous to the Mapping.items() method.
"""
return self._extensions_by_name.items()
| (self) | [
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|
31,843 | stevedore.extension | list_entry_points | Return the list of entry points for this namespace.
The entry points are not actually loaded, their list is just read and
returned.
| def list_entry_points(self):
"""Return the list of entry points for this namespace.
The entry points are not actually loaded, their list is just read and
returned.
"""
if self.namespace not in self.ENTRY_POINT_CACHE:
eps = list(_cache.get_group_all(self.namespace))
self.ENTRY_POINT_CACHE[self.namespace] = eps
return self.ENTRY_POINT_CACHE[self.namespace]
| (self) | [
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|
31,844 | stevedore.extension | map | Iterate over the extensions invoking func() for each.
The signature for func() should be::
def func(ext, *args, **kwds):
pass
The first argument to func(), 'ext', is the
:class:`~stevedore.extension.Extension` instance.
Exceptions raised from within func() are propagated up and
processing stopped if self.propagate_map_exceptions is True,
otherwise they are logged and ignored.
:param func: Callable to invoke for each extension.
:param args: Variable arguments to pass to func()
:param kwds: Keyword arguments to pass to func()
:returns: List of values returned from func()
| def map(self, func, *args, **kwds):
"""Iterate over the extensions invoking func() for each.
The signature for func() should be::
def func(ext, *args, **kwds):
pass
The first argument to func(), 'ext', is the
:class:`~stevedore.extension.Extension` instance.
Exceptions raised from within func() are propagated up and
processing stopped if self.propagate_map_exceptions is True,
otherwise they are logged and ignored.
:param func: Callable to invoke for each extension.
:param args: Variable arguments to pass to func()
:param kwds: Keyword arguments to pass to func()
:returns: List of values returned from func()
"""
if not self.extensions:
# FIXME: Use a more specific exception class here.
raise NoMatches('No %s extensions found' % self.namespace)
response = []
for e in self.extensions:
self._invoke_one_plugin(response.append, func, e, args, kwds)
return response
| (self, func, *args, **kwds) | [
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|
31,845 | stevedore.extension | map_method | Iterate over the extensions invoking a method by name.
This is equivalent of using :meth:`map` with func set to
`lambda x: x.obj.method_name()`
while being more convenient.
Exceptions raised from within the called method are propagated up
and processing stopped if self.propagate_map_exceptions is True,
otherwise they are logged and ignored.
.. versionadded:: 0.12
:param method_name: The extension method name
to call for each extension.
:param args: Variable arguments to pass to method
:param kwds: Keyword arguments to pass to method
:returns: List of values returned from methods
| def map_method(self, method_name, *args, **kwds):
"""Iterate over the extensions invoking a method by name.
This is equivalent of using :meth:`map` with func set to
`lambda x: x.obj.method_name()`
while being more convenient.
Exceptions raised from within the called method are propagated up
and processing stopped if self.propagate_map_exceptions is True,
otherwise they are logged and ignored.
.. versionadded:: 0.12
:param method_name: The extension method name
to call for each extension.
:param args: Variable arguments to pass to method
:param kwds: Keyword arguments to pass to method
:returns: List of values returned from methods
"""
return self.map(self._call_extension_method,
method_name, *args, **kwds)
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|
31,846 | stevedore.extension | names | Returns the names of the discovered extensions | def names(self):
"Returns the names of the discovered extensions"
# We want to return the names of the extensions in the order
# they would be used by map(), since some subclasses change
# that order.
return [e.name for e in self.extensions]
| (self) | [
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|
31,847 | stevedore.enabled | EnabledExtensionManager | Loads only plugins that pass a check function.
The check_func argument should return a boolean, with ``True``
indicating that the extension should be loaded and made available
and ``False`` indicating that the extension should be ignored.
:param namespace: The namespace for the entry points.
:type namespace: str
:param check_func: Function to determine which extensions to load.
:type check_func: callable, taking an :class:`Extension`
instance as argument
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged and
then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
| class EnabledExtensionManager(ExtensionManager):
"""Loads only plugins that pass a check function.
The check_func argument should return a boolean, with ``True``
indicating that the extension should be loaded and made available
and ``False`` indicating that the extension should be ignored.
:param namespace: The namespace for the entry points.
:type namespace: str
:param check_func: Function to determine which extensions to load.
:type check_func: callable, taking an :class:`Extension`
instance as argument
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged and
then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
"""
def __init__(self, namespace, check_func, invoke_on_load=False,
invoke_args=(), invoke_kwds={},
propagate_map_exceptions=False,
on_load_failure_callback=None,
verify_requirements=False,):
self.check_func = check_func
super(EnabledExtensionManager, self).__init__(
namespace,
invoke_on_load=invoke_on_load,
invoke_args=invoke_args,
invoke_kwds=invoke_kwds,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback,
verify_requirements=verify_requirements,
)
def _load_one_plugin(self, ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
ext = super(EnabledExtensionManager, self)._load_one_plugin(
ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements,
)
if ext and not self.check_func(ext):
LOG.debug('ignoring extension %r', ep.name)
return None
return ext
| (namespace, check_func, invoke_on_load=False, invoke_args=(), invoke_kwds={}, propagate_map_exceptions=False, on_load_failure_callback=None, verify_requirements=False) | [
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|
31,850 | stevedore.enabled | __init__ | null | def __init__(self, namespace, check_func, invoke_on_load=False,
invoke_args=(), invoke_kwds={},
propagate_map_exceptions=False,
on_load_failure_callback=None,
verify_requirements=False,):
self.check_func = check_func
super(EnabledExtensionManager, self).__init__(
namespace,
invoke_on_load=invoke_on_load,
invoke_args=invoke_args,
invoke_kwds=invoke_kwds,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback,
verify_requirements=verify_requirements,
)
| (self, namespace, check_func, invoke_on_load=False, invoke_args=(), invoke_kwds={}, propagate_map_exceptions=False, on_load_failure_callback=None, verify_requirements=False) | [
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|
31,853 | stevedore.extension | _init_attributes | null | def _init_attributes(self, namespace, propagate_map_exceptions=False,
on_load_failure_callback=None):
self.namespace = namespace
self.propagate_map_exceptions = propagate_map_exceptions
self._on_load_failure_callback = on_load_failure_callback
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|
31,854 | stevedore.extension | _init_plugins | null | def _init_plugins(self, extensions):
self.extensions = extensions
self._extensions_by_name_cache = None
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|
31,856 | stevedore.enabled | _load_one_plugin | null | def _load_one_plugin(self, ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
ext = super(EnabledExtensionManager, self)._load_one_plugin(
ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements,
)
if ext and not self.check_func(ext):
LOG.debug('ignoring extension %r', ep.name)
return None
return ext
| (self, ep, invoke_on_load, invoke_args, invoke_kwds, verify_requirements) | [
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|
31,864 | stevedore.extension | ExtensionManager | Base class for all of the other managers.
:param namespace: The namespace for the entry points.
:type namespace: str
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged and
then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
| class ExtensionManager(object):
"""Base class for all of the other managers.
:param namespace: The namespace for the entry points.
:type namespace: str
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged and
then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
"""
def __init__(self, namespace,
invoke_on_load=False,
invoke_args=(),
invoke_kwds={},
propagate_map_exceptions=False,
on_load_failure_callback=None,
verify_requirements=False):
self._init_attributes(
namespace,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
extensions = self._load_plugins(invoke_on_load,
invoke_args,
invoke_kwds,
verify_requirements)
self._init_plugins(extensions)
@classmethod
def make_test_instance(cls, extensions, namespace='TESTING',
propagate_map_exceptions=False,
on_load_failure_callback=None,
verify_requirements=False):
"""Construct a test ExtensionManager
Test instances are passed a list of extensions to work from rather
than loading them from entry points.
:param extensions: Pre-configured Extension instances to use
:type extensions: list of :class:`~stevedore.extension.Extension`
:param namespace: The namespace for the manager; used only for
identification since the extensions are passed in.
:type namespace: str
:param propagate_map_exceptions: When calling map, controls whether
exceptions are propagated up through the map call or whether they
are logged and then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will
be called when an entrypoint can not be loaded. The
arguments that will be provided when this is called (when
an entrypoint fails to load) are (manager, entrypoint,
exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
:return: The manager instance, initialized for testing
"""
o = cls.__new__(cls)
o._init_attributes(namespace,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
o._init_plugins(extensions)
return o
def _init_attributes(self, namespace, propagate_map_exceptions=False,
on_load_failure_callback=None):
self.namespace = namespace
self.propagate_map_exceptions = propagate_map_exceptions
self._on_load_failure_callback = on_load_failure_callback
def _init_plugins(self, extensions):
self.extensions = extensions
self._extensions_by_name_cache = None
@property
def _extensions_by_name(self):
if self._extensions_by_name_cache is None:
d = {}
for e in self.extensions:
d[e.name] = e
self._extensions_by_name_cache = d
return self._extensions_by_name_cache
ENTRY_POINT_CACHE = {}
def list_entry_points(self):
"""Return the list of entry points for this namespace.
The entry points are not actually loaded, their list is just read and
returned.
"""
if self.namespace not in self.ENTRY_POINT_CACHE:
eps = list(_cache.get_group_all(self.namespace))
self.ENTRY_POINT_CACHE[self.namespace] = eps
return self.ENTRY_POINT_CACHE[self.namespace]
def entry_points_names(self):
"""Return the list of entry points names for this namespace."""
return list(map(operator.attrgetter("name"), self.list_entry_points()))
def _load_plugins(self, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
extensions = []
for ep in self.list_entry_points():
LOG.debug('found extension %r', ep)
try:
ext = self._load_one_plugin(ep,
invoke_on_load,
invoke_args,
invoke_kwds,
verify_requirements,
)
if ext:
extensions.append(ext)
except (KeyboardInterrupt, AssertionError):
raise
except Exception as err:
if self._on_load_failure_callback is not None:
self._on_load_failure_callback(self, ep, err)
else:
# Log the reason we couldn't import the module,
# usually without a traceback. The most common
# reason is an ImportError due to a missing
# dependency, and the error message should be
# enough to debug that. If debug logging is
# enabled for our logger, provide the full
# traceback.
LOG.error('Could not load %r: %s', ep.name, err,
exc_info=LOG.isEnabledFor(logging.DEBUG))
return extensions
def _load_one_plugin(self, ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
# NOTE(dhellmann): Using require=False is deprecated in
# setuptools 11.3.
if hasattr(ep, 'resolve') and hasattr(ep, 'require'):
if verify_requirements:
ep.require()
plugin = ep.resolve()
else:
plugin = ep.load()
if invoke_on_load:
obj = plugin(*invoke_args, **invoke_kwds)
else:
obj = None
return Extension(ep.name, ep, plugin, obj)
def names(self):
"Returns the names of the discovered extensions"
# We want to return the names of the extensions in the order
# they would be used by map(), since some subclasses change
# that order.
return [e.name for e in self.extensions]
def map(self, func, *args, **kwds):
"""Iterate over the extensions invoking func() for each.
The signature for func() should be::
def func(ext, *args, **kwds):
pass
The first argument to func(), 'ext', is the
:class:`~stevedore.extension.Extension` instance.
Exceptions raised from within func() are propagated up and
processing stopped if self.propagate_map_exceptions is True,
ot | (namespace, invoke_on_load=False, invoke_args=(), invoke_kwds={}, propagate_map_exceptions=False, on_load_failure_callback=None, verify_requirements=False) | [
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|
31,867 | stevedore.extension | __init__ | null | def __init__(self, namespace,
invoke_on_load=False,
invoke_args=(),
invoke_kwds={},
propagate_map_exceptions=False,
on_load_failure_callback=None,
verify_requirements=False):
self._init_attributes(
namespace,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
extensions = self._load_plugins(invoke_on_load,
invoke_args,
invoke_kwds,
verify_requirements)
self._init_plugins(extensions)
| (self, namespace, invoke_on_load=False, invoke_args=(), invoke_kwds={}, propagate_map_exceptions=False, on_load_failure_callback=None, verify_requirements=False) | [
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|
31,873 | stevedore.extension | _load_one_plugin | null | def _load_one_plugin(self, ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
# NOTE(dhellmann): Using require=False is deprecated in
# setuptools 11.3.
if hasattr(ep, 'resolve') and hasattr(ep, 'require'):
if verify_requirements:
ep.require()
plugin = ep.resolve()
else:
plugin = ep.load()
if invoke_on_load:
obj = plugin(*invoke_args, **invoke_kwds)
else:
obj = None
return Extension(ep.name, ep, plugin, obj)
| (self, ep, invoke_on_load, invoke_args, invoke_kwds, verify_requirements) | [
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|
31,881 | stevedore.hook | HookManager | Coordinate execution of multiple extensions using a common name.
:param namespace: The namespace for the entry points.
:type namespace: str
:param name: The name of the hooks to load.
:type name: str
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
:type on_missing_entrypoints_callback: function
:param warn_on_missing_entrypoint: Flag to control whether failing
to load a plugin is reported via a log mess. Only applies if
on_missing_entrypoints_callback is None.
:type warn_on_missing_entrypoint: bool
| class HookManager(NamedExtensionManager):
"""Coordinate execution of multiple extensions using a common name.
:param namespace: The namespace for the entry points.
:type namespace: str
:param name: The name of the hooks to load.
:type name: str
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
:type on_missing_entrypoints_callback: function
:param warn_on_missing_entrypoint: Flag to control whether failing
to load a plugin is reported via a log mess. Only applies if
on_missing_entrypoints_callback is None.
:type warn_on_missing_entrypoint: bool
"""
def __init__(self, namespace, name,
invoke_on_load=False, invoke_args=(), invoke_kwds={},
on_load_failure_callback=None,
verify_requirements=False,
on_missing_entrypoints_callback=None,
# NOTE(dhellmann): This default is different from the
# base class because for hooks it is less likely to
# be an error to have no entry points present.
warn_on_missing_entrypoint=False):
super(HookManager, self).__init__(
namespace,
[name],
invoke_on_load=invoke_on_load,
invoke_args=invoke_args,
invoke_kwds=invoke_kwds,
on_load_failure_callback=on_load_failure_callback,
on_missing_entrypoints_callback=on_missing_entrypoints_callback,
verify_requirements=verify_requirements,
warn_on_missing_entrypoint=warn_on_missing_entrypoint,
)
def _init_attributes(self, namespace, names, name_order=False,
propagate_map_exceptions=False,
on_load_failure_callback=None):
super(HookManager, self)._init_attributes(
namespace, names,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
self._name = names[0]
def __getitem__(self, name):
"""Return the named extensions.
Accessing a HookManager as a dictionary (``em['name']``)
produces a list of the :class:`Extension` instance(s) with the
specified name, in the order they would be invoked by map().
"""
if name != self._name:
raise KeyError(name)
return self.extensions
| (namespace, name, invoke_on_load=False, invoke_args=(), invoke_kwds={}, on_load_failure_callback=None, verify_requirements=False, on_missing_entrypoints_callback=None, warn_on_missing_entrypoint=False) | [
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|
31,883 | stevedore.hook | __getitem__ | Return the named extensions.
Accessing a HookManager as a dictionary (``em['name']``)
produces a list of the :class:`Extension` instance(s) with the
specified name, in the order they would be invoked by map().
| def __getitem__(self, name):
"""Return the named extensions.
Accessing a HookManager as a dictionary (``em['name']``)
produces a list of the :class:`Extension` instance(s) with the
specified name, in the order they would be invoked by map().
"""
if name != self._name:
raise KeyError(name)
return self.extensions
| (self, name) | [
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|
31,884 | stevedore.hook | __init__ | null | def __init__(self, namespace, name,
invoke_on_load=False, invoke_args=(), invoke_kwds={},
on_load_failure_callback=None,
verify_requirements=False,
on_missing_entrypoints_callback=None,
# NOTE(dhellmann): This default is different from the
# base class because for hooks it is less likely to
# be an error to have no entry points present.
warn_on_missing_entrypoint=False):
super(HookManager, self).__init__(
namespace,
[name],
invoke_on_load=invoke_on_load,
invoke_args=invoke_args,
invoke_kwds=invoke_kwds,
on_load_failure_callback=on_load_failure_callback,
on_missing_entrypoints_callback=on_missing_entrypoints_callback,
verify_requirements=verify_requirements,
warn_on_missing_entrypoint=warn_on_missing_entrypoint,
)
| (self, namespace, name, invoke_on_load=False, invoke_args=(), invoke_kwds={}, on_load_failure_callback=None, verify_requirements=False, on_missing_entrypoints_callback=None, warn_on_missing_entrypoint=False) | [
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|
31,887 | stevedore.hook | _init_attributes | null | def _init_attributes(self, namespace, names, name_order=False,
propagate_map_exceptions=False,
on_load_failure_callback=None):
super(HookManager, self)._init_attributes(
namespace, names,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
self._name = names[0]
| (self, namespace, names, name_order=False, propagate_map_exceptions=False, on_load_failure_callback=None) | [
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|
31,888 | stevedore.named | _init_plugins | null | def _init_plugins(self, extensions):
super(NamedExtensionManager, self)._init_plugins(extensions)
if self._name_order:
self.extensions = [self[n] for n in self._names
if n not in self._missing_names]
| (self, extensions) | [
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|
31,898 | stevedore.named | NamedExtensionManager | Loads only the named extensions.
This is useful for explicitly enabling extensions in a
configuration file, for example.
:param namespace: The namespace for the entry points.
:type namespace: str
:param names: The names of the extensions to load.
:type names: list(str)
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param name_order: If true, sort the loaded extensions to match the
order used in ``names``.
:type name_order: bool
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged and
then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param on_missing_entrypoints_callback: Callback function that will be
called when one or more names cannot be found. The provided argument
will be a subset of the 'names' parameter.
:type on_missing_entrypoints_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
:param warn_on_missing_entrypoint: Flag to control whether failing
to load a plugin is reported via a log mess. Only applies if
on_missing_entrypoints_callback is None.
:type warn_on_missing_entrypoint: bool
| class NamedExtensionManager(ExtensionManager):
"""Loads only the named extensions.
This is useful for explicitly enabling extensions in a
configuration file, for example.
:param namespace: The namespace for the entry points.
:type namespace: str
:param names: The names of the extensions to load.
:type names: list(str)
:param invoke_on_load: Boolean controlling whether to invoke the
object returned by the entry point after the driver is loaded.
:type invoke_on_load: bool
:param invoke_args: Positional arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_args: tuple
:param invoke_kwds: Named arguments to pass when invoking
the object returned by the entry point. Only used if invoke_on_load
is True.
:type invoke_kwds: dict
:param name_order: If true, sort the loaded extensions to match the
order used in ``names``.
:type name_order: bool
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged and
then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will be called when
an entrypoint can not be loaded. The arguments that will be provided
when this is called (when an entrypoint fails to load) are
(manager, entrypoint, exception)
:type on_load_failure_callback: function
:param on_missing_entrypoints_callback: Callback function that will be
called when one or more names cannot be found. The provided argument
will be a subset of the 'names' parameter.
:type on_missing_entrypoints_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
:param warn_on_missing_entrypoint: Flag to control whether failing
to load a plugin is reported via a log mess. Only applies if
on_missing_entrypoints_callback is None.
:type warn_on_missing_entrypoint: bool
"""
def __init__(self, namespace, names,
invoke_on_load=False, invoke_args=(), invoke_kwds={},
name_order=False, propagate_map_exceptions=False,
on_load_failure_callback=None,
on_missing_entrypoints_callback=None,
verify_requirements=False,
warn_on_missing_entrypoint=True):
self._init_attributes(
namespace, names, name_order=name_order,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
extensions = self._load_plugins(invoke_on_load,
invoke_args,
invoke_kwds,
verify_requirements)
self._missing_names = set(names) - set([e.name for e in extensions])
if self._missing_names:
if on_missing_entrypoints_callback:
on_missing_entrypoints_callback(self._missing_names)
elif warn_on_missing_entrypoint:
LOG.warning('Could not load %s' %
', '.join(self._missing_names))
self._init_plugins(extensions)
@classmethod
def make_test_instance(cls, extensions, namespace='TESTING',
propagate_map_exceptions=False,
on_load_failure_callback=None,
verify_requirements=False):
"""Construct a test NamedExtensionManager
Test instances are passed a list of extensions to use rather than
loading them from entry points.
:param extensions: Pre-configured Extension instances
:type extensions: list of :class:`~stevedore.extension.Extension`
:param namespace: The namespace for the manager; used only for
identification since the extensions are passed in.
:type namespace: str
:param propagate_map_exceptions: Boolean controlling whether exceptions
are propagated up through the map call or whether they are logged
and then ignored
:type propagate_map_exceptions: bool
:param on_load_failure_callback: Callback function that will
be called when an entrypoint can not be loaded. The
arguments that will be provided when this is called (when
an entrypoint fails to load) are (manager, entrypoint,
exception)
:type on_load_failure_callback: function
:param verify_requirements: Use setuptools to enforce the
dependencies of the plugin(s) being loaded. Defaults to False.
:type verify_requirements: bool
:return: The manager instance, initialized for testing
"""
o = cls.__new__(cls)
names = [e.name for e in extensions]
o._init_attributes(namespace, names,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
o._init_plugins(extensions)
return o
def _init_attributes(self, namespace, names, name_order=False,
propagate_map_exceptions=False,
on_load_failure_callback=None):
super(NamedExtensionManager, self)._init_attributes(
namespace, propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
self._names = names
self._missing_names = set()
self._name_order = name_order
def _init_plugins(self, extensions):
super(NamedExtensionManager, self)._init_plugins(extensions)
if self._name_order:
self.extensions = [self[n] for n in self._names
if n not in self._missing_names]
def _load_one_plugin(self, ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements):
# Check the name before going any further to prevent
# undesirable code from being loaded at all if we are not
# going to use it.
if ep.name not in self._names:
return None
return super(NamedExtensionManager, self)._load_one_plugin(
ep, invoke_on_load, invoke_args, invoke_kwds,
verify_requirements,
)
| (namespace, names, invoke_on_load=False, invoke_args=(), invoke_kwds={}, name_order=False, propagate_map_exceptions=False, on_load_failure_callback=None, on_missing_entrypoints_callback=None, verify_requirements=False, warn_on_missing_entrypoint=True) | [
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|
31,901 | stevedore.named | __init__ | null | def __init__(self, namespace, names,
invoke_on_load=False, invoke_args=(), invoke_kwds={},
name_order=False, propagate_map_exceptions=False,
on_load_failure_callback=None,
on_missing_entrypoints_callback=None,
verify_requirements=False,
warn_on_missing_entrypoint=True):
self._init_attributes(
namespace, names, name_order=name_order,
propagate_map_exceptions=propagate_map_exceptions,
on_load_failure_callback=on_load_failure_callback)
extensions = self._load_plugins(invoke_on_load,
invoke_args,
invoke_kwds,
verify_requirements)
self._missing_names = set(names) - set([e.name for e in extensions])
if self._missing_names:
if on_missing_entrypoints_callback:
on_missing_entrypoints_callback(self._missing_names)
elif warn_on_missing_entrypoint:
LOG.warning('Could not load %s' %
', '.join(self._missing_names))
self._init_plugins(extensions)
| (self, namespace, names, invoke_on_load=False, invoke_args=(), invoke_kwds={}, name_order=False, propagate_map_exceptions=False, on_load_failure_callback=None, on_missing_entrypoints_callback=None, verify_requirements=False, warn_on_missing_entrypoint=True) | [
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|
31,924 | sonetel.account | Account |
Class representing the company account.
| class Account(util.Resource):
"""
Class representing the company account.
"""
def __init__(self, access_token: str):
if not access_token:
raise e.AuthException('access_token missing')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}/{const.API_ENDPOINT_ACCOUNT}/{self._accountid}'
def get(self) -> dict:
"""
Get information about your Sonetel account.
:returns: The account information if the request was processed successfully.
"""
return util.send_api_request(
token=self._token,
uri=self._url,
method='get',
)
def update(self, name: str = '', language: str = '', timezone: str = '') -> dict:
"""
Update your account information. Pass one or more of the following parameters:
:param name: String. New company name.
:param language: String. The ID of the new language you want to switch to. Changes the language you see in app.sonetel.com
:param timezone: String. The ID of the new timezone you want to switch to.
:returns: dict. The updated account information if the request was processed successfully.
"""
body = {}
if name:
body['name'] = name
if language:
body['language'] = language
if timezone:
body['timezone_details'] = {
"zone_id": timezone
}
if len(body) == 0:
return util.prepare_error(
code=const.ERR_ACCOUNT_UPDATE_BODY_EMPTY,
message='request body cannot be empty'
)
return util.send_api_request(
token=self._token,
uri=self._url,
method='put',
body=dumps(body)
)
def get_balance(self, currency: bool = False) -> str:
"""
Get the current prepaid balance in the account
:param currency: Boolean. Optional. Set to true if currency should be returned in the response.
:returns: A string representing the current prepaid balance in the Sonetel account.
"""
response = util.send_api_request(
token=self._token,
uri=self._url,
method='get',
)
balance = response['response']['credit_balance']
if currency:
balance += f" {response['response']['currency']}"
return balance
def get_accountid(self) -> str:
"""
Get your account ID.
:returns: String. Sonetel account ID.
"""
return self._accountid
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|
31,925 | sonetel.account | __init__ | null | def __init__(self, access_token: str):
if not access_token:
raise e.AuthException('access_token missing')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}/{const.API_ENDPOINT_ACCOUNT}/{self._accountid}'
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|
31,926 | sonetel.account | get |
Get information about your Sonetel account.
:returns: The account information if the request was processed successfully.
| def get(self) -> dict:
"""
Get information about your Sonetel account.
:returns: The account information if the request was processed successfully.
"""
return util.send_api_request(
token=self._token,
uri=self._url,
method='get',
)
| (self) -> dict | [
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|
31,927 | sonetel.account | get_accountid |
Get your account ID.
:returns: String. Sonetel account ID.
| def get_accountid(self) -> str:
"""
Get your account ID.
:returns: String. Sonetel account ID.
"""
return self._accountid
| (self) -> str | [
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|
31,928 | sonetel.account | get_balance |
Get the current prepaid balance in the account
:param currency: Boolean. Optional. Set to true if currency should be returned in the response.
:returns: A string representing the current prepaid balance in the Sonetel account.
| def get_balance(self, currency: bool = False) -> str:
"""
Get the current prepaid balance in the account
:param currency: Boolean. Optional. Set to true if currency should be returned in the response.
:returns: A string representing the current prepaid balance in the Sonetel account.
"""
response = util.send_api_request(
token=self._token,
uri=self._url,
method='get',
)
balance = response['response']['credit_balance']
if currency:
balance += f" {response['response']['currency']}"
return balance
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|
31,929 | sonetel.account | update |
Update your account information. Pass one or more of the following parameters:
:param name: String. New company name.
:param language: String. The ID of the new language you want to switch to. Changes the language you see in app.sonetel.com
:param timezone: String. The ID of the new timezone you want to switch to.
:returns: dict. The updated account information if the request was processed successfully.
| def update(self, name: str = '', language: str = '', timezone: str = '') -> dict:
"""
Update your account information. Pass one or more of the following parameters:
:param name: String. New company name.
:param language: String. The ID of the new language you want to switch to. Changes the language you see in app.sonetel.com
:param timezone: String. The ID of the new timezone you want to switch to.
:returns: dict. The updated account information if the request was processed successfully.
"""
body = {}
if name:
body['name'] = name
if language:
body['language'] = language
if timezone:
body['timezone_details'] = {
"zone_id": timezone
}
if len(body) == 0:
return util.prepare_error(
code=const.ERR_ACCOUNT_UPDATE_BODY_EMPTY,
message='request body cannot be empty'
)
return util.send_api_request(
token=self._token,
uri=self._url,
method='put',
body=dumps(body)
)
| (self, name: str = '', language: str = '', timezone: str = '') -> dict | [
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|
31,930 | sonetel.auth | Auth |
Authentication class. Create, refresh and fetch tokens.
| class Auth:
"""
Authentication class. Create, refresh and fetch tokens.
"""
def __init__(self, username: str, password: str):
self.__username = username
self.__password = password
# Get access token from API
token = self.create_token()
self._access_token = token['access_token']
self._refresh_token = token['refresh_token']
self._decoded_token = decode(
self._access_token,
audience='api.sonetel.com',
options={"verify_signature": False}
)
def create_token(self,
refresh_token: str = '',
grant_type: str = 'password',
refresh: str = 'yes',
):
"""
Create an API access token from the user's Sonetel email address and password.
Optionally, generate a refresh token. Set the ``grant_type`` to ``refresh_token`` to refresh an
existing access token.
**Documentation**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjExMzI3NDM3-authentication
:param refresh: Optional. Flag to return refresh token in the response. Accepted values 'yes' and 'no'. Defaults to 'yes'
:param grant_type: Optional. The OAuth2 grant type - `password` and `refresh_token` accepted. Defaults to 'password'
:param refresh_token: Optional. Pass the `refresh_token` generated from a previous request in this field to generate a new access_token.
:return: dict. The access token and refresh token if the request was processed successfully. If the request failed, the error message is returned.
"""
# Checks
if grant_type.strip().lower() not in const.CONST_TYPES_GRANT:
raise e.AuthException(f'invalid grant: {grant_type}')
if refresh.strip().lower() not in const.CONST_TYPES_REFRESH:
refresh = 'yes'
if grant_type.strip().lower() == 'refresh_token' and not refresh_token:
refresh_token = self._refresh_token
# Prepare the request body.
body = f"grant_type={grant_type}&refresh={refresh}"
# Add the refresh token to the request body if passed to the function
if grant_type == 'refresh_token':
body += f"&refresh_token={refresh_token}"
else:
body += f"&username={self.__username}&password={self.__password}"
# Prepare the request
auth = (const.CONST_JWT_USER, const.CONST_JWT_PASS)
headers = {'Content-Type': const.CONTENT_TYPE_AUTH}
# Send the request
try:
req = requests.post(
url=const.API_URI_AUTH,
data=body,
headers=headers,
auth=auth,
timeout=60
)
req.raise_for_status()
except requests.exceptions.ConnectionError as err:
return {'status': 'failed', 'error': 'ConnectionError', 'message': err}
except requests.exceptions.Timeout:
return {'status': 'failed', 'error': 'Timeout', 'message': 'Operation timed out. Please try again.'}
except requests.exceptions.HTTPError as err:
return {'status': 'failed', 'error': 'Timeout', 'message': err}
# Check the response and handle accordingly.
if req.status_code == requests.codes.ok: # pylint: disable=no-member
response_json = req.json()
if refresh_token and grant_type == 'refresh_token':
self._access_token = response_json["access_token"]
self._refresh_token = response_json["refresh_token"]
self._decoded_token = decode(
self._access_token,
audience='api.sonetel.com',
options={"verify_signature": False}
)
return response_json
return {'status': 'failed', 'error': 'Unknown error', 'message': req.text}
def get_access_token(self):
"""
Returns the access token
"""
return self._access_token if hasattr(self, '_access_token') else False
def get_refresh_token(self):
"""
Return the refresh token
"""
return self._refresh_token if hasattr(self, '_refresh_token') else False
def get_decoded_token(self):
"""
Returns the decoded token
"""
return self._decoded_token if hasattr(self, '_decoded_token') else False
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|
31,931 | sonetel.auth | __init__ | null | def __init__(self, username: str, password: str):
self.__username = username
self.__password = password
# Get access token from API
token = self.create_token()
self._access_token = token['access_token']
self._refresh_token = token['refresh_token']
self._decoded_token = decode(
self._access_token,
audience='api.sonetel.com',
options={"verify_signature": False}
)
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|
31,932 | sonetel.auth | create_token |
Create an API access token from the user's Sonetel email address and password.
Optionally, generate a refresh token. Set the ``grant_type`` to ``refresh_token`` to refresh an
existing access token.
**Documentation**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjExMzI3NDM3-authentication
:param refresh: Optional. Flag to return refresh token in the response. Accepted values 'yes' and 'no'. Defaults to 'yes'
:param grant_type: Optional. The OAuth2 grant type - `password` and `refresh_token` accepted. Defaults to 'password'
:param refresh_token: Optional. Pass the `refresh_token` generated from a previous request in this field to generate a new access_token.
:return: dict. The access token and refresh token if the request was processed successfully. If the request failed, the error message is returned.
| def create_token(self,
refresh_token: str = '',
grant_type: str = 'password',
refresh: str = 'yes',
):
"""
Create an API access token from the user's Sonetel email address and password.
Optionally, generate a refresh token. Set the ``grant_type`` to ``refresh_token`` to refresh an
existing access token.
**Documentation**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjExMzI3NDM3-authentication
:param refresh: Optional. Flag to return refresh token in the response. Accepted values 'yes' and 'no'. Defaults to 'yes'
:param grant_type: Optional. The OAuth2 grant type - `password` and `refresh_token` accepted. Defaults to 'password'
:param refresh_token: Optional. Pass the `refresh_token` generated from a previous request in this field to generate a new access_token.
:return: dict. The access token and refresh token if the request was processed successfully. If the request failed, the error message is returned.
"""
# Checks
if grant_type.strip().lower() not in const.CONST_TYPES_GRANT:
raise e.AuthException(f'invalid grant: {grant_type}')
if refresh.strip().lower() not in const.CONST_TYPES_REFRESH:
refresh = 'yes'
if grant_type.strip().lower() == 'refresh_token' and not refresh_token:
refresh_token = self._refresh_token
# Prepare the request body.
body = f"grant_type={grant_type}&refresh={refresh}"
# Add the refresh token to the request body if passed to the function
if grant_type == 'refresh_token':
body += f"&refresh_token={refresh_token}"
else:
body += f"&username={self.__username}&password={self.__password}"
# Prepare the request
auth = (const.CONST_JWT_USER, const.CONST_JWT_PASS)
headers = {'Content-Type': const.CONTENT_TYPE_AUTH}
# Send the request
try:
req = requests.post(
url=const.API_URI_AUTH,
data=body,
headers=headers,
auth=auth,
timeout=60
)
req.raise_for_status()
except requests.exceptions.ConnectionError as err:
return {'status': 'failed', 'error': 'ConnectionError', 'message': err}
except requests.exceptions.Timeout:
return {'status': 'failed', 'error': 'Timeout', 'message': 'Operation timed out. Please try again.'}
except requests.exceptions.HTTPError as err:
return {'status': 'failed', 'error': 'Timeout', 'message': err}
# Check the response and handle accordingly.
if req.status_code == requests.codes.ok: # pylint: disable=no-member
response_json = req.json()
if refresh_token and grant_type == 'refresh_token':
self._access_token = response_json["access_token"]
self._refresh_token = response_json["refresh_token"]
self._decoded_token = decode(
self._access_token,
audience='api.sonetel.com',
options={"verify_signature": False}
)
return response_json
return {'status': 'failed', 'error': 'Unknown error', 'message': req.text}
| (self, refresh_token: str = '', grant_type: str = 'password', refresh: str = 'yes') | [
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|
31,933 | sonetel.auth | get_access_token |
Returns the access token
| def get_access_token(self):
"""
Returns the access token
"""
return self._access_token if hasattr(self, '_access_token') else False
| (self) | [
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|
31,934 | sonetel.auth | get_decoded_token |
Returns the decoded token
| def get_decoded_token(self):
"""
Returns the decoded token
"""
return self._decoded_token if hasattr(self, '_decoded_token') else False
| (self) | [
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|
31,935 | sonetel.auth | get_refresh_token |
Return the refresh token
| def get_refresh_token(self):
"""
Return the refresh token
"""
return self._refresh_token if hasattr(self, '_refresh_token') else False
| (self) | [
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|
31,936 | sonetel.calls | Call |
Phone call class
| class Call(util.Resource):
"""
Phone call class
"""
def __init__(self, access_token, app_name: str = 'PythonSonetelPackage') -> None:
"""
Initiate the Call class.
:param access_token: Required. The access token generated from the Auth class.
:param app_name: The name of the app that is making the request. Defaults to 'PythonSonetelPackage'.
"""
if not access_token:
raise e.AuthException('access_token is required')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_CALLBACK}'
if len(app_name) < 2:
raise e.SonetelException('app_name must be at least 2 characters long')
self._app_name = f"{app_name}__{self._accountid}__{self._userid}"
def callback(self, num1: str, num2: str, cli1: str = 'automatic', cli2: str = 'automatic'):
"""
Use Sonetel's CallBack API to make business quality international calls at the cost of 2 local calls.
**Docs**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE1OTMzOTIy-make-calls
**Number Format:**\n
It is recommended that both the phone numbers (num1 and num2) be entered in the international E164 format with a
leading +. For example, if you want to call a US number (212) 555-1234, it should be set as `+12125551234`.
However you can also provide SIP addresses. Additionally, `num1` can be your Sonetel username - this will make
sure that the incoming call to you is handled as per your incoming settings defined in the app.
**Caller ID:**\n
It is best to use 'automatic' CLI as our system selects the best possible phone to be shown from the numbers
available in your account. If you don't have a Sonetel number, then your verified mobile number is used as CLI.
Read more at https://sonetel.com/cli
:param num1: Required. The first phone number that will be called.
This should be your phone number, SIP address or Sonetel email address.
:param num2: Required.The phone number or address that you wish to connect to.
:param cli1: Optional. The caller ID shown to the first person. Defaults to automatic.
:param cli2: Optional. The caller ID shown to the second person. Defaults to automatic.
:return: Return the status code and message as a dict.
"""
# Check if num1 and num2 are defined.
if num1 and num2:
# Initiate the callback
body = {
"app_id": f'{self._app_name}-{const.PKG_VERSION}',
"call1": num1,
"call2": num2,
"show_1": cli1,
"show_2": cli2
}
return util.send_api_request(
token=self._token,
uri=self._url,
method='post',
body=dumps(body)
)
return util.prepare_error(
code=const.ERR_CALLBACK_NUM_EMPTY,
message='num1 & num2 are required to make a call.'
)
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|
31,937 | sonetel.calls | __init__ |
Initiate the Call class.
:param access_token: Required. The access token generated from the Auth class.
:param app_name: The name of the app that is making the request. Defaults to 'PythonSonetelPackage'.
| def __init__(self, access_token, app_name: str = 'PythonSonetelPackage') -> None:
"""
Initiate the Call class.
:param access_token: Required. The access token generated from the Auth class.
:param app_name: The name of the app that is making the request. Defaults to 'PythonSonetelPackage'.
"""
if not access_token:
raise e.AuthException('access_token is required')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_CALLBACK}'
if len(app_name) < 2:
raise e.SonetelException('app_name must be at least 2 characters long')
self._app_name = f"{app_name}__{self._accountid}__{self._userid}"
| (self, access_token, app_name: str = 'PythonSonetelPackage') -> NoneType | [
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|
31,938 | sonetel.calls | callback |
Use Sonetel's CallBack API to make business quality international calls at the cost of 2 local calls.
**Docs**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE1OTMzOTIy-make-calls
**Number Format:**
It is recommended that both the phone numbers (num1 and num2) be entered in the international E164 format with a
leading +. For example, if you want to call a US number (212) 555-1234, it should be set as `+12125551234`.
However you can also provide SIP addresses. Additionally, `num1` can be your Sonetel username - this will make
sure that the incoming call to you is handled as per your incoming settings defined in the app.
**Caller ID:**
It is best to use 'automatic' CLI as our system selects the best possible phone to be shown from the numbers
available in your account. If you don't have a Sonetel number, then your verified mobile number is used as CLI.
Read more at https://sonetel.com/cli
:param num1: Required. The first phone number that will be called.
This should be your phone number, SIP address or Sonetel email address.
:param num2: Required.The phone number or address that you wish to connect to.
:param cli1: Optional. The caller ID shown to the first person. Defaults to automatic.
:param cli2: Optional. The caller ID shown to the second person. Defaults to automatic.
:return: Return the status code and message as a dict.
| def callback(self, num1: str, num2: str, cli1: str = 'automatic', cli2: str = 'automatic'):
"""
Use Sonetel's CallBack API to make business quality international calls at the cost of 2 local calls.
**Docs**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE1OTMzOTIy-make-calls
**Number Format:**\n
It is recommended that both the phone numbers (num1 and num2) be entered in the international E164 format with a
leading +. For example, if you want to call a US number (212) 555-1234, it should be set as `+12125551234`.
However you can also provide SIP addresses. Additionally, `num1` can be your Sonetel username - this will make
sure that the incoming call to you is handled as per your incoming settings defined in the app.
**Caller ID:**\n
It is best to use 'automatic' CLI as our system selects the best possible phone to be shown from the numbers
available in your account. If you don't have a Sonetel number, then your verified mobile number is used as CLI.
Read more at https://sonetel.com/cli
:param num1: Required. The first phone number that will be called.
This should be your phone number, SIP address or Sonetel email address.
:param num2: Required.The phone number or address that you wish to connect to.
:param cli1: Optional. The caller ID shown to the first person. Defaults to automatic.
:param cli2: Optional. The caller ID shown to the second person. Defaults to automatic.
:return: Return the status code and message as a dict.
"""
# Check if num1 and num2 are defined.
if num1 and num2:
# Initiate the callback
body = {
"app_id": f'{self._app_name}-{const.PKG_VERSION}',
"call1": num1,
"call2": num2,
"show_1": cli1,
"show_2": cli2
}
return util.send_api_request(
token=self._token,
uri=self._url,
method='post',
body=dumps(body)
)
return util.prepare_error(
code=const.ERR_CALLBACK_NUM_EMPTY,
message='num1 & num2 are required to make a call.'
)
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|
31,939 | sonetel.phonenumber | PhoneNumber |
Phone number class
| class PhoneNumber(util.Resource):
"""
Phone number class
"""
def __init__(self, access_token):
if not access_token:
raise e.AuthException('access_token is required')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_ACCOUNT}{self._accountid}' \
f'{const.API_ENDPOINT_NUMBERSUBSCRIPTION}'
def get(self, e164only: bool = True, number: str = '') -> dict:
"""
List all the phone numbers present in the account.
:param e164only: Optional. Boolean. Only return a list of phone numbers if set to True.
Set to True by default.
:param number: Optional. String. If you only want information about one of your numbers, pass it as a string.
**DOCS**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE2MjQ3MzI4-phone-numbers
:return: Information about the numbers assigned to account.
"""
url = self._url
if not isinstance(number, str):
number = str(number)
if number:
if is_e164(number):
url += number
else:
return util.prepare_error(
code=const.ERR_NUM_NOT_E164,
message=f'"{number}" is not a valid e164 number'
)
api_response = util.send_api_request(token=self._token, uri=url)
response = api_response['response']
# No numbers are found
if response == 'No entries found':
return {
'status': 'success',
'response': 'No entries found'
}
# Only return a list of e164 numbers, without any additional metadata
if e164only:
nums = []
for entry in response:
nums.append(entry['phnum'])
return {
'status': 'success',
'response': nums
}
# Return full response
return {
'status': 'success',
'response': response
}
def add(self, number: str) -> dict:
"""
Buy a phone number that is available. Numbers that are available for purchase can be checked
from the ``/availablephonenumber`` API endpoint.
**DOCS**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE2MjQ3MzI4-phone-numbers
:param number: the phone number you want to purchase.
:return: Dict containing the success response or an error message.
"""
if not isinstance(number, str):
number = str(number)
# Request body
if is_e164(number):
body = {
"phnum": number
}
else:
return util.prepare_error(
code=const.ERR_NUM_NOT_E164,
message=f'"{number}" is not a valid e164 number'
)
return util.send_api_request(
token=self._token,
uri=self._url,
method='post',
body=dumps(body)
)
def delete(self, number: str):
"""
Remove a number from account. The phone number is removed immediately and cannot be recovered.
:param number: The phone number to remove from account.
:return: Dict containing the success response or an error message.
"""
if not isinstance(number, str):
number = str(number)
if is_e164(number):
url = f'{self._url}{number}'
else:
return util.prepare_error(
code=const.ERR_NUM_NOT_E164,
message=f'"{number}" is not a valid e164 number'
)
return util.send_api_request(
token=self._token,
uri=url,
method='delete'
)
def update(self, number: str, connect_to_type: str, connect_to) -> dict:
"""
Update the number's call forwarding settings.
:param number: E164number for which the settings should be updated
:param connect_to: the ID of the destination where the incoming calls to this number should be forwarded.
:param connect_to_type: The destination type where the calls should be forwarded. Accepted values 'user', 'phnum', 'sip' and 'app'.
"""
# Checks
if not number:
return util.prepare_error(
code=const.ERR_NUM_UPDATE_EMPTY,
message='number is required to update call settings'
)
if not connect_to:
return util.prepare_error(
code=const.ERR_NUM_UPDATE_EMPTY,
message='connect_to is required to update call settings'
)
if connect_to_type not in const.CONST_CONNECT_TO_TYPES:
return util.prepare_error(
code=const.ERR_NUM_UPDATE_EMPTY,
message=f'invalid connect_to_type value - {connect_to_type}'
)
# Prepare request
body = {
"connect_to_type": connect_to_type,
"connect_to": connect_to
}
url = f'{self._url}{number}'
# Return result
return util.send_api_request(
token=self._token,
uri=url,
method='put',
body=dumps(body)
)
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|
31,940 | sonetel.phonenumber | __init__ | null | def __init__(self, access_token):
if not access_token:
raise e.AuthException('access_token is required')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_ACCOUNT}{self._accountid}' \
f'{const.API_ENDPOINT_NUMBERSUBSCRIPTION}'
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|
31,941 | sonetel.phonenumber | add |
Buy a phone number that is available. Numbers that are available for purchase can be checked
from the ``/availablephonenumber`` API endpoint.
**DOCS**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE2MjQ3MzI4-phone-numbers
:param number: the phone number you want to purchase.
:return: Dict containing the success response or an error message.
| def add(self, number: str) -> dict:
"""
Buy a phone number that is available. Numbers that are available for purchase can be checked
from the ``/availablephonenumber`` API endpoint.
**DOCS**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE2MjQ3MzI4-phone-numbers
:param number: the phone number you want to purchase.
:return: Dict containing the success response or an error message.
"""
if not isinstance(number, str):
number = str(number)
# Request body
if is_e164(number):
body = {
"phnum": number
}
else:
return util.prepare_error(
code=const.ERR_NUM_NOT_E164,
message=f'"{number}" is not a valid e164 number'
)
return util.send_api_request(
token=self._token,
uri=self._url,
method='post',
body=dumps(body)
)
| (self, number: str) -> dict | [
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|
31,942 | sonetel.phonenumber | delete |
Remove a number from account. The phone number is removed immediately and cannot be recovered.
:param number: The phone number to remove from account.
:return: Dict containing the success response or an error message.
| def delete(self, number: str):
"""
Remove a number from account. The phone number is removed immediately and cannot be recovered.
:param number: The phone number to remove from account.
:return: Dict containing the success response or an error message.
"""
if not isinstance(number, str):
number = str(number)
if is_e164(number):
url = f'{self._url}{number}'
else:
return util.prepare_error(
code=const.ERR_NUM_NOT_E164,
message=f'"{number}" is not a valid e164 number'
)
return util.send_api_request(
token=self._token,
uri=url,
method='delete'
)
| (self, number: str) | [
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0.04761151596903801,
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0.020399894565343857,
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0.013905810192227364,
0.018564609810709953,
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|
31,943 | sonetel.phonenumber | get |
List all the phone numbers present in the account.
:param e164only: Optional. Boolean. Only return a list of phone numbers if set to True.
Set to True by default.
:param number: Optional. String. If you only want information about one of your numbers, pass it as a string.
**DOCS**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE2MjQ3MzI4-phone-numbers
:return: Information about the numbers assigned to account.
| def get(self, e164only: bool = True, number: str = '') -> dict:
"""
List all the phone numbers present in the account.
:param e164only: Optional. Boolean. Only return a list of phone numbers if set to True.
Set to True by default.
:param number: Optional. String. If you only want information about one of your numbers, pass it as a string.
**DOCS**: https://docs.sonetel.com/docs/sonetel-documentation/YXBpOjE2MjQ3MzI4-phone-numbers
:return: Information about the numbers assigned to account.
"""
url = self._url
if not isinstance(number, str):
number = str(number)
if number:
if is_e164(number):
url += number
else:
return util.prepare_error(
code=const.ERR_NUM_NOT_E164,
message=f'"{number}" is not a valid e164 number'
)
api_response = util.send_api_request(token=self._token, uri=url)
response = api_response['response']
# No numbers are found
if response == 'No entries found':
return {
'status': 'success',
'response': 'No entries found'
}
# Only return a list of e164 numbers, without any additional metadata
if e164only:
nums = []
for entry in response:
nums.append(entry['phnum'])
return {
'status': 'success',
'response': nums
}
# Return full response
return {
'status': 'success',
'response': response
}
| (self, e164only: bool = True, number: str = '') -> dict | [
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|
31,944 | sonetel.phonenumber | update |
Update the number's call forwarding settings.
:param number: E164number for which the settings should be updated
:param connect_to: the ID of the destination where the incoming calls to this number should be forwarded.
:param connect_to_type: The destination type where the calls should be forwarded. Accepted values 'user', 'phnum', 'sip' and 'app'.
| def update(self, number: str, connect_to_type: str, connect_to) -> dict:
"""
Update the number's call forwarding settings.
:param number: E164number for which the settings should be updated
:param connect_to: the ID of the destination where the incoming calls to this number should be forwarded.
:param connect_to_type: The destination type where the calls should be forwarded. Accepted values 'user', 'phnum', 'sip' and 'app'.
"""
# Checks
if not number:
return util.prepare_error(
code=const.ERR_NUM_UPDATE_EMPTY,
message='number is required to update call settings'
)
if not connect_to:
return util.prepare_error(
code=const.ERR_NUM_UPDATE_EMPTY,
message='connect_to is required to update call settings'
)
if connect_to_type not in const.CONST_CONNECT_TO_TYPES:
return util.prepare_error(
code=const.ERR_NUM_UPDATE_EMPTY,
message=f'invalid connect_to_type value - {connect_to_type}'
)
# Prepare request
body = {
"connect_to_type": connect_to_type,
"connect_to": connect_to
}
url = f'{self._url}{number}'
# Return result
return util.send_api_request(
token=self._token,
uri=url,
method='put',
body=dumps(body)
)
| (self, number: str, connect_to_type: str, connect_to) -> dict | [
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|
31,945 | sonetel.recording | Recording |
Class representing the call recording resource.
| class Recording(util.Resource):
"""
Class representing the call recording resource.
"""
def __init__(self, access_token: str = None):
super().__init__(access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_CALL_RECORDING}'
def get(self,
start_time: str = None,
end_time: str = None,
file_access_details: bool = False,
voice_call_details: bool = False,
rec_id: str = None
):
"""
Get a list of all the call recordings.
:param start_time: The start timestamp in the format YYYYMMDDTHH:MM:SSZ. Example 20201231T23:59:59. Limit the results to recordings created after this timestamp.
:param end_time: The end timestamp in the format YYYYMMDDTHH:MM:SSZ. Example 20221123T18:59:59. Limit the results to recordings created before this timestamp.
:param rec_id: The unique recording ID. If not included, returns all the recordings.
:param file_access_details: Boolean. Include the details needed to download recordings.
:param voice_call_details: Boolean. Include the details of the voice calls.
"""
url = self._url
# Prepare the request URL based on the params passed to the method
if rec_id:
# Get a single recording
url += f'/{rec_id}'
else:
# Search for and return multiple recordings
url += f'?account_id={self._accountid}'
if util.is_valid_date(start_time) and util.is_valid_date(end_time) and util.date_diff(start_time, end_time):
url += f'&created_date_max={end_time}&created_date_min={start_time}'
fields = []
if file_access_details:
fields.append('file_access_details')
if voice_call_details:
fields.append('voice_call_details')
if len(fields) > 0:
url += '&fields=' + ','.join(fields)
return util.send_api_request(token=self._token, uri=url, method='get')
def delete(self, rec_id: str) -> dict:
"""
Delete a call recording.
:param rec_id: The ID of the recording that should be deleted
:returns: A representation of the deleted recording.
"""
url = f'{self._url}/{rec_id}'
return util.send_api_request(token=self._token, uri=url, method='delete')
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|
31,946 | sonetel.recording | __init__ | null | def __init__(self, access_token: str = None):
super().__init__(access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_CALL_RECORDING}'
| (self, access_token: Optional[str] = None) | [
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|
31,947 | sonetel.recording | delete |
Delete a call recording.
:param rec_id: The ID of the recording that should be deleted
:returns: A representation of the deleted recording.
| def delete(self, rec_id: str) -> dict:
"""
Delete a call recording.
:param rec_id: The ID of the recording that should be deleted
:returns: A representation of the deleted recording.
"""
url = f'{self._url}/{rec_id}'
return util.send_api_request(token=self._token, uri=url, method='delete')
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|
31,948 | sonetel.recording | get |
Get a list of all the call recordings.
:param start_time: The start timestamp in the format YYYYMMDDTHH:MM:SSZ. Example 20201231T23:59:59. Limit the results to recordings created after this timestamp.
:param end_time: The end timestamp in the format YYYYMMDDTHH:MM:SSZ. Example 20221123T18:59:59. Limit the results to recordings created before this timestamp.
:param rec_id: The unique recording ID. If not included, returns all the recordings.
:param file_access_details: Boolean. Include the details needed to download recordings.
:param voice_call_details: Boolean. Include the details of the voice calls.
| def get(self,
start_time: str = None,
end_time: str = None,
file_access_details: bool = False,
voice_call_details: bool = False,
rec_id: str = None
):
"""
Get a list of all the call recordings.
:param start_time: The start timestamp in the format YYYYMMDDTHH:MM:SSZ. Example 20201231T23:59:59. Limit the results to recordings created after this timestamp.
:param end_time: The end timestamp in the format YYYYMMDDTHH:MM:SSZ. Example 20221123T18:59:59. Limit the results to recordings created before this timestamp.
:param rec_id: The unique recording ID. If not included, returns all the recordings.
:param file_access_details: Boolean. Include the details needed to download recordings.
:param voice_call_details: Boolean. Include the details of the voice calls.
"""
url = self._url
# Prepare the request URL based on the params passed to the method
if rec_id:
# Get a single recording
url += f'/{rec_id}'
else:
# Search for and return multiple recordings
url += f'?account_id={self._accountid}'
if util.is_valid_date(start_time) and util.is_valid_date(end_time) and util.date_diff(start_time, end_time):
url += f'&created_date_max={end_time}&created_date_min={start_time}'
fields = []
if file_access_details:
fields.append('file_access_details')
if voice_call_details:
fields.append('voice_call_details')
if len(fields) > 0:
url += '&fields=' + ','.join(fields)
return util.send_api_request(token=self._token, uri=url, method='get')
| (self, start_time: Optional[str] = None, end_time: Optional[str] = None, file_access_details: bool = False, voice_call_details: bool = False, rec_id: Optional[str] = None) | [
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|
31,949 | sonetel.users | User |
Create and manage users in a Sonetel account
| class User(util.Resource):
"""
Create and manage users in a Sonetel account
"""
def __init__(self, access_token: str):
if not access_token:
raise e.AuthException('access_token is required')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_ACCOUNT}{self._accountid}{const.API_ENDPOINT_USER}'
def get(self, all_users: bool = False, userid: str = ''):
"""
Fetch details about all users or a specific user.
If userid is not included with the request, details of the current user are fetched.
:param all_users: Boolean. Optional. Get a list of all the users in the account. Defaults to False.
:param userid: String. Optional. ID of a specific user to get the information for.
"""
url = self._url
if userid:
url += userid
elif not all_users:
url += self._userid
return util.send_api_request(
token=self._token,
uri=url,
method='get') if util.is_valid_token(self._decoded_token) else False
def add(self,
email: str,
f_name: str,
l_name: str,
password: str,
user_type: str = 'regular'
) -> dict:
"""
Adds a new user. Account admin privilege required.
:param email: Required. String. The email address of the user.
:param f_name: Required. String. The first name of the user
:param l_name: Required. String. The last name of the user.
:param password: Required. String. The password to be used.
:param user_type: Required. String. The privilege level of the new user. Accepted values regular and admin.
Defaults to regular.
"""
# Checks
if not password:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='password cannot be empty'
)
if not email:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='email cannot be empty'
)
if not f_name:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='first name cannot be empty'
)
if not l_name:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='last name cannot be empty'
)
# Request
url = self._url
body = {
"user_fname": f_name,
"user_lname": l_name,
"email": email,
"password": password,
"type": user_type
}
return util.send_api_request(
token=self._token,
uri=url,
method='post',
body=dumps(body)
)
def delete(self, userid: str):
"""
Delete a user from your Sonetel account.
:param userid: String. Required. The unique ID of the user to be deleted.
"""
if not userid:
return util.prepare_error(
code=const.ERR_USED_ID_EMPTY,
message='user id cannot be empty'
)
url = self._url + userid
return util.send_api_request(
token=self._token,
uri=url,
method='delete'
)
def update(self, request: dict):
"""
update user settings
"""
raise NotImplementedError
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|
31,950 | sonetel.users | __init__ | null | def __init__(self, access_token: str):
if not access_token:
raise e.AuthException('access_token is required')
super().__init__(access_token=access_token)
self._url = f'{const.API_URI_BASE}{const.API_ENDPOINT_ACCOUNT}{self._accountid}{const.API_ENDPOINT_USER}'
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|
31,951 | sonetel.users | add |
Adds a new user. Account admin privilege required.
:param email: Required. String. The email address of the user.
:param f_name: Required. String. The first name of the user
:param l_name: Required. String. The last name of the user.
:param password: Required. String. The password to be used.
:param user_type: Required. String. The privilege level of the new user. Accepted values regular and admin.
Defaults to regular.
| def add(self,
email: str,
f_name: str,
l_name: str,
password: str,
user_type: str = 'regular'
) -> dict:
"""
Adds a new user. Account admin privilege required.
:param email: Required. String. The email address of the user.
:param f_name: Required. String. The first name of the user
:param l_name: Required. String. The last name of the user.
:param password: Required. String. The password to be used.
:param user_type: Required. String. The privilege level of the new user. Accepted values regular and admin.
Defaults to regular.
"""
# Checks
if not password:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='password cannot be empty'
)
if not email:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='email cannot be empty'
)
if not f_name:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='first name cannot be empty'
)
if not l_name:
return util.prepare_error(
code=const.ERR_USER_DETAIL_EMPTY,
message='last name cannot be empty'
)
# Request
url = self._url
body = {
"user_fname": f_name,
"user_lname": l_name,
"email": email,
"password": password,
"type": user_type
}
return util.send_api_request(
token=self._token,
uri=url,
method='post',
body=dumps(body)
)
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|
31,952 | sonetel.users | delete |
Delete a user from your Sonetel account.
:param userid: String. Required. The unique ID of the user to be deleted.
| def delete(self, userid: str):
"""
Delete a user from your Sonetel account.
:param userid: String. Required. The unique ID of the user to be deleted.
"""
if not userid:
return util.prepare_error(
code=const.ERR_USED_ID_EMPTY,
message='user id cannot be empty'
)
url = self._url + userid
return util.send_api_request(
token=self._token,
uri=url,
method='delete'
)
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|
31,953 | sonetel.users | get |
Fetch details about all users or a specific user.
If userid is not included with the request, details of the current user are fetched.
:param all_users: Boolean. Optional. Get a list of all the users in the account. Defaults to False.
:param userid: String. Optional. ID of a specific user to get the information for.
| def get(self, all_users: bool = False, userid: str = ''):
"""
Fetch details about all users or a specific user.
If userid is not included with the request, details of the current user are fetched.
:param all_users: Boolean. Optional. Get a list of all the users in the account. Defaults to False.
:param userid: String. Optional. ID of a specific user to get the information for.
"""
url = self._url
if userid:
url += userid
elif not all_users:
url += self._userid
return util.send_api_request(
token=self._token,
uri=url,
method='get') if util.is_valid_token(self._decoded_token) else False
| (self, all_users: bool = False, userid: str = '') | [
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|
31,954 | sonetel.users | update |
update user settings
| def update(self, request: dict):
"""
update user settings
"""
raise NotImplementedError
| (self, request: dict) | [
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|
31,964 | pingouin.utils | _check_dataframe | Checks whether data is a dataframe or can be converted to a dataframe.
If successful, a dataframe is returned. If not successful, a ValueError is
raised.
| def _check_dataframe(data=None, dv=None, between=None, within=None, subject=None, effects=None):
"""Checks whether data is a dataframe or can be converted to a dataframe.
If successful, a dataframe is returned. If not successful, a ValueError is
raised.
"""
# Check that data is a dataframe
if not isinstance(data, pd.DataFrame):
# DataMatrix objects can be safely convert to DataFrame objects. By
# first checking the name of the class, we avoid having to actually
# import DataMatrix unless it is necessary.
if data.__class__.__name__ == "DataMatrix": # noqa
try:
from datamatrix import DataMatrix, convert as cnv # noqa
except ImportError:
raise ValueError(
"Failed to convert object to pandas dataframe (DataMatrix not available)" # noqa
)
else:
if isinstance(data, DataMatrix):
data = cnv.to_pandas(data)
else:
raise ValueError("Data must be a pandas dataframe or compatible object.")
else:
raise ValueError("Data must be a pandas dataframe or compatible object.")
# Check that both dv and data are provided.
if any(v is None for v in [dv, data]):
raise ValueError("DV and data must be specified")
# Check that dv is a numeric variable
if data[dv].dtype.kind not in "fi":
raise ValueError("DV must be numeric.")
# Check that effects is provided
if effects not in ["within", "between", "interaction", "all"]:
raise ValueError("Effects must be: within, between, interaction, all")
# Check that within is a string, int or a list (rm_anova2)
if effects == "within" and not isinstance(within, (str, int, list)):
raise ValueError("within must be a string, int or a list.")
# Check that subject identifier is provided in rm_anova and friedman.
if effects == "within" and subject is None:
raise ValueError("subject must be specified when effects=within")
# Check that between is a string or a list (anova2)
if effects == "between" and not isinstance(between, (str, int, list)):
raise ValueError("between must be a string, int or a list.")
# Check that both between and within are present for interaction
if effects == "interaction":
for input in [within, between]:
if not isinstance(input, (str, int, list)):
raise ValueError("within and between must be specified when effects=interaction")
return data
| (data=None, dv=None, between=None, within=None, subject=None, effects=None) | [
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|
31,965 | pingouin.utils | _check_eftype | Check validity of eftype | def _check_eftype(eftype):
"""Check validity of eftype"""
if eftype.lower() in [
"none",
"hedges",
"cohen",
"r",
"pointbiserialr",
"eta-square",
"odds-ratio",
"auc",
"cles",
]:
return True
else:
return False
| (eftype) | [
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|
31,966 | pingouin.utils | _flatten_list | Flatten an arbitrarily nested list into a new list.
This can be useful to select pandas DataFrame columns.
From https://stackoverflow.com/a/16176969/10581531
Examples
--------
>>> from pingouin.utils import _flatten_list
>>> x = ['X1', ['M1', 'M2'], 'Y1', ['Y2']]
>>> _flatten_list(x)
['X1', 'M1', 'M2', 'Y1', 'Y2']
>>> x = ['Xaa', 'Xbb', 'Xcc']
>>> _flatten_list(x)
['Xaa', 'Xbb', 'Xcc']
>>> x = ['Xaa', ('Xbb', 'Xcc'), (1, 2), (1)]
>>> _flatten_list(x)
['Xaa', ('Xbb', 'Xcc'), (1, 2), 1]
>>> _flatten_list(x, include_tuple=True)
['Xaa', 'Xbb', 'Xcc', 1, 2, 1]
| def _flatten_list(x, include_tuple=False):
"""Flatten an arbitrarily nested list into a new list.
This can be useful to select pandas DataFrame columns.
From https://stackoverflow.com/a/16176969/10581531
Examples
--------
>>> from pingouin.utils import _flatten_list
>>> x = ['X1', ['M1', 'M2'], 'Y1', ['Y2']]
>>> _flatten_list(x)
['X1', 'M1', 'M2', 'Y1', 'Y2']
>>> x = ['Xaa', 'Xbb', 'Xcc']
>>> _flatten_list(x)
['Xaa', 'Xbb', 'Xcc']
>>> x = ['Xaa', ('Xbb', 'Xcc'), (1, 2), (1)]
>>> _flatten_list(x)
['Xaa', ('Xbb', 'Xcc'), (1, 2), 1]
>>> _flatten_list(x, include_tuple=True)
['Xaa', 'Xbb', 'Xcc', 1, 2, 1]
"""
# If x is not iterable, return x
if not isinstance(x, collections.abc.Iterable):
return x
# Initialize empty output variable
result = []
# Loop over items in x
for el in x:
# Check if element is iterable
el_is_iter = isinstance(el, collections.abc.Iterable)
if el_is_iter:
if not isinstance(el, (str, tuple)):
result.extend(_flatten_list(el))
else:
if isinstance(el, tuple) and include_tuple:
result.extend(_flatten_list(el))
else:
result.append(el)
else:
result.append(el)
# Remove None from output
result = [r for r in result if r is not None]
return result
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|
31,967 | pingouin.utils | _is_mpmath_installed | Check if mpmath is installed. | def _is_mpmath_installed(raise_error=False):
"""Check if mpmath is installed."""
try:
import mpmath # noqa
is_installed = True
except OSError: # pragma: no cover
is_installed = False
# Raise error (if needed) :
if raise_error and not is_installed: # pragma: no cover
raise OSError("mpmath needs to be installed. Please use `pip " "install mpmath`.")
return is_installed
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|
31,968 | pingouin.utils | _is_sklearn_installed | Check if sklearn is installed. | def _is_sklearn_installed(raise_error=False):
"""Check if sklearn is installed."""
try:
import sklearn # noqa
is_installed = True
except OSError: # pragma: no cover
is_installed = False
# Raise error (if needed) :
if raise_error and not is_installed: # pragma: no cover
raise OSError("sklearn needs to be installed. Please use `pip " "install scikit-learn`.")
return is_installed
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|
31,969 | pingouin.utils | _is_statsmodels_installed | Check if statsmodels is installed. | def _is_statsmodels_installed(raise_error=False):
"""Check if statsmodels is installed."""
try:
import statsmodels # noqa
is_installed = True
except OSError: # pragma: no cover
is_installed = False
# Raise error (if needed) :
if raise_error and not is_installed: # pragma: no cover
raise OSError("statsmodels needs to be installed. Please use `pip " "install statsmodels`.")
return is_installed
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|
31,970 | pingouin.utils | _perm_pval |
Compute p-values from a permutation test.
Parameters
----------
bootstat : 1D array
Permutation distribution.
estimate : float or int
Point estimate.
alternative : str
Tail for p-value. Can be either `'two-sided'` (default), `'greater'` or `'less'`.
Returns
-------
p : float
P-value.
| def _perm_pval(bootstat, estimate, alternative="two-sided"):
"""
Compute p-values from a permutation test.
Parameters
----------
bootstat : 1D array
Permutation distribution.
estimate : float or int
Point estimate.
alternative : str
Tail for p-value. Can be either `'two-sided'` (default), `'greater'` or `'less'`.
Returns
-------
p : float
P-value.
"""
assert alternative in ["two-sided", "greater", "less"], "Wrong tail argument."
assert isinstance(estimate, (int, float))
bootstat = np.asarray(bootstat)
assert bootstat.ndim == 1, "bootstat must be a 1D array."
n_boot = bootstat.size
assert n_boot >= 1, "bootstat must have at least one value."
if alternative == "greater":
p = np.greater_equal(bootstat, estimate).sum() / n_boot
elif alternative == "less":
p = np.less_equal(bootstat, estimate).sum() / n_boot
else:
p = np.greater_equal(np.fabs(bootstat), abs(estimate)).sum() / n_boot
return p
| (bootstat, estimate, alternative='two-sided') | [
0.08246979117393494,
0.0027026860043406487,
0.001735431607812643,
0.038049664348363876,
0.08260827511548996,
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0.027178330346941948,
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0.010100990533828735,
0.03860361501574516,
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0.020825179293751717,
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|
31,971 | pingouin.utils | _postprocess_dataframe | Apply some post-processing to an ouput dataframe (e.g. rounding).
Whether and how rounding is applied is governed by options specified in
`pingouin.options`. The default rounding (number of decimals) is
determined by `pingouin.options['round']`. You can specify rounding for a
given column name by the option `'round.column.<colname>'`, e.g.
`'round.column.CI95%'`. Analogously, `'round.row.<rowname>'` also works
(where `rowname`) refers to the pandas index), as well as
`'round.cell.[<rolname>]x[<colname]'`. A cell-based option is used,
if available; if not, a column-based option is used, if
available; if not, a row-based option is used, if available; if not,
the default is used. (Default `pingouin.options['round'] = None`,
i.e. no rounding is applied.)
If a round option is `callable` instead of `int`, then it will be called,
and the return value stored in the cell.
Post-processing is applied on a copy of the DataFrame, leaving the
original DataFrame untouched.
This is an internal function (no public API).
Parameters
----------
df : :py:class:`pandas.DataFrame`
Dataframe to apply post-processing to (e.g. ANOVA summary)
Returns
----------
df : :py:class:`pandas.DataFrame`
Dataframe with post-processing applied
| def _postprocess_dataframe(df):
"""Apply some post-processing to an ouput dataframe (e.g. rounding).
Whether and how rounding is applied is governed by options specified in
`pingouin.options`. The default rounding (number of decimals) is
determined by `pingouin.options['round']`. You can specify rounding for a
given column name by the option `'round.column.<colname>'`, e.g.
`'round.column.CI95%'`. Analogously, `'round.row.<rowname>'` also works
(where `rowname`) refers to the pandas index), as well as
`'round.cell.[<rolname>]x[<colname]'`. A cell-based option is used,
if available; if not, a column-based option is used, if
available; if not, a row-based option is used, if available; if not,
the default is used. (Default `pingouin.options['round'] = None`,
i.e. no rounding is applied.)
If a round option is `callable` instead of `int`, then it will be called,
and the return value stored in the cell.
Post-processing is applied on a copy of the DataFrame, leaving the
original DataFrame untouched.
This is an internal function (no public API).
Parameters
----------
df : :py:class:`pandas.DataFrame`
Dataframe to apply post-processing to (e.g. ANOVA summary)
Returns
----------
df : :py:class:`pandas.DataFrame`
Dataframe with post-processing applied
"""
df = df.copy()
for row, col in it.product(df.index, df.columns):
round_option = _get_round_setting_for(row, col)
if round_option is None:
continue
if callable(round_option):
newval = round_option(df.at[row, col])
# ensure that dtype changes are processed
df[col] = df[col].astype(type(newval))
df.at[row, col] = newval
continue
if isinstance(df.at[row, col], bool):
# No rounding if value is a boolean
continue
is_number = isinstance(df.at[row, col], numbers.Number)
is_array = isinstance(df.at[row, col], np.ndarray)
if not any([is_number, is_array]):
# No rounding if value is not a Number or an array
continue
if is_array:
is_float_array = issubclass(df.at[row, col].dtype.type, np.floating)
if not is_float_array:
# No rounding if value is not a float array
continue
df.at[row, col] = np.round(df.at[row, col], decimals=round_option)
return df
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|
31,972 | pingouin.parametric | ancova | ANCOVA with one or more covariate(s).
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 in data with the dependent variable.
between : string
Name of column in data with the between factor.
covar : string or list
Name(s) of column(s) in data with the covariate.
effsize : str
Effect size. Must be 'np2' (partial eta-squared) or 'n2'
(eta-squared).
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANCOVA summary:
* ``'Source'``: Names of the factor considered
* ``'SS'``: Sums of squares
* ``'DF'``: Degrees of freedom
* ``'F'``: F-values
* ``'p-unc'``: Uncorrected p-values
* ``'np2'``: Partial eta-squared
Notes
-----
Analysis of covariance (ANCOVA) is a general linear model which blends
ANOVA and regression. ANCOVA evaluates whether the means of a dependent
variable (dv) are equal across levels of a categorical independent
variable (between) often called a treatment, while statistically
controlling for the effects of other continuous variables that are not
of primary interest, known as covariates or nuisance variables (covar).
Pingouin uses :py:class:`statsmodels.regression.linear_model.OLS` to
compute the ANCOVA.
.. important:: Rows with missing values are automatically removed
(listwise deletion).
See Also
--------
anova : One-way and N-way ANOVA
Examples
--------
1. Evaluate the reading scores of students with different teaching method
and family income as a covariate.
>>> from pingouin import ancova, read_dataset
>>> df = read_dataset('ancova')
>>> ancova(data=df, dv='Scores', covar='Income', between='Method')
Source SS DF F p-unc np2
0 Method 571.029883 3 3.336482 0.031940 0.244077
1 Income 1678.352687 1 29.419438 0.000006 0.486920
2 Residual 1768.522313 31 NaN NaN NaN
2. Evaluate the reading scores of students with different teaching method
and family income + BMI as a covariate.
>>> ancova(data=df, dv='Scores', covar=['Income', 'BMI'], between='Method',
... effsize="n2")
Source SS DF F p-unc n2
0 Method 552.284043 3 3.232550 0.036113 0.141802
1 Income 1573.952434 1 27.637304 0.000011 0.404121
2 BMI 60.013656 1 1.053790 0.312842 0.015409
3 Residual 1708.508657 30 NaN NaN NaN
| @pf.register_dataframe_method
def ancova(data=None, dv=None, between=None, covar=None, effsize="np2"):
"""ANCOVA with one or more covariate(s).
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 in data with the dependent variable.
between : string
Name of column in data with the between factor.
covar : string or list
Name(s) of column(s) in data with the covariate.
effsize : str
Effect size. Must be 'np2' (partial eta-squared) or 'n2'
(eta-squared).
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANCOVA summary:
* ``'Source'``: Names of the factor considered
* ``'SS'``: Sums of squares
* ``'DF'``: Degrees of freedom
* ``'F'``: F-values
* ``'p-unc'``: Uncorrected p-values
* ``'np2'``: Partial eta-squared
Notes
-----
Analysis of covariance (ANCOVA) is a general linear model which blends
ANOVA and regression. ANCOVA evaluates whether the means of a dependent
variable (dv) are equal across levels of a categorical independent
variable (between) often called a treatment, while statistically
controlling for the effects of other continuous variables that are not
of primary interest, known as covariates or nuisance variables (covar).
Pingouin uses :py:class:`statsmodels.regression.linear_model.OLS` to
compute the ANCOVA.
.. important:: Rows with missing values are automatically removed
(listwise deletion).
See Also
--------
anova : One-way and N-way ANOVA
Examples
--------
1. Evaluate the reading scores of students with different teaching method
and family income as a covariate.
>>> from pingouin import ancova, read_dataset
>>> df = read_dataset('ancova')
>>> ancova(data=df, dv='Scores', covar='Income', between='Method')
Source SS DF F p-unc np2
0 Method 571.029883 3 3.336482 0.031940 0.244077
1 Income 1678.352687 1 29.419438 0.000006 0.486920
2 Residual 1768.522313 31 NaN NaN NaN
2. Evaluate the reading scores of students with different teaching method
and family income + BMI as a covariate.
>>> ancova(data=df, dv='Scores', covar=['Income', 'BMI'], between='Method',
... effsize="n2")
Source SS DF F p-unc n2
0 Method 552.284043 3 3.232550 0.036113 0.141802
1 Income 1573.952434 1 27.637304 0.000011 0.404121
2 BMI 60.013656 1 1.053790 0.312842 0.015409
3 Residual 1708.508657 30 NaN NaN NaN
"""
# Import
from pingouin.utils import _is_statsmodels_installed
_is_statsmodels_installed(raise_error=True)
from statsmodels.api import stats
from statsmodels.formula.api import ols
# Safety checks
assert effsize in ["np2", "n2"], "effsize must be 'np2' or 'n2'."
assert isinstance(data, pd.DataFrame), "data must be a pandas dataframe."
assert isinstance(between, str), (
"between must be a string. Pingouin does not support multiple "
"between factors. For more details, please see "
"https://github.com/raphaelvallat/pingouin/issues/173."
)
assert dv in data.columns, "%s is not in data." % dv
assert between in data.columns, "%s is not in data." % between
assert isinstance(covar, (str, list)), "covar must be a str or a list."
if isinstance(covar, str):
covar = [covar]
for c in covar:
assert c in data.columns, "covariate %s is not in data" % c
assert data[c].dtype.kind in "bfi", "covariate %s is not numeric" % c
# Drop missing values
data = data[_flatten_list([dv, between, covar])].dropna()
# Fit ANCOVA model
# formula = dv ~ 1 + between + covar1 + covar2 + ...
assert dv not in ["C", "Q"], "`dv` must not be 'C' or 'Q'."
assert between not in ["C", "Q"], "`between` must not be 'C' or 'Q'."
assert all(c not in ["C", "Q"] for c in covar), "`covar` must not contain 'C' or 'Q'."
formula = f"Q('{dv}') ~ C(Q('{between}'))"
for c in covar:
formula += " + Q('%s')" % (c)
model = ols(formula, data=data).fit()
# Create output dataframe
aov = stats.anova_lm(model, typ=2).reset_index()
aov.rename(
columns={"index": "Source", "sum_sq": "SS", "df": "DF", "PR(>F)": "p-unc"}, inplace=True
)
aov.at[0, "Source"] = between
for i in range(len(covar)):
aov.at[i + 1, "Source"] = covar[i]
aov["DF"] = aov["DF"].astype(int)
# Add effect sizes
if effsize == "n2":
all_effsize = (aov["SS"] / aov["SS"].sum()).to_numpy()
all_effsize[-1] = np.nan
else:
ss_resid = aov["SS"].iloc[-1]
all_effsize = aov["SS"].apply(lambda x: x / (x + ss_resid)).to_numpy()
all_effsize[-1] = np.nan
aov[effsize] = all_effsize
# Add bw as an attribute (for rm_corr function)
aov = _postprocess_dataframe(aov)
aov.bw_ = model.params.iloc[-1]
return aov
| (data=None, dv=None, between=None, covar=None, effsize='np2') | [
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|
31,973 | pingouin.distribution | anderson | Anderson-Darling test of distribution.
The Anderson-Darling test tests the null hypothesis that a sample is drawn from a population
that follows a particular distribution. For the Anderson-Darling test, the critical values
depend on which distribution is being tested against.
This function is a wrapper around :py:func:`scipy.stats.anderson`.
Parameters
----------
sample1, sample2,... : array_like
Array of sample data. They may be of different lengths.
dist : string
The type of distribution to test against. The default is 'norm'.
Must be one of 'norm', 'expon', 'logistic', 'gumbel'.
Returns
-------
from_dist : boolean
A boolean indicating if the data comes from the tested distribution (True) or not (False).
sig_level : float
The significance levels for the corresponding critical values, in %.
See :py:func:`scipy.stats.anderson` for more details.
Examples
--------
1. Test that an array comes from a normal distribution
>>> from pingouin import anderson
>>> import numpy as np
>>> np.random.seed(42)
>>> x = np.random.normal(size=100)
>>> y = np.random.normal(size=10000)
>>> z = np.random.random(1000)
>>> anderson(x)
(True, 15.0)
2. Test that multiple arrays comes from the normal distribution
>>> anderson(x, y, z)
(array([ True, True, False]), array([15., 15., 1.]))
3. Test that an array comes from the exponential distribution
>>> x = np.random.exponential(size=1000)
>>> anderson(x, dist="expon")
(True, 15.0)
| def anderson(*args, dist="norm"):
"""Anderson-Darling test of distribution.
The Anderson-Darling test tests the null hypothesis that a sample is drawn from a population
that follows a particular distribution. For the Anderson-Darling test, the critical values
depend on which distribution is being tested against.
This function is a wrapper around :py:func:`scipy.stats.anderson`.
Parameters
----------
sample1, sample2,... : array_like
Array of sample data. They may be of different lengths.
dist : string
The type of distribution to test against. The default is 'norm'.
Must be one of 'norm', 'expon', 'logistic', 'gumbel'.
Returns
-------
from_dist : boolean
A boolean indicating if the data comes from the tested distribution (True) or not (False).
sig_level : float
The significance levels for the corresponding critical values, in %.
See :py:func:`scipy.stats.anderson` for more details.
Examples
--------
1. Test that an array comes from a normal distribution
>>> from pingouin import anderson
>>> import numpy as np
>>> np.random.seed(42)
>>> x = np.random.normal(size=100)
>>> y = np.random.normal(size=10000)
>>> z = np.random.random(1000)
>>> anderson(x)
(True, 15.0)
2. Test that multiple arrays comes from the normal distribution
>>> anderson(x, y, z)
(array([ True, True, False]), array([15., 15., 1.]))
3. Test that an array comes from the exponential distribution
>>> x = np.random.exponential(size=1000)
>>> anderson(x, dist="expon")
(True, 15.0)
"""
k = len(args)
from_dist = np.zeros(k, dtype="bool")
sig_level = np.zeros(k)
for j in range(k):
st, cr, sig = scipy.stats.anderson(args[j], dist=dist)
from_dist[j] = True if (st < cr).any() else False
sig_level[j] = sig[np.argmin(np.abs(st - cr))]
if k == 1:
from_dist = from_dist[0]
sig_level = sig_level[0]
return from_dist, sig_level
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|
31,974 | pingouin.parametric | anova | One-way and *N*-way 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 in ``data`` containing the dependent variable.
between : string or list with *N* elements
Name of column(s) in ``data`` containing the between-subject factor(s).
If ``between`` is a single string, a one-way ANOVA is computed.
If ``between`` is a list with two or more elements, a *N*-way ANOVA is
performed.
Note that Pingouin will internally call statsmodels to calculate
ANOVA with 3 or more factors, or unbalanced two-way ANOVA.
ss_type : int
Specify how the sums of squares is calculated for *unbalanced* design
with 2 or more factors. Can be 1, 2 (default), or 3. This has no impact
on one-way design or N-way ANOVA with balanced data.
detailed : boolean
If True, return a detailed ANOVA table
(default True for N-way ANOVA).
effsize : str
Effect size. Must be 'np2' (partial eta-squared) or 'n2'
(eta-squared). Note that for one-way ANOVA partial eta-squared is the
same as eta-squared.
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Factor names
* ``'SS'``: Sums of squares
* ``'DF'``: Degrees of freedom
* ``'MS'``: Mean squares
* ``'F'``: F-values
* ``'p-unc'``: uncorrected p-values
* ``'np2'``: Partial eta-square effect sizes
See Also
--------
rm_anova : One-way and two-way repeated measures ANOVA
mixed_anova : Two way mixed ANOVA
welch_anova : One-way Welch ANOVA
kruskal : Non-parametric one-way ANOVA
Notes
-----
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 (:py:func:`pingouin.welch_anova`) that
better controls for type I error (Liu 2015). The homogeneity of variances
can be measured with the :py:func:`pingouin.homoscedasticity` function.
The main idea of ANOVA is to partition the variance (sums of squares)
into several components. For example, in one-way ANOVA:
.. math::
SS_{\text{total}} = SS_{\text{effect}} + SS_{\text{error}}
SS_{\text{total}} = \sum_i \sum_j (Y_{ij} - \overline{Y})^2
SS_{\text{effect}} = \sum_i n_i (\overline{Y_i} - \overline{Y})^2
SS_{\text{error}} = \sum_i \sum_j (Y_{ij} - \overline{Y}_i)^2
where :math:`i=1,...,r; j=1,...,n_i`, :math:`r` is the number of groups,
and :math:`n_i` the number of observations for the :math:`i` th group.
The F-statistics is then defined as:
.. math::
F^* = \frac{MS_{\text{effect}}}{MS_{\text{error}}} =
\frac{SS_{\text{effect}} / (r - 1)}{SS_{\text{error}} / (n_t - r)}
and the p-value can be calculated using a F-distribution with
:math:`r-1, n_t-1` 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`).
The default effect size reported in Pingouin is the partial eta-square,
which, for one-way ANOVA is the same as eta-square and generalized
eta-square.
.. math::
\eta_p^2 = \frac{SS_{\text{effect}}}{SS_{\text{effect}} +
SS_{\text{error}}}
Missing values are automatically removed. Results have been tested against
R, Matlab and JASP.
Examples
--------
One-way ANOVA
>>> import pingouin as pg
>>> df = pg.read_dataset('anova')
>>> aov = pg.anova(dv='Pain threshold', between='Hair color', data=df,
... detailed=True)
>>> aov.round(3)
Source SS DF MS F p-unc np2
0 Hair color 1360.726 3 453.575 6.791 0.004 0.576
1 Within 1001.800 15 66.787 NaN NaN NaN
Same but using a standard eta-squared instead of a partial eta-squared
effect size. Also note how here we're using the anova function directly as
a method (= built-in function) of our pandas dataframe. In that case,
we don't have to specify ``data`` anymore.
>>> df.anova(dv='Pain threshold', between='Hair color', detailed=False,
... effsize='n2')
Source ddof1 ddof2 F p-unc n2
0 Hair color 3 15 6.791407 0.004114 0.575962
Two-way ANOVA with balanced design
>>> data = pg.read_dataset('anova2')
>>> data.anova(dv="Yield", between=["Blend", "Crop"]).round(3)
Source SS DF MS F p-unc np2
0 Blend 2.042 1 2.042 0.004 0.952 0.000
1 Crop 2736.583 2 1368.292 2.525 0.108 0.219
2 Blend * Crop 2360.083 2 1180.042 2.178 0.142 0.195
3 Residual 9753.250 18 541.847 NaN NaN NaN
Two-way ANOVA with unbalanced design (requires statsmodels)
>>> data = pg.read_dataset('anova2_unbalanced')
>>> data.anova(dv="Scores", between=["Diet", "Exercise"],
... effsize="n2").round(3)
Source SS DF MS F p-unc n2
0 Diet 390.625 1.0 390.625 7.423 0.034 0.433
1 Exercise 180.625 1.0 180.625 3.432 0.113 0.200
2 Diet * Exercise 15.625 1.0 15.625 0.297 0.605 0.017
3 Residual 315.750 6.0 52.625 NaN NaN NaN
Three-way ANOVA, type 3 sums of squares (requires statsmodels)
>>> data = pg.read_dataset('anova3')
>>> data.anova(dv='Cholesterol', between=['Sex', 'Risk', 'Drug'],
... ss_type=3).round(3)
Source SS DF MS F p-unc np2
0 Sex 2.075 1.0 2.075 2.462 0.123 0.049
1 Risk 11.332 1.0 11.332 13.449 0.001 0.219
2 Drug 0.816 2.0 0.408 0.484 0.619 0.020
3 Sex * Risk 0.117 1.0 0.117 0.139 0.711 0.003
4 Sex * Drug 2.564 2.0 1.282 1.522 0.229 0.060
5 Risk * Drug 2.438 2.0 1.219 1.446 0.245 0.057
6 Sex * Risk * Drug 1.844 2.0 0.922 1.094 0.343 0.044
7 Residual 40.445 48.0 0.843 NaN NaN NaN
| @pf.register_dataframe_method
def anova(data=None, dv=None, between=None, ss_type=2, detailed=False, effsize="np2"):
"""One-way and *N*-way 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 in ``data`` containing the dependent variable.
between : string or list with *N* elements
Name of column(s) in ``data`` containing the between-subject factor(s).
If ``between`` is a single string, a one-way ANOVA is computed.
If ``between`` is a list with two or more elements, a *N*-way ANOVA is
performed.
Note that Pingouin will internally call statsmodels to calculate
ANOVA with 3 or more factors, or unbalanced two-way ANOVA.
ss_type : int
Specify how the sums of squares is calculated for *unbalanced* design
with 2 or more factors. Can be 1, 2 (default), or 3. This has no impact
on one-way design or N-way ANOVA with balanced data.
detailed : boolean
If True, return a detailed ANOVA table
(default True for N-way ANOVA).
effsize : str
Effect size. Must be 'np2' (partial eta-squared) or 'n2'
(eta-squared). Note that for one-way ANOVA partial eta-squared is the
same as eta-squared.
Returns
-------
aov : :py:class:`pandas.DataFrame`
ANOVA summary:
* ``'Source'``: Factor names
* ``'SS'``: Sums of squares
* ``'DF'``: Degrees of freedom
* ``'MS'``: Mean squares
* ``'F'``: F-values
* ``'p-unc'``: uncorrected p-values
* ``'np2'``: Partial eta-square effect sizes
See Also
--------
rm_anova : One-way and two-way repeated measures ANOVA
mixed_anova : Two way mixed ANOVA
welch_anova : One-way Welch ANOVA
kruskal : Non-parametric one-way ANOVA
Notes
-----
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 (:py:func:`pingouin.welch_anova`) that
better controls for type I error (Liu 2015). The homogeneity of variances
can be measured with the :py:func:`pingouin.homoscedasticity` function.
The main idea of ANOVA is to partition the variance (sums of squares)
into several components. For example, in one-way ANOVA:
.. math::
SS_{\\text{total}} = SS_{\\text{effect}} + SS_{\\text{error}}
SS_{\\text{total}} = \\sum_i \\sum_j (Y_{ij} - \\overline{Y})^2
SS_{\\text{effect}} = \\sum_i n_i (\\overline{Y_i} - \\overline{Y})^2
SS_{\\text{error}} = \\sum_i \\sum_j (Y_{ij} - \\overline{Y}_i)^2
where :math:`i=1,...,r; j=1,...,n_i`, :math:`r` is the number of groups,
and :math:`n_i` the number of observations for the :math:`i` th group.
The F-statistics is then defined as:
.. math::
F^* = \\frac{MS_{\\text{effect}}}{MS_{\\text{error}}} =
\\frac{SS_{\\text{effect}} / (r - 1)}{SS_{\\text{error}} / (n_t - r)}
and the p-value can be calculated using a F-distribution with
:math:`r-1, n_t-1` 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`).
The default effect size reported in Pingouin is the partial eta-square,
which, for one-way ANOVA is the same as eta-square and generalized
eta-square.
.. math::
\\eta_p^2 = \\frac{SS_{\\text{effect}}}{SS_{\\text{effect}} +
SS_{\\text{error}}}
Missing values are automatically removed. Results have been tested against
R, Matlab and JASP.
Examples
--------
One-way ANOVA
>>> import pingouin as pg
>>> df = pg.read_dataset('anova')
>>> aov = pg.anova(dv='Pain threshold', between='Hair color', data=df,
... detailed=True)
>>> aov.round(3)
Source SS DF MS F p-unc np2
0 Hair color 1360.726 3 453.575 6.791 0.004 0.576
1 Within 1001.800 15 66.787 NaN NaN NaN
Same but using a standard eta-squared instead of a partial eta-squared
effect size. Also note how here we're using the anova function directly as
a method (= built-in function) of our pandas dataframe. In that case,
we don't have to specify ``data`` anymore.
>>> df.anova(dv='Pain threshold', between='Hair color', detailed=False,
... effsize='n2')
Source ddof1 ddof2 F p-unc n2
0 Hair color 3 15 6.791407 0.004114 0.575962
Two-way ANOVA with balanced design
>>> data = pg.read_dataset('anova2')
>>> data.anova(dv="Yield", between=["Blend", "Crop"]).round(3)
Source SS DF MS F p-unc np2
0 Blend 2.042 1 2.042 0.004 0.952 0.000
1 Crop 2736.583 2 1368.292 2.525 0.108 0.219
2 Blend * Crop 2360.083 2 1180.042 2.178 0.142 0.195
3 Residual 9753.250 18 541.847 NaN NaN NaN
Two-way ANOVA with unbalanced design (requires statsmodels)
>>> data = pg.read_dataset('anova2_unbalanced')
>>> data.anova(dv="Scores", between=["Diet", "Exercise"],
... effsize="n2").round(3)
Source SS DF MS F p-unc n2
0 Diet 390.625 1.0 390.625 7.423 0.034 0.433
1 Exercise 180.625 1.0 180.625 3.432 0.113 0.200
2 Diet * Exercise 15.625 1.0 15.625 0.297 0.605 0.017
3 Residual 315.750 6.0 52.625 NaN NaN NaN
Three-way ANOVA, type 3 sums of squares (requires statsmodels)
>>> data = pg.read_dataset('anova3')
>>> data.anova(dv='Cholesterol', between=['Sex', 'Risk', 'Drug'],
... ss_type=3).round(3)
Source SS DF MS F p-unc np2
0 Sex 2.075 1.0 2.075 2.462 0.123 0.049
1 Risk 11.332 1.0 11.332 13.449 0.001 0.219
2 Drug 0.816 2.0 0.408 0.484 0.619 0.020
3 Sex * Risk 0.117 1.0 0.117 0.139 0.711 0.003
4 Sex * Drug 2.564 2.0 1.282 1.522 0.229 0.060
5 Risk * Drug 2.438 2.0 1.219 1.446 0.245 0.057
6 Sex * Risk * Drug 1.844 2.0 0.922 1.094 0.343 0.044
7 Residual 40.445 48.0 0.843 NaN NaN NaN
"""
assert effsize in ["np2", "n2"], "effsize must be 'np2' or 'n2'."
if isinstance(between, list):
if len(between) == 0:
raise ValueError("between is empty.")
elif len(between) == 1:
between = between[0]
elif len(between) == 2:
# Two factors with balanced design = Pingouin implementation
# Two factors with unbalanced design = statsmodels
return anova2(dv=dv, between=between, data=data, ss_type=ss_type, effsize=effsize)
else:
# 3 or more factors with (un)-balanced design = statsmodels
return anovan(dv=dv, between=between, data=data, ss_type=ss_type, effsize=effsize)
# Check data
data = _check_dataframe(dv=dv, between=between, data=data, effects="between")
# Drop missing values
data = data[[dv, between]].dropna()
# Reset index (avoid duplicate axis error)
data = data.reset_index(drop=True)
n_groups = data[between].nunique()
N = data[dv].size
# Calculate sums of squares
grp = data.groupby(between, observed=True, group_keys=False)[dv]
# Between effect
ssbetween = (
(grp.mean(numeric_only=True) - data[dv].mean(numeric_only=True)) ** 2 * grp.count()
).sum()
# Within effect (= error between)
# = (grp.var(ddof=0) * grp.count()).sum()
sserror = grp.transform(lambda x: (x - x.mean()) ** 2).sum | (data=None, dv=None, between=None, ss_type=2, detailed=False, effsize='np2') | [
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|
31,975 | pingouin.bayesian | bayesfactor_binom |
Bayes factor of a binomial test with :math:`k` successes,
:math:`n` trials and base probability :math:`p`. This means that
the null hypothesis is that the probability is :math:`p`. It is
compared against the alternative hypothesis that :math:`p` is from
the Beta distribution with parameters :math:`(a, b)`. By default,
both :math:`a` and :math:`b` are 1, making the alternative
hypothesis equivalent to the uniform distribution, i.e., we are
completely uninformed about :math:`p`.
Parameters
----------
k : int
Number of successes.
n : int
Number of trials.
p : float
Base probability of success (range from 0 to 1).
a : float
The "a" parameter of the Beta distribution.
b : float
The "b" parameter of the Beta distribution.
Returns
-------
bf10 : float
The Bayes Factor quantifies the evidence in favour of the
alternative hypothesis, where the null hypothesis is that
the random variable is binomially distributed with base probability
:math:`p`.
See also
--------
bayesfactor_pearson : Bayes Factor of a correlation
bayesfactor_ttest : Bayes Factor of a T-test
Notes
-----
Adapted from a Matlab code found at
https://github.com/anne-urai/Tools/blob/master/stats/BayesFactors/binombf.m
The Bayes Factor is given by the formula below:
.. math::
BF_{10} = \frac{\int_0^1 \binom{n}{k}g^k(1-g)^{n-k}}
{\binom{n}{k} p^k (1-p)^{n-k}}
References
----------
* http://pcl.missouri.edu/bf-binomial
* https://en.wikipedia.org/wiki/Bayes_factor
Examples
--------
We want to determine if a coin if fair. After tossing the coin 200 times
in a row, we report 115 heads (hereafter referred to as "successes") and 85
tails ("failures"). The Bayes Factor can be easily computed using Pingouin:
>>> import pingouin as pg
>>> bf = float(pg.bayesfactor_binom(k=115, n=200, p=0.5))
>>> # Note that Pingouin returns the BF-alt by default.
>>> # BF-null is simply 1 / BF-alt
>>> print("BF-null: %.3f, BF-alt: %.3f" % (1 / bf, bf))
BF-null: 1.197, BF-alt: 0.835
Since the Bayes Factor of the null hypothesis ("the coin is fair") is
higher than the Bayes Factor of the alternative hypothesis
("the coin is not fair"), we can conclude that there is more evidence to
support the fact that the coin is indeed fair. However, the strength of the
evidence in favor of the null hypothesis (1.197) is "barely worth
mentionning" according to Jeffreys's rule of thumb.
Interestingly, a frequentist alternative to this test would give very
different results. It can be performed using the
:py:func:`scipy.stats.binom_test` function:
>>> from scipy.stats import binomtest
>>> result = binomtest(k=115, n=200, p=0.5)
>>> round(result.pvalue, 5)
0.04004
The binomial test rejects the null hypothesis that the coin is fair at the
5% significance level (p=0.04). Thus, whereas a frequentist hypothesis test
would yield significant results at the 5% significance level, the Bayes
factor indicates preference of the null hypothesis to the alternative
hypothesis that we know nothing about p.
We can use a more informed alternative hypothesis too, if desirable. E.g.,
the original test using Beta(5, 4) as the alternative hypothesis:
>>> bf = pg.bayesfactor_binom(k=115, n=200, p=0.5, a=5, b=4)
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 1.930
Using a different base probability of successes:
>>> bf = pg.bayesfactor_binom(k=100, n=1000, p=0.1)
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 0.024
| def bayesfactor_binom(k, n, p=0.5, a=1, b=1):
"""
Bayes factor of a binomial test with :math:`k` successes,
:math:`n` trials and base probability :math:`p`. This means that
the null hypothesis is that the probability is :math:`p`. It is
compared against the alternative hypothesis that :math:`p` is from
the Beta distribution with parameters :math:`(a, b)`. By default,
both :math:`a` and :math:`b` are 1, making the alternative
hypothesis equivalent to the uniform distribution, i.e., we are
completely uninformed about :math:`p`.
Parameters
----------
k : int
Number of successes.
n : int
Number of trials.
p : float
Base probability of success (range from 0 to 1).
a : float
The "a" parameter of the Beta distribution.
b : float
The "b" parameter of the Beta distribution.
Returns
-------
bf10 : float
The Bayes Factor quantifies the evidence in favour of the
alternative hypothesis, where the null hypothesis is that
the random variable is binomially distributed with base probability
:math:`p`.
See also
--------
bayesfactor_pearson : Bayes Factor of a correlation
bayesfactor_ttest : Bayes Factor of a T-test
Notes
-----
Adapted from a Matlab code found at
https://github.com/anne-urai/Tools/blob/master/stats/BayesFactors/binombf.m
The Bayes Factor is given by the formula below:
.. math::
BF_{10} = \\frac{\\int_0^1 \\binom{n}{k}g^k(1-g)^{n-k}}
{\\binom{n}{k} p^k (1-p)^{n-k}}
References
----------
* http://pcl.missouri.edu/bf-binomial
* https://en.wikipedia.org/wiki/Bayes_factor
Examples
--------
We want to determine if a coin if fair. After tossing the coin 200 times
in a row, we report 115 heads (hereafter referred to as "successes") and 85
tails ("failures"). The Bayes Factor can be easily computed using Pingouin:
>>> import pingouin as pg
>>> bf = float(pg.bayesfactor_binom(k=115, n=200, p=0.5))
>>> # Note that Pingouin returns the BF-alt by default.
>>> # BF-null is simply 1 / BF-alt
>>> print("BF-null: %.3f, BF-alt: %.3f" % (1 / bf, bf))
BF-null: 1.197, BF-alt: 0.835
Since the Bayes Factor of the null hypothesis ("the coin is fair") is
higher than the Bayes Factor of the alternative hypothesis
("the coin is not fair"), we can conclude that there is more evidence to
support the fact that the coin is indeed fair. However, the strength of the
evidence in favor of the null hypothesis (1.197) is "barely worth
mentionning" according to Jeffreys's rule of thumb.
Interestingly, a frequentist alternative to this test would give very
different results. It can be performed using the
:py:func:`scipy.stats.binom_test` function:
>>> from scipy.stats import binomtest
>>> result = binomtest(k=115, n=200, p=0.5)
>>> round(result.pvalue, 5)
0.04004
The binomial test rejects the null hypothesis that the coin is fair at the
5% significance level (p=0.04). Thus, whereas a frequentist hypothesis test
would yield significant results at the 5% significance level, the Bayes
factor indicates preference of the null hypothesis to the alternative
hypothesis that we know nothing about p.
We can use a more informed alternative hypothesis too, if desirable. E.g.,
the original test using Beta(5, 4) as the alternative hypothesis:
>>> bf = pg.bayesfactor_binom(k=115, n=200, p=0.5, a=5, b=4)
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 1.930
Using a different base probability of successes:
>>> bf = pg.bayesfactor_binom(k=100, n=1000, p=0.1)
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 0.024
"""
from scipy.stats import beta, binom
assert 0 < p < 1, "p must be between 0 and 1."
assert isinstance(k, int), "k must be int."
assert isinstance(n, int), "n must be int."
assert k <= n, "k (successes) cannot be higher than n (trials)."
assert a > 0, "a must be positive."
assert b > 0, "b must be positive."
def fun(g):
return beta.pdf(g, a, b) * binom.pmf(k, n, g)
bf10 = quad(fun, 0, 1)[0] / binom.pmf(k, n, p)
return bf10
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|
31,976 | pingouin.bayesian | bayesfactor_pearson |
Bayes Factor of a Pearson correlation.
Parameters
----------
r : float
Pearson correlation coefficient.
n : int
Sample size.
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 : str
Method to compute the Bayes Factor. Can be "ly" (default) or
"wetzels". The former has an exact analytical solution, while the
latter requires integral solving (and is therefore slower). "wetzels"
was the default in Pingouin <= 0.2.5. See Notes for details.
kappa : float
Kappa factor. This is sometimes called the *rscale* parameter, and
is only used when ``method`` is "ly".
Returns
-------
bf : float
Bayes Factor (BF10).
The Bayes Factor quantifies the evidence in favour of the alternative
hypothesis.
See also
--------
corr : (Robust) correlation between two variables
pairwise_corr : Pairwise correlation between columns of a pandas DataFrame
bayesfactor_ttest : Bayes Factor of a T-test
bayesfactor_binom : Bayes Factor of a binomial test
Notes
-----
To compute the Bayes Factor directly from the raw data, use the
:py:func:`pingouin.corr` function.
The two-sided **Wetzels Bayes Factor** (also called *JZS Bayes Factor*)
is calculated using the equation 13 and associated R code of [1]_:
.. math::
\text{BF}_{10}(n, r) = \frac{\sqrt{n/2}}{\gamma(1/2)}*
\int_{0}^{\infty}e((n-2)/2)*
log(1+g)+(-(n-1)/2)log(1+(1-r^2)*g)+(-3/2)log(g)-n/2g
where :math:`n` is the sample size, :math:`r` is the Pearson correlation
coefficient and :math:`g` is is an auxiliary variable that is integrated
out numerically. Since the Wetzels Bayes Factor requires solving an
integral, it is slower than the analytical solution described below.
The two-sided **Ly Bayes Factor** (also called *Jeffreys
exact Bayes Factor*) is calculated using equation 25 of [2]_:
.. math::
\text{BF}_{10;k}(n, r) = \frac{2^{\frac{k-2}{k}}\sqrt{\pi}}
{\beta(\frac{1}{k}, \frac{1}{k})} \cdot
\frac{\Gamma(\frac{2+k(n-1)}{2k})}{\Gamma(\frac{2+nk}{2k})}
\cdot 2F_1(\frac{n-1}{2}, \frac{n-1}{2}, \frac{2+nk}{2k}, r^2)
The one-sided version is described in eq. 27 and 28 of Ly et al, 2016.
Please take note that the one-sided test requires the
`mpmath <http://mpmath.org/>`_ package.
Results have been validated against JASP and the BayesFactor R package.
References
----------
.. [1] Ly, A., Verhagen, J. & Wagenmakers, E.-J. Harold Jeffreys’s default
Bayes factor hypothesis tests: Explanation, extension, and
application in psychology. J. Math. Psychol. 72, 19–32 (2016).
.. [2] Wetzels, R. & Wagenmakers, E.-J. A default Bayesian hypothesis test
for correlations and partial correlations. Psychon. Bull. Rev. 19,
1057–1064 (2012).
Examples
--------
Bayes Factor of a Pearson correlation
>>> from pingouin import bayesfactor_pearson
>>> r, n = 0.6, 20
>>> bf = bayesfactor_pearson(r, n)
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 10.634
Compare to Wetzels method:
>>> bf = bayesfactor_pearson(r, n, method='wetzels')
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 8.221
One-sided test
>>> bf10pos = bayesfactor_pearson(r, n, alternative='greater')
>>> bf10neg = bayesfactor_pearson(r, n, alternative='less')
>>> print("BF-pos: %.3f, BF-neg: %.3f" % (bf10pos, bf10neg))
BF-pos: 21.185, BF-neg: 0.082
| def bayesfactor_pearson(r, n, alternative="two-sided", method="ly", kappa=1.0):
"""
Bayes Factor of a Pearson correlation.
Parameters
----------
r : float
Pearson correlation coefficient.
n : int
Sample size.
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 : str
Method to compute the Bayes Factor. Can be "ly" (default) or
"wetzels". The former has an exact analytical solution, while the
latter requires integral solving (and is therefore slower). "wetzels"
was the default in Pingouin <= 0.2.5. See Notes for details.
kappa : float
Kappa factor. This is sometimes called the *rscale* parameter, and
is only used when ``method`` is "ly".
Returns
-------
bf : float
Bayes Factor (BF10).
The Bayes Factor quantifies the evidence in favour of the alternative
hypothesis.
See also
--------
corr : (Robust) correlation between two variables
pairwise_corr : Pairwise correlation between columns of a pandas DataFrame
bayesfactor_ttest : Bayes Factor of a T-test
bayesfactor_binom : Bayes Factor of a binomial test
Notes
-----
To compute the Bayes Factor directly from the raw data, use the
:py:func:`pingouin.corr` function.
The two-sided **Wetzels Bayes Factor** (also called *JZS Bayes Factor*)
is calculated using the equation 13 and associated R code of [1]_:
.. math::
\\text{BF}_{10}(n, r) = \\frac{\\sqrt{n/2}}{\\gamma(1/2)}*
\\int_{0}^{\\infty}e((n-2)/2)*
log(1+g)+(-(n-1)/2)log(1+(1-r^2)*g)+(-3/2)log(g)-n/2g
where :math:`n` is the sample size, :math:`r` is the Pearson correlation
coefficient and :math:`g` is is an auxiliary variable that is integrated
out numerically. Since the Wetzels Bayes Factor requires solving an
integral, it is slower than the analytical solution described below.
The two-sided **Ly Bayes Factor** (also called *Jeffreys
exact Bayes Factor*) is calculated using equation 25 of [2]_:
.. math::
\\text{BF}_{10;k}(n, r) = \\frac{2^{\\frac{k-2}{k}}\\sqrt{\\pi}}
{\\beta(\\frac{1}{k}, \\frac{1}{k})} \\cdot
\\frac{\\Gamma(\\frac{2+k(n-1)}{2k})}{\\Gamma(\\frac{2+nk}{2k})}
\\cdot 2F_1(\\frac{n-1}{2}, \\frac{n-1}{2}, \\frac{2+nk}{2k}, r^2)
The one-sided version is described in eq. 27 and 28 of Ly et al, 2016.
Please take note that the one-sided test requires the
`mpmath <http://mpmath.org/>`_ package.
Results have been validated against JASP and the BayesFactor R package.
References
----------
.. [1] Ly, A., Verhagen, J. & Wagenmakers, E.-J. Harold Jeffreys’s default
Bayes factor hypothesis tests: Explanation, extension, and
application in psychology. J. Math. Psychol. 72, 19–32 (2016).
.. [2] Wetzels, R. & Wagenmakers, E.-J. A default Bayesian hypothesis test
for correlations and partial correlations. Psychon. Bull. Rev. 19,
1057–1064 (2012).
Examples
--------
Bayes Factor of a Pearson correlation
>>> from pingouin import bayesfactor_pearson
>>> r, n = 0.6, 20
>>> bf = bayesfactor_pearson(r, n)
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 10.634
Compare to Wetzels method:
>>> bf = bayesfactor_pearson(r, n, method='wetzels')
>>> print("Bayes Factor: %.3f" % bf)
Bayes Factor: 8.221
One-sided test
>>> bf10pos = bayesfactor_pearson(r, n, alternative='greater')
>>> bf10neg = bayesfactor_pearson(r, n, alternative='less')
>>> print("BF-pos: %.3f, BF-neg: %.3f" % (bf10pos, bf10neg))
BF-pos: 21.185, BF-neg: 0.082
"""
from scipy.special import gamma, betaln, hyp2f1
assert method.lower() in ["ly", "wetzels"], "Method not recognized."
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
# Wrong input
if not np.isfinite(r) or n < 2:
return np.nan
assert -1 <= r <= 1, "r must be between -1 and 1."
if alternative != "two-sided" and method.lower() == "wetzels":
warnings.warn(
"One-sided Bayes Factor are not supported by the "
"Wetzels's method. Switching to method='ly'."
)
method = "ly"
if method.lower() == "wetzels":
# Wetzels & Wagenmakers, 2012. Integral solving
def fun(g, r, n):
return exp(
((n - 2) / 2) * log(1 + g)
+ (-(n - 1) / 2) * log(1 + (1 - r**2) * g)
+ (-3 / 2) * log(g)
+ -n / (2 * g)
)
integr = quad(fun, 0, np.inf, args=(r, n))[0]
bf10 = np.sqrt(n / 2) / gamma(1 / 2) * integr
else:
# Ly et al, 2016. Analytical solution.
k = kappa
lbeta = betaln(1 / k, 1 / k)
log_hyperterm = log(hyp2f1(((n - 1) / 2), ((n - 1) / 2), ((n + 2 / k) / 2), r**2))
bf10 = exp(
(1 - 2 / k) * log(2)
+ 0.5 * log(pi)
- lbeta
+ lgamma((n + 2 / k - 1) / 2)
- lgamma((n + 2 / k) / 2)
+ log_hyperterm
)
if alternative != "two-sided":
# Directional test.
# We need mpmath for the generalized hypergeometric function
from .utils import _is_mpmath_installed
_is_mpmath_installed(raise_error=True)
from mpmath import hyp3f2
hyper_term = float(hyp3f2(1, n / 2, n / 2, 3 / 2, (2 + k * (n + 1)) / (2 * k), r**2))
log_term = 2 * (lgamma(n / 2) - lgamma((n - 1) / 2)) - lbeta
C = 2 ** ((3 * k - 2) / k) * k * r / (2 + (n - 1) * k) * exp(log_term) * hyper_term
bf10neg = bf10 - C
bf10pos = 2 * bf10 - bf10neg
if alternative == "greater":
# We expect the correlation to be positive
bf10 = bf10pos
else:
# We expect the correlation to be negative
bf10 = bf10neg
return bf10
| (r, n, alternative='two-sided', method='ly', kappa=1.0) | [
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|
31,977 | pingouin.bayesian | bayesfactor_ttest |
Bayes Factor of a T-test.
Parameters
----------
t : float
T-value of the T-test
nx : int
Sample size of first group
ny : int
Sample size of second group (only needed in case of an independent
two-sample T-test)
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".
.. warning:: One-sided Bayes Factor (BF) are simply obtained by
doubling the two-sided BF, which is not the same behavior
as R or JASP. Be extra careful when interpretating one-sided BF,
and if you can, always double-check your results.
r : float
Cauchy scale 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
:math:`\sqrt{2} / 2 \approx 0.707`.
Returns
-------
bf : float
Scaled Jeffrey-Zellner-Siow (JZS) Bayes Factor (BF10).
The Bayes Factor quantifies the evidence in favour of the
alternative hypothesis.
See also
--------
ttest : T-test
pairwise_test : Pairwise T-tests
bayesfactor_pearson : Bayes Factor of a correlation
bayesfactor_binom : Bayes Factor of a binomial test
Notes
-----
Adapted from a Matlab code found at
https://github.com/anne-urai/Tools/tree/master/stats/BayesFactors
If you would like to compute the Bayes Factor directly from the raw data
instead of from the T-value, use the :py:func:`pingouin.ttest` function.
The JZS Bayes Factor is approximated using the formula described
in ref [1]_:
.. math::
\text{BF}_{10} = \frac{\int_{0}^{\infty}(1 + Ngr^2)^{-1/2}
(1 + \frac{t^2}{v(1 + Ngr^2)})^{-(v+1) / 2}(2\pi)^{-1/2}g^
{-3/2}e^{-1/2g}}{(1 + \frac{t^2}{v})^{-(v+1) / 2}}
where :math:`t` is the T-value, :math:`v` the degrees of freedom,
:math:`N` the sample size, :math:`r` the Cauchy scale factor
(= prior on effect size) and :math:`g` is is an auxiliary variable
that is integrated out numerically.
Results have been validated against JASP and the BayesFactor R package.
References
----------
.. [1] 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. Bayes Factor of an independent two-sample T-test
>>> from pingouin import bayesfactor_ttest
>>> bf = bayesfactor_ttest(3.5, 20, 20)
>>> print("Bayes Factor: %.3f (two-sample independent)" % bf)
Bayes Factor: 26.743 (two-sample independent)
2. Bayes Factor of a paired two-sample T-test
>>> bf = bayesfactor_ttest(3.5, 20, 20, paired=True)
>>> print("Bayes Factor: %.3f (two-sample paired)" % bf)
Bayes Factor: 17.185 (two-sample paired)
3. Now specifying the direction of the test
>>> tval = -3.5
>>> bf_greater = bayesfactor_ttest(tval, 20, alternative='greater')
>>> bf_less = bayesfactor_ttest(tval, 20, alternative='less')
>>> print("BF10-greater: %.3f | BF10-less: %.3f" % (bf_greater, bf_less))
BF10-greater: 0.029 | BF10-less: 34.369
| def bayesfactor_ttest(t, nx, ny=None, paired=False, alternative="two-sided", r=0.707):
"""
Bayes Factor of a T-test.
Parameters
----------
t : float
T-value of the T-test
nx : int
Sample size of first group
ny : int
Sample size of second group (only needed in case of an independent
two-sample T-test)
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".
.. warning:: One-sided Bayes Factor (BF) are simply obtained by
doubling the two-sided BF, which is not the same behavior
as R or JASP. Be extra careful when interpretating one-sided BF,
and if you can, always double-check your results.
r : float
Cauchy scale 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
:math:`\\sqrt{2} / 2 \\approx 0.707`.
Returns
-------
bf : float
Scaled Jeffrey-Zellner-Siow (JZS) Bayes Factor (BF10).
The Bayes Factor quantifies the evidence in favour of the
alternative hypothesis.
See also
--------
ttest : T-test
pairwise_test : Pairwise T-tests
bayesfactor_pearson : Bayes Factor of a correlation
bayesfactor_binom : Bayes Factor of a binomial test
Notes
-----
Adapted from a Matlab code found at
https://github.com/anne-urai/Tools/tree/master/stats/BayesFactors
If you would like to compute the Bayes Factor directly from the raw data
instead of from the T-value, use the :py:func:`pingouin.ttest` function.
The JZS Bayes Factor is approximated using the formula described
in ref [1]_:
.. math::
\\text{BF}_{10} = \\frac{\\int_{0}^{\\infty}(1 + Ngr^2)^{-1/2}
(1 + \\frac{t^2}{v(1 + Ngr^2)})^{-(v+1) / 2}(2\\pi)^{-1/2}g^
{-3/2}e^{-1/2g}}{(1 + \\frac{t^2}{v})^{-(v+1) / 2}}
where :math:`t` is the T-value, :math:`v` the degrees of freedom,
:math:`N` the sample size, :math:`r` the Cauchy scale factor
(= prior on effect size) and :math:`g` is is an auxiliary variable
that is integrated out numerically.
Results have been validated against JASP and the BayesFactor R package.
References
----------
.. [1] 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. Bayes Factor of an independent two-sample T-test
>>> from pingouin import bayesfactor_ttest
>>> bf = bayesfactor_ttest(3.5, 20, 20)
>>> print("Bayes Factor: %.3f (two-sample independent)" % bf)
Bayes Factor: 26.743 (two-sample independent)
2. Bayes Factor of a paired two-sample T-test
>>> bf = bayesfactor_ttest(3.5, 20, 20, paired=True)
>>> print("Bayes Factor: %.3f (two-sample paired)" % bf)
Bayes Factor: 17.185 (two-sample paired)
3. Now specifying the direction of the test
>>> tval = -3.5
>>> bf_greater = bayesfactor_ttest(tval, 20, alternative='greater')
>>> bf_less = bayesfactor_ttest(tval, 20, alternative='less')
>>> print("BF10-greater: %.3f | BF10-less: %.3f" % (bf_greater, bf_less))
BF10-greater: 0.029 | BF10-less: 34.369
"""
# Check tail
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
one_sample = True if ny is None or ny == 1 else False
# Check T-value
assert isinstance(t, (int, float)), "The T-value must be a int or a float."
if not np.isfinite(t):
return np.nan
# Function to be integrated
def fun(g, t, n, r, df):
return (
(1 + n * g * r**2) ** (-0.5)
* (1 + t**2 / ((1 + n * g * r**2) * df)) ** (-(df + 1) / 2)
* (2 * pi) ** (-0.5)
* g ** (-3.0 / 2)
* exp(-1 / (2 * g))
)
# Define n and degrees of freedom
if one_sample or paired:
n = nx
df = n - 1
else:
n = nx * ny / (nx + ny)
df = nx + ny - 2
# JZS Bayes factor calculation: eq. 1 in Rouder et al. (2009)
integr = quad(fun, 0, np.inf, args=(t, n, r, df))[0]
bf10 = 1 / ((1 + t**2 / df) ** (-(df + 1) / 2) / integr)
# Tail
tail_binary = "two-sided" if alternative == "two-sided" else "one-sided"
bf10 = bf10 * (1 / 0.5) if tail_binary == "one-sided" else bf10
# Now check the direction of the test
if ((alternative == "greater" and t < 0) or (alternative == "less" and t > 0)) and bf10 > 1:
bf10 = 1 / bf10
return bf10
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|
31,979 | pingouin.multivariate | box_m | Test equality of covariance matrices using the Box's M test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Long-format dataframe.
dvs : list
Dependent variables.
group : str
Grouping variable.
alpha : float
Significance level. Default is 0.001 as recommended in [2]_. A
non-significant p-value (higher than alpha) indicates that the
covariance matrices are homogenous (= equal).
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'Chi2'``: Test statistic
* ``'pval'``: p-value
* ``'df'``: The Chi-Square statistic's degree of freedom
* ``'equal_cov'``: True if ``data`` has equal covariance
Notes
-----
.. warning:: Box's M test is susceptible to errors if the data does not
meet the assumption of multivariate normality or if the sample size is
too large or small [3]_.
Pingouin uses :py:meth:`pandas.DataFrameGroupBy.cov` to calculate the
variance-covariance matrix of each group. Missing values are automatically
excluded from the calculation by Pandas.
Mathematical expressions can be found in [1]_.
This function has been tested against the boxM package of the `biotools`
R package [4]_.
References
----------
.. [1] Rencher, A. C. (2003). Methods of multivariate analysis (Vol. 492).
John Wiley & Sons.
.. [2] Hahs-Vaughn, D. (2016). Applied Multivariate Statistical Concepts.
Taylor & Francis.
.. [3] https://en.wikipedia.org/wiki/Box%27s_M_test
.. [4] https://cran.r-project.org/web/packages/biotools/index.html
Examples
--------
1. Box M test with 3 dependent variables of 4 groups (equal sample size)
>>> import pandas as pd
>>> import pingouin as pg
>>> from scipy.stats import multivariate_normal as mvn
>>> data = pd.DataFrame(mvn.rvs(size=(100, 3), random_state=42),
... columns=['A', 'B', 'C'])
>>> data['group'] = [1] * 25 + [2] * 25 + [3] * 25 + [4] * 25
>>> data.head()
A B C group
0 0.496714 -0.138264 0.647689 1
1 1.523030 -0.234153 -0.234137 1
2 1.579213 0.767435 -0.469474 1
3 0.542560 -0.463418 -0.465730 1
4 0.241962 -1.913280 -1.724918 1
>>> pg.box_m(data, dvs=['A', 'B', 'C'], group='group')
Chi2 df pval equal_cov
box 11.634185 18.0 0.865537 True
2. Box M test with 3 dependent variables of 2 groups (unequal sample size)
>>> data = pd.DataFrame(mvn.rvs(size=(30, 2), random_state=42),
... columns=['A', 'B'])
>>> data['group'] = [1] * 20 + [2] * 10
>>> pg.box_m(data, dvs=['A', 'B'], group='group')
Chi2 df pval equal_cov
box 0.706709 3.0 0.871625 True
| def box_m(data, dvs, group, alpha=0.001):
"""Test equality of covariance matrices using the Box's M test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Long-format dataframe.
dvs : list
Dependent variables.
group : str
Grouping variable.
alpha : float
Significance level. Default is 0.001 as recommended in [2]_. A
non-significant p-value (higher than alpha) indicates that the
covariance matrices are homogenous (= equal).
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'Chi2'``: Test statistic
* ``'pval'``: p-value
* ``'df'``: The Chi-Square statistic's degree of freedom
* ``'equal_cov'``: True if ``data`` has equal covariance
Notes
-----
.. warning:: Box's M test is susceptible to errors if the data does not
meet the assumption of multivariate normality or if the sample size is
too large or small [3]_.
Pingouin uses :py:meth:`pandas.DataFrameGroupBy.cov` to calculate the
variance-covariance matrix of each group. Missing values are automatically
excluded from the calculation by Pandas.
Mathematical expressions can be found in [1]_.
This function has been tested against the boxM package of the `biotools`
R package [4]_.
References
----------
.. [1] Rencher, A. C. (2003). Methods of multivariate analysis (Vol. 492).
John Wiley & Sons.
.. [2] Hahs-Vaughn, D. (2016). Applied Multivariate Statistical Concepts.
Taylor & Francis.
.. [3] https://en.wikipedia.org/wiki/Box%27s_M_test
.. [4] https://cran.r-project.org/web/packages/biotools/index.html
Examples
--------
1. Box M test with 3 dependent variables of 4 groups (equal sample size)
>>> import pandas as pd
>>> import pingouin as pg
>>> from scipy.stats import multivariate_normal as mvn
>>> data = pd.DataFrame(mvn.rvs(size=(100, 3), random_state=42),
... columns=['A', 'B', 'C'])
>>> data['group'] = [1] * 25 + [2] * 25 + [3] * 25 + [4] * 25
>>> data.head()
A B C group
0 0.496714 -0.138264 0.647689 1
1 1.523030 -0.234153 -0.234137 1
2 1.579213 0.767435 -0.469474 1
3 0.542560 -0.463418 -0.465730 1
4 0.241962 -1.913280 -1.724918 1
>>> pg.box_m(data, dvs=['A', 'B', 'C'], group='group')
Chi2 df pval equal_cov
box 11.634185 18.0 0.865537 True
2. Box M test with 3 dependent variables of 2 groups (unequal sample size)
>>> data = pd.DataFrame(mvn.rvs(size=(30, 2), random_state=42),
... columns=['A', 'B'])
>>> data['group'] = [1] * 20 + [2] * 10
>>> pg.box_m(data, dvs=['A', 'B'], group='group')
Chi2 df pval equal_cov
box 0.706709 3.0 0.871625 True
"""
# Safety checks
from scipy.stats import chi2
assert isinstance(data, pd.DataFrame), "data must be a pandas dataframe."
assert group in data.columns, "The grouping variable is not in data."
assert set(dvs).issubset(data.columns), "The DVs are not in data."
grp = data.groupby(group, observed=True)[dvs]
assert grp.ngroups > 1, "Data must have at least two columns."
# Calculate covariance matrix and descriptive statistics
# - n_covs is the number of covariance matrices
# - n_dvs is the number of variables
# - n_samp is the number of samples in each covariance matrix
# - nobs is the total number of observations
covs = grp.cov(numeric_only=True)
n_covs, n_dvs = covs.index.levshape
n_samp = grp.count().iloc[:, 0].to_numpy() # NaN are excluded by .count
nobs = n_samp.sum()
v = n_samp - 1
# Calculate pooled covariance matrix (S) and M statistics
covs = covs.to_numpy().reshape(n_covs, n_dvs, -1)
S = (covs * v[..., None, None]).sum(axis=0) / (nobs - n_covs)
# The following lines might raise an error if the covariance matrices are
# not invertible (e.g. missing values in input).
S_det = np.linalg.det(S)
M = ((np.linalg.det(covs) / S_det) ** (v / 2)).prod()
# Calculate C in reference [1] (page 257-259)
if len(np.unique(n_samp)) == 1:
# All groups have same number of samples
c = ((n_covs + 1) * (2 * n_dvs**2 + 3 * n_dvs - 1)) / (
6 * n_covs * (n_dvs + 1) * (nobs / n_covs - 1)
)
else:
# Unequal sample size
c = (2 * n_dvs**2 + 3 * n_dvs - 1) / (6 * (n_dvs + 1) * (n_covs - 1))
c *= (1 / v).sum() - 1 / v.sum()
# Calculate U statistics and degree of fredom
u = -2 * (1 - c) * np.log(M)
df = 0.5 * n_dvs * (n_dvs + 1) * (n_covs - 1)
p = chi2.sf(u, df)
equal_cov = True if p > alpha else False
stats = pd.DataFrame(
index=["box"], data={"Chi2": [u], "df": [df], "pval": [p], "equal_cov": [equal_cov]}
)
return _postprocess_dataframe(stats)
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|
31,980 | pingouin.contingency | chi2_independence |
Chi-squared independence tests between two categorical variables.
The test is computed for different values of :math:`\lambda`: 1, 2/3, 0,
-1/2, -1 and -2 (Cressie and Read, 1984).
Parameters
----------
data : :py:class:`pandas.DataFrame`
The dataframe containing the ocurrences for the test.
x, y : string
The variables names for the Chi-squared test. Must be names of columns
in ``data``.
correction : bool
Whether to apply Yates' correction when the degree of freedom of the
observed contingency table is 1 (Yates 1934).
Returns
-------
expected : :py:class:`pandas.DataFrame`
The expected contingency table of frequencies.
observed : :py:class:`pandas.DataFrame`
The (corrected or not) observed contingency table of frequencies.
stats : :py:class:`pandas.DataFrame`
The test summary, containing four columns:
* ``'test'``: The statistic name
* ``'lambda'``: The :math:`\lambda` value used for the power divergence statistic
* ``'chi2'``: The test statistic
* ``'pval'``: The p-value of the test
* ``'cramer'``: The Cramer's V effect size
* ``'power'``: The statistical power of the test
Notes
-----
From Wikipedia:
*The chi-squared test is used to determine whether there is a significant
difference between the expected frequencies and the observed frequencies
in one or more categories.*
As application examples, this test can be used to *i*) evaluate the
quality of a categorical variable in a classification problem or to *ii*)
check the similarity between two categorical variables. In the first
example, a good categorical predictor and the class column should present
high :math:`\chi^2` and low p-value. In the second example, similar
categorical variables should present low :math:`\chi^2` and high p-value.
This function is a wrapper around the
:py:func:`scipy.stats.power_divergence` function.
.. warning :: As a general guideline for the consistency of this test, the
observed and the expected contingency tables should not have cells
with frequencies lower than 5.
References
----------
* Cressie, N., & Read, T. R. (1984). Multinomial goodness‐of‐fit
tests. Journal of the Royal Statistical Society: Series B
(Methodological), 46(3), 440-464.
* Yates, F. (1934). Contingency Tables Involving Small Numbers and the
:math:`\chi^2` Test. Supplement to the Journal of the Royal
Statistical Society, 1, 217-235.
Examples
--------
Let's see if gender is a good categorical predictor for the presence of
heart disease.
>>> import pingouin as pg
>>> data = pg.read_dataset('chi2_independence')
>>> data['sex'].value_counts(ascending=True)
sex
0 96
1 207
Name: count, dtype: int64
If gender is not a good predictor for heart disease, we should expect the
same 96:207 ratio across the target classes.
>>> expected, observed, stats = pg.chi2_independence(data, x='sex',
... y='target')
>>> expected
target 0 1
sex
0 43.722772 52.277228
1 94.277228 112.722772
Let's see what the data tells us.
>>> observed
target 0 1
sex
0 24.5 71.5
1 113.5 93.5
The proportion is lower on the class 0 and higher on the class 1. The
tests should be sensitive to this difference.
>>> stats.round(3)
test lambda chi2 dof pval cramer power
0 pearson 1.000 22.717 1.0 0.0 0.274 0.997
1 cressie-read 0.667 22.931 1.0 0.0 0.275 0.998
2 log-likelihood 0.000 23.557 1.0 0.0 0.279 0.998
3 freeman-tukey -0.500 24.220 1.0 0.0 0.283 0.998
4 mod-log-likelihood -1.000 25.071 1.0 0.0 0.288 0.999
5 neyman -2.000 27.458 1.0 0.0 0.301 0.999
Very low p-values indeed. The gender qualifies as a good predictor for the
presence of heart disease on this dataset.
| def chi2_independence(data, x, y, correction=True):
"""
Chi-squared independence tests between two categorical variables.
The test is computed for different values of :math:`\\lambda`: 1, 2/3, 0,
-1/2, -1 and -2 (Cressie and Read, 1984).
Parameters
----------
data : :py:class:`pandas.DataFrame`
The dataframe containing the ocurrences for the test.
x, y : string
The variables names for the Chi-squared test. Must be names of columns
in ``data``.
correction : bool
Whether to apply Yates' correction when the degree of freedom of the
observed contingency table is 1 (Yates 1934).
Returns
-------
expected : :py:class:`pandas.DataFrame`
The expected contingency table of frequencies.
observed : :py:class:`pandas.DataFrame`
The (corrected or not) observed contingency table of frequencies.
stats : :py:class:`pandas.DataFrame`
The test summary, containing four columns:
* ``'test'``: The statistic name
* ``'lambda'``: The :math:`\\lambda` value used for the power\
divergence statistic
* ``'chi2'``: The test statistic
* ``'pval'``: The p-value of the test
* ``'cramer'``: The Cramer's V effect size
* ``'power'``: The statistical power of the test
Notes
-----
From Wikipedia:
*The chi-squared test is used to determine whether there is a significant
difference between the expected frequencies and the observed frequencies
in one or more categories.*
As application examples, this test can be used to *i*) evaluate the
quality of a categorical variable in a classification problem or to *ii*)
check the similarity between two categorical variables. In the first
example, a good categorical predictor and the class column should present
high :math:`\\chi^2` and low p-value. In the second example, similar
categorical variables should present low :math:`\\chi^2` and high p-value.
This function is a wrapper around the
:py:func:`scipy.stats.power_divergence` function.
.. warning :: As a general guideline for the consistency of this test, the
observed and the expected contingency tables should not have cells
with frequencies lower than 5.
References
----------
* Cressie, N., & Read, T. R. (1984). Multinomial goodness‐of‐fit
tests. Journal of the Royal Statistical Society: Series B
(Methodological), 46(3), 440-464.
* Yates, F. (1934). Contingency Tables Involving Small Numbers and the
:math:`\\chi^2` Test. Supplement to the Journal of the Royal
Statistical Society, 1, 217-235.
Examples
--------
Let's see if gender is a good categorical predictor for the presence of
heart disease.
>>> import pingouin as pg
>>> data = pg.read_dataset('chi2_independence')
>>> data['sex'].value_counts(ascending=True)
sex
0 96
1 207
Name: count, dtype: int64
If gender is not a good predictor for heart disease, we should expect the
same 96:207 ratio across the target classes.
>>> expected, observed, stats = pg.chi2_independence(data, x='sex',
... y='target')
>>> expected
target 0 1
sex
0 43.722772 52.277228
1 94.277228 112.722772
Let's see what the data tells us.
>>> observed
target 0 1
sex
0 24.5 71.5
1 113.5 93.5
The proportion is lower on the class 0 and higher on the class 1. The
tests should be sensitive to this difference.
>>> stats.round(3)
test lambda chi2 dof pval cramer power
0 pearson 1.000 22.717 1.0 0.0 0.274 0.997
1 cressie-read 0.667 22.931 1.0 0.0 0.275 0.998
2 log-likelihood 0.000 23.557 1.0 0.0 0.279 0.998
3 freeman-tukey -0.500 24.220 1.0 0.0 0.283 0.998
4 mod-log-likelihood -1.000 25.071 1.0 0.0 0.288 0.999
5 neyman -2.000 27.458 1.0 0.0 0.301 0.999
Very low p-values indeed. The gender qualifies as a good predictor for the
presence of heart disease on this dataset.
"""
# Python code inspired by SciPy's chi2_contingency
assert isinstance(data, pd.DataFrame), "data must be a pandas DataFrame."
assert isinstance(x, (str, int)), "x must be a string or int."
assert isinstance(y, (str, int)), "y must be a string or int."
assert all(col in data.columns for col in (x, y)), "columns are not in dataframe."
assert isinstance(correction, bool), "correction must be a boolean."
observed = pd.crosstab(data[x], data[y])
if observed.size == 0:
raise ValueError("No data; observed has size 0.")
expected = pd.DataFrame(expected_freq(observed), index=observed.index, columns=observed.columns)
# All count frequencies should be at least 5
for df, name in zip([observed, expected], ["observed", "expected"]):
if (df < 5).any(axis=None):
warnings.warn(f"Low count on {name} frequencies.")
dof = float(expected.size - sum(expected.shape) + expected.ndim - 1)
if dof == 1 and correction:
# Adjust `observed` according to Yates' correction for continuity.
observed = observed + 0.5 * np.sign(expected - observed)
ddof = observed.size - 1 - dof
n = data.shape[0]
stats = []
names = [
"pearson",
"cressie-read",
"log-likelihood",
"freeman-tukey",
"mod-log-likelihood",
"neyman",
]
for name, lambda_ in zip(names, [1.0, 2 / 3, 0.0, -1 / 2, -1.0, -2.0]):
if dof == 0:
chi2, p, cramer, power = 0.0, 1.0, np.nan, np.nan
else:
chi2, p = power_divergence(observed, expected, ddof=ddof, axis=None, lambda_=lambda_)
dof_cramer = min(expected.shape) - 1
cramer = np.sqrt(chi2 / (n * dof_cramer))
power = power_chi2(dof=dof, w=cramer, n=n, alpha=0.05)
stats.append(
{
"test": name,
"lambda": lambda_,
"chi2": chi2,
"dof": dof,
"pval": p,
"cramer": cramer,
"power": power,
}
)
stats = pd.DataFrame(stats)[["test", "lambda", "chi2", "dof", "pval", "cramer", "power"]]
return expected, observed, _postprocess_dataframe(stats)
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|
31,981 | pingouin.contingency | chi2_mcnemar |
Performs the exact and approximated versions of McNemar's test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
The dataframe containing the ocurrences for the test. Each row must
represent either a subject or a pair of subjects.
x, y : string
The variables names for the McNemar's test. Must be names of columns
in ``data``.
If each row of ``data`` represents a subject, then ``x`` and ``y`` must
be columns containing dichotomous measurements in two different
contexts. For instance: the presence of pain before and after a certain
treatment.
If each row of ``data`` represents a pair of subjects, then ``x`` and
``y`` must be columns containing dichotomous measurements for each of
the subjects. For instance: a positive response to a certain drug in
the control group and in the test group, supposing that each pair
contains a subject in each group.
The 2x2 crosstab is created using the
:py:func:`pingouin.dichotomous_crosstab` function.
.. warning:: Missing values are not allowed.
correction : bool
Whether to apply the correction for continuity (Edwards, A. 1948).
Returns
-------
observed : :py:class:`pandas.DataFrame`
The observed contingency table of frequencies.
stats : :py:class:`pandas.DataFrame`
The test summary:
* ``'chi2'``: The test statistic
* ``'dof'``: The degree of freedom
* ``'p-approx'``: The approximated p-value
* ``'p-exact'``: The exact p-value
Notes
-----
The McNemar's test is compatible with dichotomous paired data, generally
used to assert the effectiveness of a certain procedure, such as a
treatment or the use of a drug. "Dichotomous" means that the values of the
measurements are binary. "Paired data" means that each measurement is done
twice, either on the same subject in two different moments or in two
similar (paired) subjects from different groups (e.g.: control/test). In
order to better understand the idea behind McNemar's test, let's illustrate
it with an example.
Suppose that we wanted to compare the effectiveness of two different
treatments (X and Y) for athlete's foot on a certain group of `n` people.
To achieve this, we measured their responses to such treatments on each
foot. The observed data summary was:
* Number of people with good responses to X and Y: `a`
* Number of people with good response to X and bad response to Y: `b`
* Number of people with bad response to X and good response to Y: `c`
* Number of people with bad responses to X and Y: `d`
Now consider the two groups:
1. The group of people who had good response to X (`a` + `b` subjects)
2. The group of people who had good response to Y (`a` + `c` subjects)
If the treatments have the same effectiveness, we should expect the
probabilities of having good responses to be the same, regardless of the
treatment. Mathematically, such statement can be translated into the
following equation:
.. math::
\frac{a+b}{n} = \frac{a+c}{n} \Rightarrow b = c
Thus, this test should indicate higher statistical significances for higher
distances between `b` and `c` (McNemar, Q. 1947):
.. math::
\chi^2 = \frac{(b - c)^2}{b + c}
References
----------
* Edwards, A. L. (1948). Note on the "correction for continuity" in
testing the significance of the difference between correlated
proportions. Psychometrika, 13(3), 185-187.
* McNemar, Q. (1947). Note on the sampling error of the difference
between correlated proportions or percentages. Psychometrika, 12(2),
153-157.
Examples
--------
>>> import pingouin as pg
>>> data = pg.read_dataset('chi2_mcnemar')
>>> observed, stats = pg.chi2_mcnemar(data, 'treatment_X', 'treatment_Y')
>>> observed
treatment_Y 0 1
treatment_X
0 20 40
1 8 12
In this case, `c` (40) seems to be a significantly greater than `b` (8).
The McNemar test should be sensitive to this.
>>> stats
chi2 dof p-approx p-exact
mcnemar 20.020833 1 0.000008 0.000003
| def chi2_mcnemar(data, x, y, correction=True):
"""
Performs the exact and approximated versions of McNemar's test.
Parameters
----------
data : :py:class:`pandas.DataFrame`
The dataframe containing the ocurrences for the test. Each row must
represent either a subject or a pair of subjects.
x, y : string
The variables names for the McNemar's test. Must be names of columns
in ``data``.
If each row of ``data`` represents a subject, then ``x`` and ``y`` must
be columns containing dichotomous measurements in two different
contexts. For instance: the presence of pain before and after a certain
treatment.
If each row of ``data`` represents a pair of subjects, then ``x`` and
``y`` must be columns containing dichotomous measurements for each of
the subjects. For instance: a positive response to a certain drug in
the control group and in the test group, supposing that each pair
contains a subject in each group.
The 2x2 crosstab is created using the
:py:func:`pingouin.dichotomous_crosstab` function.
.. warning:: Missing values are not allowed.
correction : bool
Whether to apply the correction for continuity (Edwards, A. 1948).
Returns
-------
observed : :py:class:`pandas.DataFrame`
The observed contingency table of frequencies.
stats : :py:class:`pandas.DataFrame`
The test summary:
* ``'chi2'``: The test statistic
* ``'dof'``: The degree of freedom
* ``'p-approx'``: The approximated p-value
* ``'p-exact'``: The exact p-value
Notes
-----
The McNemar's test is compatible with dichotomous paired data, generally
used to assert the effectiveness of a certain procedure, such as a
treatment or the use of a drug. "Dichotomous" means that the values of the
measurements are binary. "Paired data" means that each measurement is done
twice, either on the same subject in two different moments or in two
similar (paired) subjects from different groups (e.g.: control/test). In
order to better understand the idea behind McNemar's test, let's illustrate
it with an example.
Suppose that we wanted to compare the effectiveness of two different
treatments (X and Y) for athlete's foot on a certain group of `n` people.
To achieve this, we measured their responses to such treatments on each
foot. The observed data summary was:
* Number of people with good responses to X and Y: `a`
* Number of people with good response to X and bad response to Y: `b`
* Number of people with bad response to X and good response to Y: `c`
* Number of people with bad responses to X and Y: `d`
Now consider the two groups:
1. The group of people who had good response to X (`a` + `b` subjects)
2. The group of people who had good response to Y (`a` + `c` subjects)
If the treatments have the same effectiveness, we should expect the
probabilities of having good responses to be the same, regardless of the
treatment. Mathematically, such statement can be translated into the
following equation:
.. math::
\\frac{a+b}{n} = \\frac{a+c}{n} \\Rightarrow b = c
Thus, this test should indicate higher statistical significances for higher
distances between `b` and `c` (McNemar, Q. 1947):
.. math::
\\chi^2 = \\frac{(b - c)^2}{b + c}
References
----------
* Edwards, A. L. (1948). Note on the "correction for continuity" in
testing the significance of the difference between correlated
proportions. Psychometrika, 13(3), 185-187.
* McNemar, Q. (1947). Note on the sampling error of the difference
between correlated proportions or percentages. Psychometrika, 12(2),
153-157.
Examples
--------
>>> import pingouin as pg
>>> data = pg.read_dataset('chi2_mcnemar')
>>> observed, stats = pg.chi2_mcnemar(data, 'treatment_X', 'treatment_Y')
>>> observed
treatment_Y 0 1
treatment_X
0 20 40
1 8 12
In this case, `c` (40) seems to be a significantly greater than `b` (8).
The McNemar test should be sensitive to this.
>>> stats
chi2 dof p-approx p-exact
mcnemar 20.020833 1 0.000008 0.000003
"""
# Python code initially inspired by statsmodel's mcnemar
assert isinstance(data, pd.DataFrame), "data must be a pandas DataFrame."
assert all(
isinstance(column, (str, int)) for column in (x, y)
), "column names must be string or int."
assert all(column in data.columns for column in (x, y)), "columns are not in dataframe."
for column in (x, y):
if data[column].isna().any():
raise ValueError("Null values are not allowed.")
observed = dichotomous_crosstab(data, x, y)
# Careful, the order of b and c is inverted compared to wikipedia
# because the colums / rows of the crosstab is [0, 1] and not [1, 0].
c, b = observed.at[0, 1], observed.at[1, 0]
n_discordants = b + c
if (b, c) == (0, 0):
raise ValueError(
"McNemar's test does not work if the secondary "
+ "diagonal of the observed data summary does not "
+ "have values different from 0."
)
chi2 = (abs(b - c) - int(correction)) ** 2 / n_discordants
pexact = min(1, 2 * binom.cdf(min(b, c), n_discordants, 0.5))
stats = {
"chi2": chi2,
"dof": 1,
"p-approx": sp_chi2.sf(chi2, 1),
"p-exact": pexact,
# 'p-mid': pexact - binom.pmf(b, n_discordants, 0.5)
}
stats = pd.DataFrame(stats, index=["mcnemar"])
return observed, _postprocess_dataframe(stats)
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|
31,982 | pingouin.circular | circ_axial | Transforms n-axial data to a common scale.
Parameters
----------
angles : array
Sample of angles in radians
n : int
Number of modes
Returns
-------
angles : float
Transformed angles
Notes
-----
Tranform data with multiple modes (known as axial data) to a unimodal
sample, for the purpose of certain analysis such as computation of a
mean resultant vector (see Berens 2009).
Examples
--------
Transform degrees to unimodal radians in the Berens 2009 neuro dataset.
>>> import numpy as np
>>> from pingouin import read_dataset
>>> from pingouin.circular import circ_axial
>>> df = read_dataset('circular')
>>> angles = df['Orientation'].to_numpy()
>>> angles = circ_axial(np.deg2rad(angles), 2)
| def circ_axial(angles, n):
"""Transforms n-axial data to a common scale.
Parameters
----------
angles : array
Sample of angles in radians
n : int
Number of modes
Returns
-------
angles : float
Transformed angles
Notes
-----
Tranform data with multiple modes (known as axial data) to a unimodal
sample, for the purpose of certain analysis such as computation of a
mean resultant vector (see Berens 2009).
Examples
--------
Transform degrees to unimodal radians in the Berens 2009 neuro dataset.
>>> import numpy as np
>>> from pingouin import read_dataset
>>> from pingouin.circular import circ_axial
>>> df = read_dataset('circular')
>>> angles = df['Orientation'].to_numpy()
>>> angles = circ_axial(np.deg2rad(angles), 2)
"""
angles = np.asarray(angles)
return np.remainder(angles * n, 2 * np.pi)
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|
31,983 | pingouin.circular | circ_corrcc | Correlation coefficient between two circular variables.
Parameters
----------
x : 1-D array_like
First circular variable (expressed in radians).
y : 1-D array_like
Second circular variable (expressed in radians).
correction_uniform : bool
Use correction for uniform marginals.
Returns
-------
r : float
Correlation coefficient.
pval : float
Uncorrected p-value.
Notes
-----
Adapted from the CircStats MATLAB toolbox [1]_.
The range of ``x`` and ``y`` must be either
:math:`[0, 2\pi]` or :math:`[-\pi, \pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
Please note that NaN are automatically removed.
If the ``correction_uniform`` is True, an alternative equation from
[2]_ (p. 177) is used. If the marginal distribution of ``x`` or ``y`` is
uniform, the mean is not well defined, which leads to wrong estimates
of the circular correlation. The alternative equation corrects for this
by choosing the means in a way that maximizes the positive or negative
correlation.
References
----------
.. [1] Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular
Statistics. Journal of Statistical Software, Articles, 31(10), 1–21.
https://doi.org/10.18637/jss.v031.i10
.. [2] Jammalamadaka, S. R., & Sengupta, A. (2001). Topics in circular
statistics (Vol. 5). world scientific.
Examples
--------
Compute the r and p-value of two circular variables
>>> from pingouin import circ_corrcc
>>> x = [0.785, 1.570, 3.141, 3.839, 5.934]
>>> y = [0.593, 1.291, 2.879, 3.892, 6.108]
>>> r, pval = circ_corrcc(x, y)
>>> print(round(r, 3), round(pval, 4))
0.942 0.0658
With the correction for uniform marginals
>>> r, pval = circ_corrcc(x, y, correction_uniform=True)
>>> print(round(r, 3), round(pval, 4))
0.547 0.2859
| def circ_corrcc(x, y, correction_uniform=False):
"""Correlation coefficient between two circular variables.
Parameters
----------
x : 1-D array_like
First circular variable (expressed in radians).
y : 1-D array_like
Second circular variable (expressed in radians).
correction_uniform : bool
Use correction for uniform marginals.
Returns
-------
r : float
Correlation coefficient.
pval : float
Uncorrected p-value.
Notes
-----
Adapted from the CircStats MATLAB toolbox [1]_.
The range of ``x`` and ``y`` must be either
:math:`[0, 2\\pi]` or :math:`[-\\pi, \\pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
Please note that NaN are automatically removed.
If the ``correction_uniform`` is True, an alternative equation from
[2]_ (p. 177) is used. If the marginal distribution of ``x`` or ``y`` is
uniform, the mean is not well defined, which leads to wrong estimates
of the circular correlation. The alternative equation corrects for this
by choosing the means in a way that maximizes the positive or negative
correlation.
References
----------
.. [1] Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular
Statistics. Journal of Statistical Software, Articles, 31(10), 1–21.
https://doi.org/10.18637/jss.v031.i10
.. [2] Jammalamadaka, S. R., & Sengupta, A. (2001). Topics in circular
statistics (Vol. 5). world scientific.
Examples
--------
Compute the r and p-value of two circular variables
>>> from pingouin import circ_corrcc
>>> x = [0.785, 1.570, 3.141, 3.839, 5.934]
>>> y = [0.593, 1.291, 2.879, 3.892, 6.108]
>>> r, pval = circ_corrcc(x, y)
>>> print(round(r, 3), round(pval, 4))
0.942 0.0658
With the correction for uniform marginals
>>> r, pval = circ_corrcc(x, y, correction_uniform=True)
>>> print(round(r, 3), round(pval, 4))
0.547 0.2859
"""
x = np.asarray(x)
y = np.asarray(y)
assert x.size == y.size, "x and y must have the same length."
# Remove NA
x, y = remove_na(x, y, paired=True)
n = x.size
# Compute correlation coefficient
x_sin = np.sin(x - circ_mean(x))
y_sin = np.sin(y - circ_mean(y))
if not correction_uniform:
# Similar to np.corrcoef(x_sin, y_sin)[0][1]
r = np.sum(x_sin * y_sin) / np.sqrt(np.sum(x_sin**2) * np.sum(y_sin**2))
else:
r_minus = np.abs(np.sum(np.exp((x - y) * 1j)))
r_plus = np.abs(np.sum(np.exp((x + y) * 1j)))
denom = 2 * np.sqrt(np.sum(x_sin**2) * np.sum(y_sin**2))
r = (r_minus - r_plus) / denom
# Compute T- and p-values
tval = (
np.sqrt((n * (x_sin**2).mean() * (y_sin**2).mean()) / np.mean(x_sin**2 * y_sin**2))
* r
)
# Approximately distributed as a standard normal
pval = 2 * norm.sf(abs(tval))
return r, pval
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|
31,984 | pingouin.circular | circ_corrcl | Correlation coefficient between one circular and one linear variable
random variables.
Parameters
----------
x : 1-D array_like
First circular variable (expressed in radians).
The range of ``x`` must be either :math:`[0, 2\pi]` or
:math:`[-\pi, \pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
y : 1-D array_like
Second circular variable (linear)
Returns
-------
r : float
Correlation coefficient
pval : float
Uncorrected p-value
Notes
-----
Please note that NaN are automatically removed from datasets.
Examples
--------
Compute the r and p-value between one circular and one linear variables.
>>> from pingouin import circ_corrcl
>>> x = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> y = [1.593, 1.291, -0.248, -2.892, 0.102]
>>> r, pval = circ_corrcl(x, y)
>>> print(round(r, 3), round(pval, 3))
0.109 0.971
| def circ_corrcl(x, y):
"""Correlation coefficient between one circular and one linear variable
random variables.
Parameters
----------
x : 1-D array_like
First circular variable (expressed in radians).
The range of ``x`` must be either :math:`[0, 2\\pi]` or
:math:`[-\\pi, \\pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
y : 1-D array_like
Second circular variable (linear)
Returns
-------
r : float
Correlation coefficient
pval : float
Uncorrected p-value
Notes
-----
Please note that NaN are automatically removed from datasets.
Examples
--------
Compute the r and p-value between one circular and one linear variables.
>>> from pingouin import circ_corrcl
>>> x = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> y = [1.593, 1.291, -0.248, -2.892, 0.102]
>>> r, pval = circ_corrcl(x, y)
>>> print(round(r, 3), round(pval, 3))
0.109 0.971
"""
from scipy.stats import pearsonr, chi2
x = np.asarray(x)
y = np.asarray(y)
assert x.size == y.size, "x and y must have the same length."
# Remove NA
x, y = remove_na(x, y, paired=True)
n = x.size
# Compute correlation coefficent for sin and cos independently
rxs = pearsonr(y, np.sin(x))[0]
rxc = pearsonr(y, np.cos(x))[0]
rcs = pearsonr(np.sin(x), np.cos(x))[0]
# Compute angular-linear correlation (equ. 27.47)
r = np.sqrt((rxc**2 + rxs**2 - 2 * rxc * rxs * rcs) / (1 - rcs**2))
# Compute p-value
pval = chi2.sf(n * r**2, 2)
return r, pval
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|
31,985 | pingouin.circular | circ_mean | Mean direction for (binned) circular data.
Parameters
----------
angles : array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\pi]` or :math:`[-\pi, \pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
axis : int or None
Compute along this dimension. Default is the first axis (0).
Returns
-------
mu : float
Circular mean, in radians.
See also
--------
scipy.stats.circmean, scipy.stats.circstd, pingouin.circ_r
Notes
-----
From Wikipedia:
*In mathematics, a mean of circular quantities is a mean which is sometimes
better-suited for quantities like angles, daytimes, and fractional parts
of real numbers. This is necessary since most of the usual means may not be
appropriate on circular quantities. For example, the arithmetic mean of 0°
and 360° is 180°, which is misleading because for most purposes 360° is
the same thing as 0°.
As another example, the "average time" between 11 PM and 1 AM is either
midnight or noon, depending on whether the two times are part of a single
night or part of a single calendar day.*
The circular mean of a set of angles :math:`\alpha` is defined by:
.. math::
\bar{\alpha} = \text{angle} \left ( \sum_{j=1}^n \exp(i \cdot
\alpha_j) \right )
For binned angles with weights :math:`w`, this becomes:
.. math::
\bar{\alpha} = \text{angle} \left ( \sum_{j=1}^n w \cdot
\exp(i \cdot \alpha_j) \right )
Missing values in ``angles`` are omitted from the calculations.
References
----------
* https://en.wikipedia.org/wiki/Mean_of_circular_quantities
* Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular
Statistics. Journal of Statistical Software, Articles, 31(10),
1–21. https://doi.org/10.18637/jss.v031.i10
Examples
--------
1. Circular mean of a 1-D array of angles, in radians
>>> import pingouin as pg
>>> angles = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> round(pg.circ_mean(angles), 4)
1.013
Compare with SciPy:
>>> from scipy.stats import circmean
>>> import numpy as np
>>> round(circmean(angles, low=0, high=2*np.pi), 4)
1.013
2. Using a 2-D array of angles in degrees
>>> np.random.seed(123)
>>> deg = np.random.randint(low=0, high=360, size=(3, 5))
>>> deg
array([[322, 98, 230, 17, 83],
[106, 123, 57, 214, 225],
[ 96, 113, 126, 47, 73]])
We first need to convert from degrees to radians:
>>> rad = np.round(pg.convert_angles(deg, low=0, high=360), 4)
>>> rad
array([[-0.6632, 1.7104, -2.2689, 0.2967, 1.4486],
[ 1.85 , 2.1468, 0.9948, -2.5482, -2.3562],
[ 1.6755, 1.9722, 2.1991, 0.8203, 1.2741]])
>>> pg.circ_mean(rad) # On the first axis (default)
array([1.27532162, 1.94336576, 2.23195927, 0.52110503, 1.80240563])
>>> pg.circ_mean(rad, axis=-1) # On the last axis (default)
array([0.68920819, 2.49334852, 1.5954149 ])
>>> round(pg.circ_mean(rad, axis=None), 4) # Across the entire array
1.6954
Missing values are omitted from the calculations:
>>> rad[0, 0] = np.nan
>>> pg.circ_mean(rad)
array([1.76275 , 1.94336576, 2.23195927, 0.52110503, 1.80240563])
3. Using binned angles
>>> np.random.seed(123)
>>> nbins = 18 # Number of bins to divide the unit circle
>>> angles_bins = np.linspace(0, 2 * np.pi, nbins)
>>> # w represents the number of incidences per bins, or "weights".
>>> w = np.random.randint(low=0, high=5, size=angles_bins.size)
>>> round(pg.circ_mean(angles_bins, w), 4)
0.606
| def circ_mean(angles, w=None, axis=0):
"""Mean direction for (binned) circular data.
Parameters
----------
angles : array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\\pi]` or :math:`[-\\pi, \\pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
axis : int or None
Compute along this dimension. Default is the first axis (0).
Returns
-------
mu : float
Circular mean, in radians.
See also
--------
scipy.stats.circmean, scipy.stats.circstd, pingouin.circ_r
Notes
-----
From Wikipedia:
*In mathematics, a mean of circular quantities is a mean which is sometimes
better-suited for quantities like angles, daytimes, and fractional parts
of real numbers. This is necessary since most of the usual means may not be
appropriate on circular quantities. For example, the arithmetic mean of 0°
and 360° is 180°, which is misleading because for most purposes 360° is
the same thing as 0°.
As another example, the "average time" between 11 PM and 1 AM is either
midnight or noon, depending on whether the two times are part of a single
night or part of a single calendar day.*
The circular mean of a set of angles :math:`\\alpha` is defined by:
.. math::
\\bar{\\alpha} = \\text{angle} \\left ( \\sum_{j=1}^n \\exp(i \\cdot
\\alpha_j) \\right )
For binned angles with weights :math:`w`, this becomes:
.. math::
\\bar{\\alpha} = \\text{angle} \\left ( \\sum_{j=1}^n w \\cdot
\\exp(i \\cdot \\alpha_j) \\right )
Missing values in ``angles`` are omitted from the calculations.
References
----------
* https://en.wikipedia.org/wiki/Mean_of_circular_quantities
* Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular
Statistics. Journal of Statistical Software, Articles, 31(10),
1–21. https://doi.org/10.18637/jss.v031.i10
Examples
--------
1. Circular mean of a 1-D array of angles, in radians
>>> import pingouin as pg
>>> angles = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> round(pg.circ_mean(angles), 4)
1.013
Compare with SciPy:
>>> from scipy.stats import circmean
>>> import numpy as np
>>> round(circmean(angles, low=0, high=2*np.pi), 4)
1.013
2. Using a 2-D array of angles in degrees
>>> np.random.seed(123)
>>> deg = np.random.randint(low=0, high=360, size=(3, 5))
>>> deg
array([[322, 98, 230, 17, 83],
[106, 123, 57, 214, 225],
[ 96, 113, 126, 47, 73]])
We first need to convert from degrees to radians:
>>> rad = np.round(pg.convert_angles(deg, low=0, high=360), 4)
>>> rad
array([[-0.6632, 1.7104, -2.2689, 0.2967, 1.4486],
[ 1.85 , 2.1468, 0.9948, -2.5482, -2.3562],
[ 1.6755, 1.9722, 2.1991, 0.8203, 1.2741]])
>>> pg.circ_mean(rad) # On the first axis (default)
array([1.27532162, 1.94336576, 2.23195927, 0.52110503, 1.80240563])
>>> pg.circ_mean(rad, axis=-1) # On the last axis (default)
array([0.68920819, 2.49334852, 1.5954149 ])
>>> round(pg.circ_mean(rad, axis=None), 4) # Across the entire array
1.6954
Missing values are omitted from the calculations:
>>> rad[0, 0] = np.nan
>>> pg.circ_mean(rad)
array([1.76275 , 1.94336576, 2.23195927, 0.52110503, 1.80240563])
3. Using binned angles
>>> np.random.seed(123)
>>> nbins = 18 # Number of bins to divide the unit circle
>>> angles_bins = np.linspace(0, 2 * np.pi, nbins)
>>> # w represents the number of incidences per bins, or "weights".
>>> w = np.random.randint(low=0, high=5, size=angles_bins.size)
>>> round(pg.circ_mean(angles_bins, w), 4)
0.606
"""
angles = np.asarray(angles)
_checkangles(angles) # Check that angles is in radians
w = np.asarray(w) if w is not None else np.ones(angles.shape)
assert angles.shape == w.shape, "Input dimensions do not match"
return np.angle(np.nansum(np.multiply(w, np.exp(1j * angles)), axis=axis))
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|
31,986 | pingouin.circular | circ_r | Mean resultant vector length for circular data.
Parameters
----------
angles : array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\pi]` or :math:`[-\pi, \pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
d : float
Spacing (in radians) of bin centers for binned data. If supplied,
a correction factor is used to correct for bias in the estimation
of r.
axis : int or None
Compute along this dimension. Default is the first axis (0).
Returns
-------
r : float
Circular mean vector length.
See also
--------
pingouin.circ_mean
Notes
-----
The length of the mean resultant vector is a crucial quantity for the
measurement of circular spread or hypothesis testing in directional
statistics. The closer it is to one, the more concentrated the data
sample is around the mean direction (Berens 2009).
The circular vector length of a set of angles :math:`\alpha` is defined
by:
.. math::
\bar{\alpha} = \frac{1}{N}\left \| \sum_{j=1}^n
\exp(i \cdot \alpha_j) \right \|
Missing values in ``angles`` are omitted from the calculations.
References
----------
* https://en.wikipedia.org/wiki/Mean_of_circular_quantities
* Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular
Statistics. Journal of Statistical Software, Articles, 31(10),
1–21. https://doi.org/10.18637/jss.v031.i10
Examples
--------
1. Mean resultant vector length of a 1-D array of angles, in radians
>>> import pingouin as pg
>>> angles = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> r = pg.circ_r(angles)
>>> round(r, 4)
0.4972
Note that there is a close relationship between the vector length and the
circular standard deviation, i.e. :math:`\sigma = \sqrt{-2 \ln R}`:
>>> import numpy as np
>>> round(np.sqrt(-2 * np.log(r)), 4)
1.1821
which gives similar result as SciPy built-in function:
>>> from scipy.stats import circstd
>>> round(circstd(angles), 4)
1.1821
Sanity check: if all angles are the same, the vector length should be one:
>>> angles = [3.14, 3.14, 3.14, 3.14]
>>> round(pg.circ_r(angles), 4)
1.0
2. Using a 2-D array of angles in degrees
>>> np.random.seed(123)
>>> deg = np.random.randint(low=0, high=360, size=(3, 5))
>>> deg
array([[322, 98, 230, 17, 83],
[106, 123, 57, 214, 225],
[ 96, 113, 126, 47, 73]])
We first need to convert from degrees to radians:
>>> rad = np.round(pg.convert_angles(deg, low=0, high=360), 4)
>>> rad
array([[-0.6632, 1.7104, -2.2689, 0.2967, 1.4486],
[ 1.85 , 2.1468, 0.9948, -2.5482, -2.3562],
[ 1.6755, 1.9722, 2.1991, 0.8203, 1.2741]])
>>> pg.circ_r(rad) # On the first axis (default)
array([0.46695499, 0.98398294, 0.3723287 , 0.31103746, 0.42527149])
>>> pg.circ_r(rad, axis=-1) # On the last axis (default)
array([0.28099998, 0.45456096, 0.88261161])
>>> round(pg.circ_r(rad, axis=None), 4) # Across the entire array
0.4486
Missing values are omitted from the calculations:
>>> rad[0, 0] = np.nan
>>> pg.circ_r(rad)
array([0.99619613, 0.98398294, 0.3723287 , 0.31103746, 0.42527149])
3. Using binned angles
>>> np.random.seed(123)
>>> nbins = 18 # Number of bins to divide the unit circle
>>> angles_bins = np.linspace(0, 2 * np.pi, nbins)
>>> # w represents the number of incidences per bins, or "weights".
>>> w = np.random.randint(low=0, high=5, size=angles_bins.size)
>>> round(pg.circ_r(angles_bins, w), 4)
0.3642
| def circ_r(angles, w=None, d=None, axis=0):
"""Mean resultant vector length for circular data.
Parameters
----------
angles : array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\\pi]` or :math:`[-\\pi, \\pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
d : float
Spacing (in radians) of bin centers for binned data. If supplied,
a correction factor is used to correct for bias in the estimation
of r.
axis : int or None
Compute along this dimension. Default is the first axis (0).
Returns
-------
r : float
Circular mean vector length.
See also
--------
pingouin.circ_mean
Notes
-----
The length of the mean resultant vector is a crucial quantity for the
measurement of circular spread or hypothesis testing in directional
statistics. The closer it is to one, the more concentrated the data
sample is around the mean direction (Berens 2009).
The circular vector length of a set of angles :math:`\\alpha` is defined
by:
.. math::
\\bar{\\alpha} = \\frac{1}{N}\\left \\| \\sum_{j=1}^n
\\exp(i \\cdot \\alpha_j) \\right \\|
Missing values in ``angles`` are omitted from the calculations.
References
----------
* https://en.wikipedia.org/wiki/Mean_of_circular_quantities
* Berens, P. (2009). CircStat: A MATLAB Toolbox for Circular
Statistics. Journal of Statistical Software, Articles, 31(10),
1–21. https://doi.org/10.18637/jss.v031.i10
Examples
--------
1. Mean resultant vector length of a 1-D array of angles, in radians
>>> import pingouin as pg
>>> angles = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> r = pg.circ_r(angles)
>>> round(r, 4)
0.4972
Note that there is a close relationship between the vector length and the
circular standard deviation, i.e. :math:`\\sigma = \\sqrt{-2 \\ln R}`:
>>> import numpy as np
>>> round(np.sqrt(-2 * np.log(r)), 4)
1.1821
which gives similar result as SciPy built-in function:
>>> from scipy.stats import circstd
>>> round(circstd(angles), 4)
1.1821
Sanity check: if all angles are the same, the vector length should be one:
>>> angles = [3.14, 3.14, 3.14, 3.14]
>>> round(pg.circ_r(angles), 4)
1.0
2. Using a 2-D array of angles in degrees
>>> np.random.seed(123)
>>> deg = np.random.randint(low=0, high=360, size=(3, 5))
>>> deg
array([[322, 98, 230, 17, 83],
[106, 123, 57, 214, 225],
[ 96, 113, 126, 47, 73]])
We first need to convert from degrees to radians:
>>> rad = np.round(pg.convert_angles(deg, low=0, high=360), 4)
>>> rad
array([[-0.6632, 1.7104, -2.2689, 0.2967, 1.4486],
[ 1.85 , 2.1468, 0.9948, -2.5482, -2.3562],
[ 1.6755, 1.9722, 2.1991, 0.8203, 1.2741]])
>>> pg.circ_r(rad) # On the first axis (default)
array([0.46695499, 0.98398294, 0.3723287 , 0.31103746, 0.42527149])
>>> pg.circ_r(rad, axis=-1) # On the last axis (default)
array([0.28099998, 0.45456096, 0.88261161])
>>> round(pg.circ_r(rad, axis=None), 4) # Across the entire array
0.4486
Missing values are omitted from the calculations:
>>> rad[0, 0] = np.nan
>>> pg.circ_r(rad)
array([0.99619613, 0.98398294, 0.3723287 , 0.31103746, 0.42527149])
3. Using binned angles
>>> np.random.seed(123)
>>> nbins = 18 # Number of bins to divide the unit circle
>>> angles_bins = np.linspace(0, 2 * np.pi, nbins)
>>> # w represents the number of incidences per bins, or "weights".
>>> w = np.random.randint(low=0, high=5, size=angles_bins.size)
>>> round(pg.circ_r(angles_bins, w), 4)
0.3642
"""
angles = np.asarray(angles)
_checkangles(angles) # Check that angles is in radians
w = np.asarray(w) if w is not None else np.ones(angles.shape)
assert angles.shape == w.shape, "Input dimensions do not match."
# Add np.nan in weight vector (otherwise nansum(w) is wrong)
w = w.astype(float)
w[np.isnan(angles)] = np.nan
# Compute weighted sum of cos and sin of angles:
r = np.nansum(np.multiply(w, np.exp(1j * angles)), axis=axis)
# Calculate vector length:
r = np.abs(r) / np.nansum(w, axis=axis)
# For data with known spacing, apply correction factor
if d is not None:
c = d / 2 / np.sin(d / 2)
r = c * r
return r
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|
31,987 | pingouin.circular | circ_rayleigh | Rayleigh test for non-uniformity of circular data.
Parameters
----------
angles : 1-D array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\pi]` or :math:`[-\pi, \pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
d : float
Spacing (in radians) of bin centers for binned data. If supplied,
a correction factor is used to correct for bias in the estimation
of r.
Returns
-------
z : float
Z-statistic
pval : float
P-value
Notes
-----
The Rayleigh test asks how large the resultant vector length R must be
to indicate a non-uniform distribution (Fisher 1995).
H0: the population is uniformly distributed around the circle
HA: the populatoin is not distributed uniformly around the circle
The assumptions for the Rayleigh test are that (1) the distribution has
only one mode and (2) the data is sampled from a von Mises distribution.
Examples
--------
1. Simple Rayleigh test for non-uniformity of circular data.
>>> from pingouin import circ_rayleigh
>>> x = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> z, pval = circ_rayleigh(x)
>>> print(round(z, 3), round(pval, 6))
1.236 0.304844
2. Specifying w and d
>>> z, pval = circ_rayleigh(x, w=[.1, .2, .3, .4, .5], d=0.2)
>>> print(round(z, 3), round(pval, 6))
0.278 0.806997
| def circ_rayleigh(angles, w=None, d=None):
"""Rayleigh test for non-uniformity of circular data.
Parameters
----------
angles : 1-D array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\\pi]` or :math:`[-\\pi, \\pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
d : float
Spacing (in radians) of bin centers for binned data. If supplied,
a correction factor is used to correct for bias in the estimation
of r.
Returns
-------
z : float
Z-statistic
pval : float
P-value
Notes
-----
The Rayleigh test asks how large the resultant vector length R must be
to indicate a non-uniform distribution (Fisher 1995).
H0: the population is uniformly distributed around the circle
HA: the populatoin is not distributed uniformly around the circle
The assumptions for the Rayleigh test are that (1) the distribution has
only one mode and (2) the data is sampled from a von Mises distribution.
Examples
--------
1. Simple Rayleigh test for non-uniformity of circular data.
>>> from pingouin import circ_rayleigh
>>> x = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> z, pval = circ_rayleigh(x)
>>> print(round(z, 3), round(pval, 6))
1.236 0.304844
2. Specifying w and d
>>> z, pval = circ_rayleigh(x, w=[.1, .2, .3, .4, .5], d=0.2)
>>> print(round(z, 3), round(pval, 6))
0.278 0.806997
"""
angles = np.asarray(angles)
_checkangles(angles) # Check that angles is in radians
if w is None:
r = circ_r(angles)
n = len(angles)
else:
assert len(angles) == len(w), "Input dimensions do not match"
r = circ_r(angles, w, d)
n = np.sum(w)
# Compute Rayleigh's statistic
R = n * r
z = (R**2) / n
# Compute p value using approxation in Zar (1999), p. 617
pval = np.exp(np.sqrt(1 + 4 * n + 4 * (n**2 - R**2)) - (1 + 2 * n))
return z, pval
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|
31,988 | pingouin.circular | circ_vtest | V test for non-uniformity of circular data with a specified
mean direction.
Parameters
----------
angles : 1-D array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\pi]` or :math:`[-\pi, \pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
dir : float
Suspected mean direction (angle in radians).
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
d : float
Spacing (in radians) of bin centers for binned data. If supplied,
a correction factor is used to correct for bias in the estimation
of r.
Returns
-------
V : float
V-statistic
pval : float
P-value
Notes
-----
H0: the population is uniformly distributed around the circle.
HA: the population is not distributed uniformly around the circle but
has a mean of dir.
Note: Not rejecting H0 may mean that the population is uniformly
distributed around the circle OR that it has a mode but that this mode
is not centered at dir.
The V test has more power than the Rayleigh test and is preferred if
there is reason to believe in a specific mean direction.
Adapted from the Matlab Circular Statistics Toolbox.
Examples
--------
1. V-test for non-uniformity of circular data.
>>> from pingouin import circ_vtest
>>> x = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> v, pval = circ_vtest(x, dir=1)
>>> print(round(v, 3), pval)
2.486 0.05794648732225438
2. Specifying w and d
>>> v, pval = circ_vtest(x, dir=0.5, w=[.1, .2, .3, .4, .5], d=0.2)
>>> print(round(v, 3), round(pval, 5))
0.637 0.23086
| def circ_vtest(angles, dir=0.0, w=None, d=None):
"""V test for non-uniformity of circular data with a specified
mean direction.
Parameters
----------
angles : 1-D array_like
Samples of angles in radians. The range of ``angles`` must be either
:math:`[0, 2\\pi]` or :math:`[-\\pi, \\pi]`. If ``angles`` is not
expressed in radians (e.g. degrees or 24-hours), please use the
:py:func:`pingouin.convert_angles` function prior to using the present
function.
dir : float
Suspected mean direction (angle in radians).
w : array_like
Number of incidences per bins (i.e. "weights"), in case of binned angle
data.
d : float
Spacing (in radians) of bin centers for binned data. If supplied,
a correction factor is used to correct for bias in the estimation
of r.
Returns
-------
V : float
V-statistic
pval : float
P-value
Notes
-----
H0: the population is uniformly distributed around the circle.
HA: the population is not distributed uniformly around the circle but
has a mean of dir.
Note: Not rejecting H0 may mean that the population is uniformly
distributed around the circle OR that it has a mode but that this mode
is not centered at dir.
The V test has more power than the Rayleigh test and is preferred if
there is reason to believe in a specific mean direction.
Adapted from the Matlab Circular Statistics Toolbox.
Examples
--------
1. V-test for non-uniformity of circular data.
>>> from pingouin import circ_vtest
>>> x = [0.785, 1.570, 3.141, 0.839, 5.934]
>>> v, pval = circ_vtest(x, dir=1)
>>> print(round(v, 3), pval)
2.486 0.05794648732225438
2. Specifying w and d
>>> v, pval = circ_vtest(x, dir=0.5, w=[.1, .2, .3, .4, .5], d=0.2)
>>> print(round(v, 3), round(pval, 5))
0.637 0.23086
"""
angles = np.asarray(angles)
if w is None:
r = circ_r(angles)
mu = circ_mean(angles)
n = len(angles)
else:
assert len(angles) == len(w), "Input dimensions do not match"
r = circ_r(angles, w, d)
mu = circ_mean(angles, w)
n = np.sum(w)
# Compute Rayleigh and V statistics
R = n * r
v = R * np.cos(mu - dir)
# Compute p value
u = v * np.sqrt(2 / n)
pval = 1 - norm.cdf(u)
return v, pval
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|
31,990 | pingouin.nonparametric | cochran | Cochran Q test. A special case of the Friedman test when the dependent
variable is binary.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Both wide and long-format dataframe are supported for this test.
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-subject factor (only required if ``data`` is in
long format). Two or more within-factor are not currently supported.
subject : string
Name of column containing the subject/rater identifier (only required if ``data`` is in
long format).
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'Q'``: The Cochran Q statistic
* ``'p-unc'``: Uncorrected p-value
* ``'dof'``: degrees of freedom
Notes
-----
The Cochran Q test [1]_ is a non-parametric test for ANOVA with repeated
measures where the dependent variable is binary.
The Q statistics is defined as:
.. math:: Q = \frac{(r-1)(r\sum_j^rx_j^2-N^2)}{rN-\sum_i^nx_i^2}
where :math:`N` is the total sum of all observations, :math:`j=1,...,r`
where :math:`r` is the number of repeated measures, :math:`i=1,...,n` where
:math:`n` is the number of observations per condition.
The p-value is then approximated using a chi-square distribution with
:math:`r-1` degrees of freedom:
.. math:: Q \sim \chi^2(r-1)
Data are expected to be in 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.
References
----------
.. [1] Cochran, W.G., 1950. The comparison of percentages in matched
samples. Biometrika 37, 256–266.
https://doi.org/10.1093/biomet/37.3-4.256
Examples
--------
Compute the Cochran Q test for repeated measurements.
>>> from pingouin import cochran, read_dataset
>>> df = read_dataset('cochran')
>>> cochran(data=df, dv='Energetic', within='Time', subject='Subject')
Source dof Q p-unc
cochran Time 2 6.705882 0.034981
Same but using a wide-format dataframe
>>> df_wide = df.pivot_table(index="Subject", columns="Time", values="Energetic")
>>> cochran(df_wide)
Source dof Q p-unc
cochran Within 2 6.705882 0.034981
| def cochran(data=None, dv=None, within=None, subject=None):
"""Cochran Q test. A special case of the Friedman test when the dependent
variable is binary.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Both wide and long-format dataframe are supported for this test.
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-subject factor (only required if ``data`` is in
long format). Two or more within-factor are not currently supported.
subject : string
Name of column containing the subject/rater identifier (only required if ``data`` is in
long format).
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'Q'``: The Cochran Q statistic
* ``'p-unc'``: Uncorrected p-value
* ``'dof'``: degrees of freedom
Notes
-----
The Cochran Q test [1]_ is a non-parametric test for ANOVA with repeated
measures where the dependent variable is binary.
The Q statistics is defined as:
.. math:: Q = \\frac{(r-1)(r\\sum_j^rx_j^2-N^2)}{rN-\\sum_i^nx_i^2}
where :math:`N` is the total sum of all observations, :math:`j=1,...,r`
where :math:`r` is the number of repeated measures, :math:`i=1,...,n` where
:math:`n` is the number of observations per condition.
The p-value is then approximated using a chi-square distribution with
:math:`r-1` degrees of freedom:
.. math:: Q \\sim \\chi^2(r-1)
Data are expected to be in 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.
References
----------
.. [1] Cochran, W.G., 1950. The comparison of percentages in matched
samples. Biometrika 37, 256–266.
https://doi.org/10.1093/biomet/37.3-4.256
Examples
--------
Compute the Cochran Q test for repeated measurements.
>>> from pingouin import cochran, read_dataset
>>> df = read_dataset('cochran')
>>> cochran(data=df, dv='Energetic', within='Time', subject='Subject')
Source dof Q p-unc
cochran Time 2 6.705882 0.034981
Same but using a wide-format dataframe
>>> df_wide = df.pivot_table(index="Subject", columns="Time", values="Energetic")
>>> cochran(df_wide)
Source dof Q p-unc
cochran Within 2 6.705882 0.034981
"""
# 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().dropna() # Listwise deletion of missing values
assert data.shape[0] > 2, "Data must have at least 3 non-missing rows."
assert data.shape[1] > 1, "Data must contain at least two columns."
data["Subj"] = np.arange(data.shape[0])
data = data.melt(id_vars="Subj", var_name="Within", value_name="DV")
subject, within, dv = "Subj", "Within", "DV"
# Check data
data = _check_dataframe(dv=dv, within=within, data=data, subject=subject, effects="within")
assert not data[within].isnull().any(), "Cannot have missing values in `within`."
assert not data[subject].isnull().any(), "Cannot have missing values in `subject`."
# 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()
# Groupby and extract size
grp = data.groupby(within, observed=True)[dv]
grp_s = data.groupby(subject, observed=True)[dv]
k = data[within].nunique()
dof = k - 1
# n = grp.count().unique()[0]
# Q statistic and p-value
q = (dof * (k * np.sum(grp.sum() ** 2) - grp.sum().sum() ** 2)) / (
k * grp.sum().sum() - np.sum(grp_s.sum() ** 2)
)
p_unc = scipy.stats.chi2.sf(q, dof)
# Create output dataframe
stats = pd.DataFrame({"Source": within, "dof": dof, "Q": q, "p-unc": p_unc}, index=["cochran"])
return _postprocess_dataframe(stats)
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|
31,991 | pingouin.effsize | compute_bootci | Bootstrapped confidence intervals of univariate and bivariate functions.
Parameters
----------
x : 1D-array or list
First sample. Required for both bivariate and univariate functions.
y : 1D-array, list, or None
Second sample. Required only for bivariate functions.
func : str or custom function
Function to compute the bootstrapped statistic. Accepted string values are:
* ``'pearson'``: Pearson correlation (bivariate, paired x and y)
* ``'spearman'``: Spearman correlation (bivariate, paired x and y)
* ``'cohen'``: Cohen d effect size (bivariate, paired or unpaired x and y)
* ``'hedges'``: Hedges g effect size (bivariate, paired or unpaired x and y)
* ``'mean'``: Mean (univariate = only x)
* ``'std'``: Standard deviation (univariate)
* ``'var'``: Variance (univariate)
method : str
Method to compute the confidence intervals (see Notes):
* ``'cper'``: Bias-corrected percentile method (default)
* ``'norm'``: Normal approximation with bootstrapped bias and standard error
* ``'per'``: Simple percentile
paired : boolean
Indicates whether x and y are paired or not. For example, for correlation functions or
paired T-test, x and y are assumed to be paired. Pingouin will resample the pairs
(x_i, y_i) when paired=True, and resample x and y separately when paired=False.
If paired=True, x and y must have the same number of elements.
confidence : float
Confidence level (0.95 = 95%)
n_boot : int
Number of bootstrap iterations. The higher, the better, the slower.
decimals : int
Number of rounded decimals.
seed : int or None
Random seed for generating bootstrap samples.
return_dist : boolean
If True, return the confidence intervals and the bootstrapped distribution (e.g. for
plotting purposes).
Returns
-------
ci : array
Bootstrapped confidence intervals.
Notes
-----
Results have been tested against the
`bootci <https://www.mathworks.com/help/stats/bootci.html>`_ Matlab function.
Since version 1.7, SciPy also includes a built-in bootstrap function
:py:func:`scipy.stats.bootstrap`. The SciPy implementation has two advantages over Pingouin: it
is faster when using ``vectorized=True``, and it supports the bias-corrected and accelerated
(BCa) confidence intervals for univariate functions. However, unlike Pingouin, it does not
return the bootstrap distribution.
The percentile bootstrap method (``per``) is defined as the
:math:`100 \times \frac{\alpha}{2}` and :math:`100 \times \frac{1 - \alpha}{2}`
percentiles of the distribution of :math:`\theta` estimates obtained from resampling, where
:math:`\alpha` is the level of significance (1 - confidence, default = 0.05 for 95% CIs).
The bias-corrected percentile method (``cper``) corrects for bias of the bootstrap
distribution. This method is different from the BCa method — the default in Matlab and SciPy —
which corrects for both bias and skewness of the bootstrap distribution using jackknife
resampling.
The normal approximation method (``norm``) calculates the confidence intervals with the
standard normal distribution using bootstrapped bias and standard error.
References
----------
* DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical science,
189-212.
* Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application (Vol. 1).
Cambridge university press.
* Jung, Lee, Gupta, & Cho (2019). Comparison of bootstrap confidence interval methods for
GSCA using a Monte Carlo simulation. Frontiers in psychology, 10, 2215.
Examples
--------
1. Bootstrapped 95% confidence interval of a Pearson correlation
>>> import pingouin as pg
>>> import numpy as np
>>> rng = np.random.default_rng(42)
>>> x = rng.normal(loc=4, scale=2, size=100)
>>> y = rng.normal(loc=3, scale=1, size=100)
>>> stat = np.corrcoef(x, y)[0][1]
>>> ci = pg.compute_bootci(x, y, func='pearson', paired=True, seed=42, decimals=4)
>>> print(round(stat, 4), ci)
0.0945 [-0.098 0.2738]
Let's compare to SciPy's built-in bootstrap function
>>> from scipy.stats import bootstrap
>>> bt_scipy = bootstrap(
... data=(x, y), statistic=lambda x, y: np.corrcoef(x, y)[0][1],
... method="basic", vectorized=False, n_resamples=2000, paired=True, random_state=42)
>>> np.round(bt_scipy.confidence_interval, 4)
array([-0.0952, 0.2883])
2. Bootstrapped 95% confidence interval of a Cohen d
>>> stat = pg.compute_effsize(x, y, eftype='cohen')
>>> ci = pg.compute_bootci(x, y, func='cohen', seed=42, decimals=3)
>>> print(round(stat, 4), ci)
0.7009 [0.403 1.009]
3. Bootstrapped confidence interval of a standard deviation (univariate)
>>> import numpy as np
>>> stat = np.std(x, ddof=1)
>>> ci = pg.compute_bootci(x, func='std', seed=123)
>>> print(round(stat, 4), ci)
1.5534 [1.38 1.8 ]
Compare to SciPy's built-in bootstrap function, which returns the bias-corrected and
accelerated CIs (see Notes).
>>> def std(x, axis):
... return np.std(x, ddof=1, axis=axis)
>>> bt_scipy = bootstrap(data=(x, ), statistic=std, n_resamples=2000, random_state=123)
>>> np.round(bt_scipy.confidence_interval, 2)
array([1.39, 1.81])
Changing the confidence intervals type in Pingouin
>>> pg.compute_bootci(x, func='std', seed=123, method="norm")
array([1.37, 1.76])
>>> pg.compute_bootci(x, func='std', seed=123, method="percentile")
array([1.35, 1.75])
4. Bootstrapped confidence interval using a custom univariate function
>>> from scipy.stats import skew
>>> round(skew(x), 4), pg.compute_bootci(x, func=skew, n_boot=10000, seed=123)
(-0.137, array([-0.55, 0.32]))
5. Bootstrapped confidence interval using a custom bivariate function. Here, x and y are not
paired and can therefore have different sizes.
>>> def mean_diff(x, y):
... return np.mean(x) - np.mean(y)
>>> y2 = rng.normal(loc=3, scale=1, size=200) # y2 has 200 samples, x has 100
>>> ci = pg.compute_bootci(x, y2, func=mean_diff, n_boot=10000, seed=123)
>>> print(round(mean_diff(x, y2), 2), ci)
0.88 [0.54 1.21]
We can also get the bootstrapped distribution
>>> ci, bt = pg.compute_bootci(x, y2, func=mean_diff, n_boot=10000, return_dist=True, seed=9)
>>> print(f"The bootstrap distribution has {bt.size} samples. The mean and standard "
... f"{bt.mean():.4f} ± {bt.std():.4f}")
The bootstrap distribution has 10000 samples. The mean and standard 0.8807 ± 0.1704
| def compute_bootci(
x,
y=None,
func=None,
method="cper",
paired=False,
confidence=0.95,
n_boot=2000,
decimals=2,
seed=None,
return_dist=False,
):
"""Bootstrapped confidence intervals of univariate and bivariate functions.
Parameters
----------
x : 1D-array or list
First sample. Required for both bivariate and univariate functions.
y : 1D-array, list, or None
Second sample. Required only for bivariate functions.
func : str or custom function
Function to compute the bootstrapped statistic. Accepted string values are:
* ``'pearson'``: Pearson correlation (bivariate, paired x and y)
* ``'spearman'``: Spearman correlation (bivariate, paired x and y)
* ``'cohen'``: Cohen d effect size (bivariate, paired or unpaired x and y)
* ``'hedges'``: Hedges g effect size (bivariate, paired or unpaired x and y)
* ``'mean'``: Mean (univariate = only x)
* ``'std'``: Standard deviation (univariate)
* ``'var'``: Variance (univariate)
method : str
Method to compute the confidence intervals (see Notes):
* ``'cper'``: Bias-corrected percentile method (default)
* ``'norm'``: Normal approximation with bootstrapped bias and standard error
* ``'per'``: Simple percentile
paired : boolean
Indicates whether x and y are paired or not. For example, for correlation functions or
paired T-test, x and y are assumed to be paired. Pingouin will resample the pairs
(x_i, y_i) when paired=True, and resample x and y separately when paired=False.
If paired=True, x and y must have the same number of elements.
confidence : float
Confidence level (0.95 = 95%)
n_boot : int
Number of bootstrap iterations. The higher, the better, the slower.
decimals : int
Number of rounded decimals.
seed : int or None
Random seed for generating bootstrap samples.
return_dist : boolean
If True, return the confidence intervals and the bootstrapped distribution (e.g. for
plotting purposes).
Returns
-------
ci : array
Bootstrapped confidence intervals.
Notes
-----
Results have been tested against the
`bootci <https://www.mathworks.com/help/stats/bootci.html>`_ Matlab function.
Since version 1.7, SciPy also includes a built-in bootstrap function
:py:func:`scipy.stats.bootstrap`. The SciPy implementation has two advantages over Pingouin: it
is faster when using ``vectorized=True``, and it supports the bias-corrected and accelerated
(BCa) confidence intervals for univariate functions. However, unlike Pingouin, it does not
return the bootstrap distribution.
The percentile bootstrap method (``per``) is defined as the
:math:`100 \\times \\frac{\\alpha}{2}` and :math:`100 \\times \\frac{1 - \\alpha}{2}`
percentiles of the distribution of :math:`\\theta` estimates obtained from resampling, where
:math:`\\alpha` is the level of significance (1 - confidence, default = 0.05 for 95% CIs).
The bias-corrected percentile method (``cper``) corrects for bias of the bootstrap
distribution. This method is different from the BCa method — the default in Matlab and SciPy —
which corrects for both bias and skewness of the bootstrap distribution using jackknife
resampling.
The normal approximation method (``norm``) calculates the confidence intervals with the
standard normal distribution using bootstrapped bias and standard error.
References
----------
* DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical science,
189-212.
* Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application (Vol. 1).
Cambridge university press.
* Jung, Lee, Gupta, & Cho (2019). Comparison of bootstrap confidence interval methods for
GSCA using a Monte Carlo simulation. Frontiers in psychology, 10, 2215.
Examples
--------
1. Bootstrapped 95% confidence interval of a Pearson correlation
>>> import pingouin as pg
>>> import numpy as np
>>> rng = np.random.default_rng(42)
>>> x = rng.normal(loc=4, scale=2, size=100)
>>> y = rng.normal(loc=3, scale=1, size=100)
>>> stat = np.corrcoef(x, y)[0][1]
>>> ci = pg.compute_bootci(x, y, func='pearson', paired=True, seed=42, decimals=4)
>>> print(round(stat, 4), ci)
0.0945 [-0.098 0.2738]
Let's compare to SciPy's built-in bootstrap function
>>> from scipy.stats import bootstrap
>>> bt_scipy = bootstrap(
... data=(x, y), statistic=lambda x, y: np.corrcoef(x, y)[0][1],
... method="basic", vectorized=False, n_resamples=2000, paired=True, random_state=42)
>>> np.round(bt_scipy.confidence_interval, 4)
array([-0.0952, 0.2883])
2. Bootstrapped 95% confidence interval of a Cohen d
>>> stat = pg.compute_effsize(x, y, eftype='cohen')
>>> ci = pg.compute_bootci(x, y, func='cohen', seed=42, decimals=3)
>>> print(round(stat, 4), ci)
0.7009 [0.403 1.009]
3. Bootstrapped confidence interval of a standard deviation (univariate)
>>> import numpy as np
>>> stat = np.std(x, ddof=1)
>>> ci = pg.compute_bootci(x, func='std', seed=123)
>>> print(round(stat, 4), ci)
1.5534 [1.38 1.8 ]
Compare to SciPy's built-in bootstrap function, which returns the bias-corrected and
accelerated CIs (see Notes).
>>> def std(x, axis):
... return np.std(x, ddof=1, axis=axis)
>>> bt_scipy = bootstrap(data=(x, ), statistic=std, n_resamples=2000, random_state=123)
>>> np.round(bt_scipy.confidence_interval, 2)
array([1.39, 1.81])
Changing the confidence intervals type in Pingouin
>>> pg.compute_bootci(x, func='std', seed=123, method="norm")
array([1.37, 1.76])
>>> pg.compute_bootci(x, func='std', seed=123, method="percentile")
array([1.35, 1.75])
4. Bootstrapped confidence interval using a custom univariate function
>>> from scipy.stats import skew
>>> round(skew(x), 4), pg.compute_bootci(x, func=skew, n_boot=10000, seed=123)
(-0.137, array([-0.55, 0.32]))
5. Bootstrapped confidence interval using a custom bivariate function. Here, x and y are not
paired and can therefore have different sizes.
>>> def mean_diff(x, y):
... return np.mean(x) - np.mean(y)
>>> y2 = rng.normal(loc=3, scale=1, size=200) # y2 has 200 samples, x has 100
>>> ci = pg.compute_bootci(x, y2, func=mean_diff, n_boot=10000, seed=123)
>>> print(round(mean_diff(x, y2), 2), ci)
0.88 [0.54 1.21]
We can also get the bootstrapped distribution
>>> ci, bt = pg.compute_bootci(x, y2, func=mean_diff, n_boot=10000, return_dist=True, seed=9)
>>> print(f"The bootstrap distribution has {bt.size} samples. The mean and standard "
... f"{bt.mean():.4f} ± {bt.std():.4f}")
The bootstrap distribution has 10000 samples. The mean and standard 0.8807 ± 0.1704
"""
from inspect import isfunction, isroutine
from scipy.stats import norm
# Check other arguments
assert isinstance(confidence, float)
assert 0 < confidence < 1, "confidence must be between 0 and 1."
assert method in ["norm", "normal", "percentile", "per", "cpercentile", "cper"]
assert isfunction(func) or isinstance(func, str) or isroutine(func), (
"func must be a function (e.g. np.mean, custom function) or a string (e.g. 'pearson'). "
"See documentation for more details."
)
vectorizable = False
# Check x
x = np.asarray(x)
nx = x.size
assert x.ndim == 1, "x must be one-dimensional."
assert nx > 1, "x must have more than one element."
# Check y
if y is not None:
y = np.asarray(y)
ny = y.size
assert y.ndim == 1, "y must be one-dimensional."
assert ny > 1, "y must have more than one element."
if paired:
assert nx == ny, "x and y must have the same number of elements when paired=True."
# Check string functions
if isinstance(func, str):
func_str = "%s" % func
| (x, y=None, func=None, method='cper', paired=False, confidence=0.95, n_boot=2000, decimals=2, seed=None, return_dist=False) | [
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|
31,992 | pingouin.effsize | compute_effsize | Calculate effect size between two set of observations.
Parameters
----------
x : np.array or list
First set of observations.
y : np.array or list
Second set of observations.
paired : boolean
If True, uses Cohen d-avg formula to correct for repeated measurements
(see Notes).
eftype : string
Desired output effect size.
Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'pointbiserialr'``: Point-biserial correlation
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
Returns
-------
ef : float
Effect size
See Also
--------
convert_effsize : Conversion between effect sizes.
compute_effsize_from_t : Convert a T-statistic to an effect size.
Notes
-----
Missing values are automatically removed from the data. If ``x`` and ``y`` are paired, the
entire row is removed.
If ``x`` and ``y`` are independent, the Cohen :math:`d` is:
.. math::
d = \frac{\overline{X} - \overline{Y}}
{\sqrt{\frac{(n_{1} - 1)\sigma_{1}^{2} + (n_{2} - 1)
\sigma_{2}^{2}}{n1 + n2 - 2}}}
If ``x`` and ``y`` are paired, the Cohen :math:`d_{avg}` is computed:
.. math::
d_{avg} = \frac{\overline{X} - \overline{Y}}
{\sqrt{\frac{(\sigma_1^2 + \sigma_2^2)}{2}}}
The Cohen's d is a biased estimate of the population effect size, especially for small samples
(n < 20). It is often preferable to use the corrected Hedges :math:`g` instead:
.. math:: g = d \times (1 - \frac{3}{4(n_1 + n_2) - 9})
The common language effect size is the proportion of pairs where ``x`` is higher than ``y``
(calculated with a brute-force approach where each observation of ``x`` is paired to each
observation of ``y``, see :py:func:`pingouin.wilcoxon` for more details):
.. math:: \text{CL} = P(X > Y) + .5 \times P(X = Y)
For other effect sizes, Pingouin will first calculate a Cohen :math:`d` and then use the
:py:func:`pingouin.convert_effsize` to convert to the desired effect size.
References
----------
* Lakens, D., 2013. Calculating and reporting effect sizes to
facilitate cumulative science: a practical primer for t-tests and
ANOVAs. Front. Psychol. 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
* Cumming, Geoff. Understanding the new statistics: Effect sizes,
confidence intervals, and meta-analysis. Routledge, 2013.
* https://osf.io/vbdah/
Examples
--------
1. Cohen d from two independent samples.
>>> import numpy as np
>>> import pingouin as pg
>>> x = [1, 2, 3, 4]
>>> y = [3, 4, 5, 6, 7]
>>> pg.compute_effsize(x, y, paired=False, eftype='cohen')
-1.707825127659933
The sign of the Cohen d will be opposite if we reverse the order of
``x`` and ``y``:
>>> pg.compute_effsize(y, x, paired=False, eftype='cohen')
1.707825127659933
2. Hedges g from two paired samples.
>>> x = [1, 2, 3, 4, 5, 6, 7]
>>> y = [1, 3, 5, 7, 9, 11, 13]
>>> pg.compute_effsize(x, y, paired=True, eftype='hedges')
-0.8222477210374874
3. Common Language Effect Size.
>>> pg.compute_effsize(x, y, eftype='cles')
0.2857142857142857
In other words, there are ~29% of pairs where ``x`` is higher than ``y``,
which means that there are ~71% of pairs where ``x`` is *lower* than ``y``.
This can be easily verified by changing the order of ``x`` and ``y``:
>>> pg.compute_effsize(y, x, eftype='cles')
0.7142857142857143
| def compute_effsize(x, y, paired=False, eftype="cohen"):
"""Calculate effect size between two set of observations.
Parameters
----------
x : np.array or list
First set of observations.
y : np.array or list
Second set of observations.
paired : boolean
If True, uses Cohen d-avg formula to correct for repeated measurements
(see Notes).
eftype : string
Desired output effect size.
Available methods are:
* ``'none'``: no effect size
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'r'``: Pearson correlation coefficient
* ``'pointbiserialr'``: Point-biserial correlation
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'CLES'``: Common Language Effect Size
Returns
-------
ef : float
Effect size
See Also
--------
convert_effsize : Conversion between effect sizes.
compute_effsize_from_t : Convert a T-statistic to an effect size.
Notes
-----
Missing values are automatically removed from the data. If ``x`` and ``y`` are paired, the
entire row is removed.
If ``x`` and ``y`` are independent, the Cohen :math:`d` is:
.. math::
d = \\frac{\\overline{X} - \\overline{Y}}
{\\sqrt{\\frac{(n_{1} - 1)\\sigma_{1}^{2} + (n_{2} - 1)
\\sigma_{2}^{2}}{n1 + n2 - 2}}}
If ``x`` and ``y`` are paired, the Cohen :math:`d_{avg}` is computed:
.. math::
d_{avg} = \\frac{\\overline{X} - \\overline{Y}}
{\\sqrt{\\frac{(\\sigma_1^2 + \\sigma_2^2)}{2}}}
The Cohen's d is a biased estimate of the population effect size, especially for small samples
(n < 20). It is often preferable to use the corrected Hedges :math:`g` instead:
.. math:: g = d \\times (1 - \\frac{3}{4(n_1 + n_2) - 9})
The common language effect size is the proportion of pairs where ``x`` is higher than ``y``
(calculated with a brute-force approach where each observation of ``x`` is paired to each
observation of ``y``, see :py:func:`pingouin.wilcoxon` for more details):
.. math:: \\text{CL} = P(X > Y) + .5 \\times P(X = Y)
For other effect sizes, Pingouin will first calculate a Cohen :math:`d` and then use the
:py:func:`pingouin.convert_effsize` to convert to the desired effect size.
References
----------
* Lakens, D., 2013. Calculating and reporting effect sizes to
facilitate cumulative science: a practical primer for t-tests and
ANOVAs. Front. Psychol. 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
* Cumming, Geoff. Understanding the new statistics: Effect sizes,
confidence intervals, and meta-analysis. Routledge, 2013.
* https://osf.io/vbdah/
Examples
--------
1. Cohen d from two independent samples.
>>> import numpy as np
>>> import pingouin as pg
>>> x = [1, 2, 3, 4]
>>> y = [3, 4, 5, 6, 7]
>>> pg.compute_effsize(x, y, paired=False, eftype='cohen')
-1.707825127659933
The sign of the Cohen d will be opposite if we reverse the order of
``x`` and ``y``:
>>> pg.compute_effsize(y, x, paired=False, eftype='cohen')
1.707825127659933
2. Hedges g from two paired samples.
>>> x = [1, 2, 3, 4, 5, 6, 7]
>>> y = [1, 3, 5, 7, 9, 11, 13]
>>> pg.compute_effsize(x, y, paired=True, eftype='hedges')
-0.8222477210374874
3. Common Language Effect Size.
>>> pg.compute_effsize(x, y, eftype='cles')
0.2857142857142857
In other words, there are ~29% of pairs where ``x`` is higher than ``y``,
which means that there are ~71% of pairs where ``x`` is *lower* than ``y``.
This can be easily verified by changing the order of ``x`` and ``y``:
>>> pg.compute_effsize(y, x, eftype='cles')
0.7142857142857143
"""
# Check arguments
if not _check_eftype(eftype):
err = f"Could not interpret input '{eftype}'"
raise ValueError(err)
x = np.asarray(x)
y = np.asarray(y)
if x.size != y.size and paired:
warnings.warn("x and y have unequal sizes. Switching to " "paired == False.")
paired = False
# Remove rows with missing values
x, y = remove_na(x, y, paired=paired)
nx, ny = x.size, y.size
if ny == 1:
# Case 1: One-sample Test
d = (x.mean() - y) / x.std(ddof=1)
return d
if eftype.lower() == "r":
# Return correlation coefficient (useful for CI bootstrapping)
r, _ = pearsonr(x, y)
return r
elif eftype.lower() == "cles":
# Compute exact CLES (see pingouin.wilcoxon)
diff = x[:, None] - y
return np.where(diff == 0, 0.5, diff > 0).mean()
else:
# Compute unbiased Cohen's d effect size
if not paired:
# https://en.wikipedia.org/wiki/Effect_size
dof = nx + ny - 2
poolsd = np.sqrt(((nx - 1) * x.var(ddof=1) + (ny - 1) * y.var(ddof=1)) / dof)
d = (x.mean() - y.mean()) / poolsd
else:
# Report Cohen d-avg (Cumming 2012; Lakens 2013)
# Careful, the formula in Lakens 2013 is wrong. Updated in Pingouin
# v0.3.4 to use the formula provided by Cummings 2012.
# Before that the denominator was just (SD1 + SD2) / 2
d = (x.mean() - y.mean()) / np.sqrt((x.var(ddof=1) + y.var(ddof=1)) / 2)
return convert_effsize(d, "cohen", eftype, nx=nx, ny=ny)
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|
31,993 | pingouin.effsize | compute_effsize_from_t | Compute effect size from a T-value.
Parameters
----------
tval : float
T-value
nx, ny : int, optional
Group sample sizes.
N : int, optional
Total sample size (will not be used if nx and ny are specified)
eftype : string, optional
Desired output effect size.
Returns
-------
ef : float
Effect size
See Also
--------
compute_effsize : Calculate effect size between two set of observations.
convert_effsize : Conversion between effect sizes.
Notes
-----
If both nx and ny are specified, the formula to convert from *t* to *d* is:
.. math:: d = t * \sqrt{\frac{1}{n_x} + \frac{1}{n_y}}
If only N (total sample size) is specified, the formula is:
.. math:: d = \frac{2t}{\sqrt{N}}
Examples
--------
1. Compute effect size from a T-value when both sample sizes are known.
>>> from pingouin import compute_effsize_from_t
>>> tval, nx, ny = 2.90, 35, 25
>>> d = compute_effsize_from_t(tval, nx=nx, ny=ny, eftype='cohen')
>>> print(d)
0.7593982580212534
2. Compute effect size when only total sample size is known (nx+ny)
>>> tval, N = 2.90, 60
>>> d = compute_effsize_from_t(tval, N=N, eftype='cohen')
>>> print(d)
0.7487767802667672
| def compute_effsize_from_t(tval, nx=None, ny=None, N=None, eftype="cohen"):
"""Compute effect size from a T-value.
Parameters
----------
tval : float
T-value
nx, ny : int, optional
Group sample sizes.
N : int, optional
Total sample size (will not be used if nx and ny are specified)
eftype : string, optional
Desired output effect size.
Returns
-------
ef : float
Effect size
See Also
--------
compute_effsize : Calculate effect size between two set of observations.
convert_effsize : Conversion between effect sizes.
Notes
-----
If both nx and ny are specified, the formula to convert from *t* to *d* is:
.. math:: d = t * \\sqrt{\\frac{1}{n_x} + \\frac{1}{n_y}}
If only N (total sample size) is specified, the formula is:
.. math:: d = \\frac{2t}{\\sqrt{N}}
Examples
--------
1. Compute effect size from a T-value when both sample sizes are known.
>>> from pingouin import compute_effsize_from_t
>>> tval, nx, ny = 2.90, 35, 25
>>> d = compute_effsize_from_t(tval, nx=nx, ny=ny, eftype='cohen')
>>> print(d)
0.7593982580212534
2. Compute effect size when only total sample size is known (nx+ny)
>>> tval, N = 2.90, 60
>>> d = compute_effsize_from_t(tval, N=N, eftype='cohen')
>>> print(d)
0.7487767802667672
"""
if not _check_eftype(eftype):
err = f"Could not interpret input '{eftype}'"
raise ValueError(err)
if not isinstance(tval, float):
err = "T-value must be float"
raise ValueError(err)
# Compute Cohen d (Lakens, 2013)
if nx is not None and ny is not None:
d = tval * np.sqrt(1 / nx + 1 / ny)
elif N is not None:
d = 2 * tval / np.sqrt(N)
else:
raise ValueError("You must specify either nx + ny, or just N")
return convert_effsize(d, "cohen", eftype, nx=nx, ny=ny)
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|
31,994 | pingouin.effsize | compute_esci | Parametric confidence intervals around a Cohen d or a correlation coefficient.
Parameters
----------
stat : float
Original effect size. Must be either a correlation coefficient or a Cohen-type effect size
(Cohen d or Hedges g).
nx, ny : int
Length of vector x and y.
paired : bool
Indicates if the effect size was estimated from a paired sample. This is only relevant for
cohen or hedges effect size.
eftype : string
Effect size type. Must be "r" (correlation) or "cohen" (Cohen d or Hedges g).
confidence : float
Confidence level (0.95 = 95%)
decimals : int
Number of rounded decimals.
alternative : string
Defines the alternative hypothesis, or tail for the correlation coefficient. Must be one of
"two-sided" (default), "greater" or "less". This parameter only has an effect if ``eftype``
is "r".
Returns
-------
ci : array
Desired converted effect size
Notes
-----
To compute the parametric confidence interval around a **Pearson r correlation** coefficient,
one must first apply a Fisher's r-to-z transformation:
.. math:: z = 0.5 \cdot \ln \frac{1 + r}{1 - r} = \text{arctanh}(r)
and compute the standard error:
.. math:: \text{SE} = \frac{1}{\sqrt{n - 3}}
where :math:`n` is the sample size.
The lower and upper confidence intervals - *in z-space* - are then given by:
.. math:: \text{ci}_z = z \pm \text{crit} \cdot \text{SE}
where :math:`\text{crit}` is the critical value of the normal distribution corresponding to
the desired confidence level (e.g. 1.96 in case of a 95% confidence interval).
These confidence intervals can then be easily converted back to *r-space*:
.. math::
\text{ci}_r = \frac{\exp(2 \cdot \text{ci}_z) - 1}
{\exp(2 \cdot \text{ci}_z) + 1} = \text{tanh}(\text{ci}_z)
A formula for calculating the confidence interval for a **Cohen d effect size** is given by
Hedges and Olkin (1985, p86). If the effect size estimate from the sample is :math:`d`, then
it follows a T distribution with standard error:
.. math::
\text{SE} = \sqrt{\frac{n_x + n_y}{n_x \cdot n_y} +
\frac{d^2}{2 (n_x + n_y)}}
where :math:`n_x` and :math:`n_y` are the sample sizes of the two groups.
In one-sample test or paired test, this becomes:
.. math::
\text{SE} = \sqrt{\frac{1}{n_x} + \frac{d^2}{2 n_x}}
The lower and upper confidence intervals are then given by:
.. math:: \text{ci}_d = d \pm \text{crit} \cdot \text{SE}
where :math:`\text{crit}` is the critical value of the T distribution corresponding to the
desired confidence level.
References
----------
* https://en.wikipedia.org/wiki/Fisher_transformation
* Hedges, L., and Ingram Olkin. "Statistical models for meta-analysis." (1985).
* http://www.leeds.ac.uk/educol/documents/00002182.htm
* https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5133225/
Examples
--------
1. Confidence interval of a Pearson correlation coefficient
>>> import pingouin as pg
>>> x = [3, 4, 6, 7, 5, 6, 7, 3, 5, 4, 2]
>>> y = [4, 6, 6, 7, 6, 5, 5, 2, 3, 4, 1]
>>> nx, ny = len(x), len(y)
>>> stat = pg.compute_effsize(x, y, eftype='r')
>>> ci = pg.compute_esci(stat=stat, nx=nx, ny=ny, eftype='r')
>>> print(round(stat, 4), ci)
0.7468 [0.27 0.93]
2. Confidence interval of a Cohen d
>>> stat = pg.compute_effsize(x, y, eftype='cohen')
>>> ci = pg.compute_esci(stat, nx=nx, ny=ny, eftype='cohen', decimals=3)
>>> print(round(stat, 4), ci)
0.1538 [-0.737 1.045]
| def compute_esci(
stat=None,
nx=None,
ny=None,
paired=False,
eftype="cohen",
confidence=0.95,
decimals=2,
alternative="two-sided",
):
"""Parametric confidence intervals around a Cohen d or a correlation coefficient.
Parameters
----------
stat : float
Original effect size. Must be either a correlation coefficient or a Cohen-type effect size
(Cohen d or Hedges g).
nx, ny : int
Length of vector x and y.
paired : bool
Indicates if the effect size was estimated from a paired sample. This is only relevant for
cohen or hedges effect size.
eftype : string
Effect size type. Must be "r" (correlation) or "cohen" (Cohen d or Hedges g).
confidence : float
Confidence level (0.95 = 95%)
decimals : int
Number of rounded decimals.
alternative : string
Defines the alternative hypothesis, or tail for the correlation coefficient. Must be one of
"two-sided" (default), "greater" or "less". This parameter only has an effect if ``eftype``
is "r".
Returns
-------
ci : array
Desired converted effect size
Notes
-----
To compute the parametric confidence interval around a **Pearson r correlation** coefficient,
one must first apply a Fisher's r-to-z transformation:
.. math:: z = 0.5 \\cdot \\ln \\frac{1 + r}{1 - r} = \\text{arctanh}(r)
and compute the standard error:
.. math:: \\text{SE} = \\frac{1}{\\sqrt{n - 3}}
where :math:`n` is the sample size.
The lower and upper confidence intervals - *in z-space* - are then given by:
.. math:: \\text{ci}_z = z \\pm \\text{crit} \\cdot \\text{SE}
where :math:`\\text{crit}` is the critical value of the normal distribution corresponding to
the desired confidence level (e.g. 1.96 in case of a 95% confidence interval).
These confidence intervals can then be easily converted back to *r-space*:
.. math::
\\text{ci}_r = \\frac{\\exp(2 \\cdot \\text{ci}_z) - 1}
{\\exp(2 \\cdot \\text{ci}_z) + 1} = \\text{tanh}(\\text{ci}_z)
A formula for calculating the confidence interval for a **Cohen d effect size** is given by
Hedges and Olkin (1985, p86). If the effect size estimate from the sample is :math:`d`, then
it follows a T distribution with standard error:
.. math::
\\text{SE} = \\sqrt{\\frac{n_x + n_y}{n_x \\cdot n_y} +
\\frac{d^2}{2 (n_x + n_y)}}
where :math:`n_x` and :math:`n_y` are the sample sizes of the two groups.
In one-sample test or paired test, this becomes:
.. math::
\\text{SE} = \\sqrt{\\frac{1}{n_x} + \\frac{d^2}{2 n_x}}
The lower and upper confidence intervals are then given by:
.. math:: \\text{ci}_d = d \\pm \\text{crit} \\cdot \\text{SE}
where :math:`\\text{crit}` is the critical value of the T distribution corresponding to the
desired confidence level.
References
----------
* https://en.wikipedia.org/wiki/Fisher_transformation
* Hedges, L., and Ingram Olkin. "Statistical models for meta-analysis." (1985).
* http://www.leeds.ac.uk/educol/documents/00002182.htm
* https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5133225/
Examples
--------
1. Confidence interval of a Pearson correlation coefficient
>>> import pingouin as pg
>>> x = [3, 4, 6, 7, 5, 6, 7, 3, 5, 4, 2]
>>> y = [4, 6, 6, 7, 6, 5, 5, 2, 3, 4, 1]
>>> nx, ny = len(x), len(y)
>>> stat = pg.compute_effsize(x, y, eftype='r')
>>> ci = pg.compute_esci(stat=stat, nx=nx, ny=ny, eftype='r')
>>> print(round(stat, 4), ci)
0.7468 [0.27 0.93]
2. Confidence interval of a Cohen d
>>> stat = pg.compute_effsize(x, y, eftype='cohen')
>>> ci = pg.compute_esci(stat, nx=nx, ny=ny, eftype='cohen', decimals=3)
>>> print(round(stat, 4), ci)
0.1538 [-0.737 1.045]
"""
from scipy.stats import norm, t
assert eftype.lower() in ["r", "pearson", "spearman", "cohen", "d", "g", "hedges"]
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
assert stat is not None and nx is not None
assert isinstance(confidence, float)
assert 0 < confidence < 1, "confidence must be between 0 and 1."
if eftype.lower() in ["r", "pearson", "spearman"]:
z = np.arctanh(stat) # R-to-z transform
se = 1 / np.sqrt(nx - 3)
# See https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/cor.test.R
if alternative == "two-sided":
crit = np.abs(norm.ppf((1 - confidence) / 2))
ci_z = np.array([z - crit * se, z + crit * se])
elif alternative == "greater":
crit = norm.ppf(confidence)
ci_z = np.array([z - crit * se, np.inf])
else: # alternative = "less"
crit = norm.ppf(confidence)
ci_z = np.array([-np.inf, z + crit * se])
ci = np.tanh(ci_z) # Transform back to r
else:
# Cohen d. Results are different than JASP which uses a non-central T
# distribution. See github.com/jasp-stats/jasp-issues/issues/525
if ny == 1 or paired:
# One-sample or paired. Results vary slightly from the cohen.d R
# function which uses instead:
# >>> sqrt((n / (n / 2)^2) + .5*(dd^2 / n)) -- one-sample
# >>> sqrt( (1/n1 + dd^2/(2*n1))*(2-2*r)); -- paired
# where r is the correlation between samples
# https://github.com/mtorchiano/effsize/blob/master/R/CohenD.R
# However, Pingouin uses the formulas on www.real-statistics.com
se = np.sqrt(1 / nx + stat**2 / (2 * nx))
dof = nx - 1
else:
# Independent two-samples: give same results as R:
# >>> cohen.d(..., paired = FALSE, noncentral=FALSE)
se = np.sqrt(((nx + ny) / (nx * ny)) + (stat**2) / (2 * (nx + ny)))
dof = nx + ny - 2
crit = np.abs(t.ppf((1 - confidence) / 2, dof))
ci = np.array([stat - crit * se, stat + crit * se])
return np.round(ci, decimals)
| (stat=None, nx=None, ny=None, paired=False, eftype='cohen', confidence=0.95, decimals=2, alternative='two-sided') | [
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|
31,997 | pingouin.circular | convert_angles | Element-wise conversion of arbitrary-unit circular quantities
to radians.
.. versionadded:: 0.3.4
Parameters
----------
angles : array_like
Circular data.
low : float or int, optional
Low boundary for ``angles`` range. Default is 0.
high : float or int, optional
High boundary for ``angles`` range. Default is 360
(for degrees to radians conversion).
positive : boolean
If True, radians are mapped on the :math:`[0, 2\pi]`. Otherwise,
the resulting angles are mapped from :math:`[-\pi, \pi)` (default).
Returns
-------
radians : array_like
Circular data in radians.
Notes
-----
The formula to convert a set of angles :math:`\alpha` from an arbitrary
range :math:`[\text{high},\text{low}]` to radians
:math:`[0, 2\pi]` is:
.. math::
\alpha_r = \frac{2\pi\alpha}{\text{high} - \text{low}}
If ``positive=False`` (default), the resulting angles in
radians :math:`\alpha_r` are then wrapped to the :math:`[-\pi, \pi)`
range:
.. math::
(\text{angle} + \pi) \mod 2 \pi - \pi
Examples
--------
1. Convert degrees to radians
>>> from pingouin import convert_angles
>>> a = [0, 360, 180, 90, 45, 270]
>>> convert_angles(a, low=0, high=360)
array([ 0. , 0. , -3.14159265, 1.57079633, 0.78539816,
-1.57079633])
with ``positive=True``:
>>> convert_angles(a, low=0, high=360, positive=True)
array([0. , 6.28318531, 3.14159265, 1.57079633, 0.78539816,
4.71238898])
2. Convert hours (24h-format) to radians
>>> sleep_onset = [22.5, 23.25, 24, 0.5, 1]
>>> convert_angles(sleep_onset, low=0, high=24)
array([-0.39269908, -0.19634954, 0. , 0.13089969, 0.26179939])
3. Convert radians from :math:`[0, 2\pi]` to :math:`[-\pi, \pi)`:
>>> import numpy as np
>>> rad = [0.1, 3.14, 5, 2, 6]
>>> convert_angles(rad, low=0, high=2*np.pi)
array([ 0.1 , 3.14 , -1.28318531, 2. , -0.28318531])
4. Convert degrees from a 2-D array
>>> np.random.seed(123)
>>> deg = np.random.randint(low=0, high=360, size=(3, 4))
>>> convert_angles(deg)
array([[-0.66322512, 1.71042267, -2.26892803, 0.29670597],
[ 1.44862328, 1.85004901, 2.14675498, 0.99483767],
[-2.54818071, -2.35619449, 1.67551608, 1.97222205]])
| def convert_angles(angles, low=0, high=360, positive=False):
"""Element-wise conversion of arbitrary-unit circular quantities
to radians.
.. versionadded:: 0.3.4
Parameters
----------
angles : array_like
Circular data.
low : float or int, optional
Low boundary for ``angles`` range. Default is 0.
high : float or int, optional
High boundary for ``angles`` range. Default is 360
(for degrees to radians conversion).
positive : boolean
If True, radians are mapped on the :math:`[0, 2\\pi]`. Otherwise,
the resulting angles are mapped from :math:`[-\\pi, \\pi)` (default).
Returns
-------
radians : array_like
Circular data in radians.
Notes
-----
The formula to convert a set of angles :math:`\\alpha` from an arbitrary
range :math:`[\\text{high},\\text{low}]` to radians
:math:`[0, 2\\pi]` is:
.. math::
\\alpha_r = \\frac{2\\pi\\alpha}{\\text{high} - \\text{low}}
If ``positive=False`` (default), the resulting angles in
radians :math:`\\alpha_r` are then wrapped to the :math:`[-\\pi, \\pi)`
range:
.. math::
(\\text{angle} + \\pi) \\mod 2 \\pi - \\pi
Examples
--------
1. Convert degrees to radians
>>> from pingouin import convert_angles
>>> a = [0, 360, 180, 90, 45, 270]
>>> convert_angles(a, low=0, high=360)
array([ 0. , 0. , -3.14159265, 1.57079633, 0.78539816,
-1.57079633])
with ``positive=True``:
>>> convert_angles(a, low=0, high=360, positive=True)
array([0. , 6.28318531, 3.14159265, 1.57079633, 0.78539816,
4.71238898])
2. Convert hours (24h-format) to radians
>>> sleep_onset = [22.5, 23.25, 24, 0.5, 1]
>>> convert_angles(sleep_onset, low=0, high=24)
array([-0.39269908, -0.19634954, 0. , 0.13089969, 0.26179939])
3. Convert radians from :math:`[0, 2\\pi]` to :math:`[-\\pi, \\pi)`:
>>> import numpy as np
>>> rad = [0.1, 3.14, 5, 2, 6]
>>> convert_angles(rad, low=0, high=2*np.pi)
array([ 0.1 , 3.14 , -1.28318531, 2. , -0.28318531])
4. Convert degrees from a 2-D array
>>> np.random.seed(123)
>>> deg = np.random.randint(low=0, high=360, size=(3, 4))
>>> convert_angles(deg)
array([[-0.66322512, 1.71042267, -2.26892803, 0.29670597],
[ 1.44862328, 1.85004901, 2.14675498, 0.99483767],
[-2.54818071, -2.35619449, 1.67551608, 1.97222205]])
"""
assert isinstance(positive, bool)
assert isinstance(high, (int, float)), "high must be numeric"
assert isinstance(low, (int, float)), "low must be numeric"
ptp = high - low
assert ptp > 0, "high - low must be strictly positive."
angles = np.asarray(angles)
assert np.nanmin(angles) >= low, "angles cannot be >= low."
assert np.nanmax(angles) <= high, "angles cannot be <= high."
# Map to [0, 2pi] range
rad = angles * (2 * np.pi) / ptp
if not positive:
# https://stackoverflow.com/a/29237626/10581531
# Map to [-pi, pi) range:
rad = (rad + np.pi) % (2 * np.pi) - np.pi # [-pi, pi)
# Map to (-pi, pi] range:
# rad = np.angle(np.exp(1j * rad))
# rad = -1 * ((-rad + np.pi) % (2 * np.pi) - np.pi)
return rad
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|
31,998 | pingouin.effsize | convert_effsize | Conversion between effect sizes.
Parameters
----------
ef : float
Original effect size.
input_type : string
Effect size type of ef. Must be ``'cohen'`` or ``'pointbiserialr'``.
output_type : string
Desired effect size type. Available methods are:
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'pointbiserialr'``: Point-biserial correlation
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'none'``: pass-through (return ``ef``)
nx, ny : int, optional
Length of vector x and y. Required to convert to Hedges g.
Returns
-------
ef : float
Desired converted effect size
See Also
--------
compute_effsize : Calculate effect size between two set of observations.
compute_effsize_from_t : Convert a T-statistic to an effect size.
Notes
-----
The formula to convert from a`point-biserial correlation
<https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient>`_ **r** to **d** is
given in [1]_:
.. math:: d = \frac{2r_{pb}}{\sqrt{1 - r_{pb}^2}}
The formula to convert **d** to a point-biserial correlation **r** is given in [2]_:
.. math::
r_{pb} = \frac{d}{\sqrt{d^2 + \frac{(n_x + n_y)^2 - 2(n_x + n_y)}
{n_xn_y}}}
The formula to convert **d** to :math:`\eta^2` is given in [3]_:
.. math:: \eta^2 = \frac{(0.5 d)^2}{1 + (0.5 d)^2}
The formula to convert **d** to an odds-ratio is given in [4]_:
.. math:: \text{OR} = \exp (\frac{d \pi}{\sqrt{3}})
The formula to convert **d** to area under the curve is given in [5]_:
.. math:: \text{AUC} = \mathcal{N}_{cdf}(\frac{d}{\sqrt{2}})
References
----------
.. [1] Rosenthal, Robert. "Parametric measures of effect size."
The handbook of research synthesis 621 (1994): 231-244.
.. [2] McGrath, Robert E., and Gregory J. Meyer. "When effect sizes
disagree: the case of r and d." Psychological methods 11.4 (2006): 386.
.. [3] Cohen, Jacob. "Statistical power analysis for the behavioral
sciences. 2nd." (1988).
.. [4] Borenstein, Michael, et al. "Effect sizes for continuous data."
The handbook of research synthesis and meta-analysis 2 (2009): 221-235.
.. [5] Ruscio, John. "A probability-based measure of effect size:
Robustness to base rates and other factors." Psychological methods 1
3.1 (2008): 19.
Examples
--------
1. Convert from Cohen d to eta-square
>>> import pingouin as pg
>>> d = .45
>>> eta = pg.convert_effsize(d, 'cohen', 'eta-square')
>>> print(eta)
0.048185603807257595
2. Convert from Cohen d to Hegdes g (requires the sample sizes of each
group)
>>> pg.convert_effsize(.45, 'cohen', 'hedges', nx=10, ny=10)
0.4309859154929578
3. Convert a point-biserial correlation to Cohen d
>>> rpb = 0.40
>>> d = pg.convert_effsize(rpb, 'pointbiserialr', 'cohen')
>>> print(d)
0.8728715609439696
4. Reverse operation: convert Cohen d to a point-biserial correlation
>>> pg.convert_effsize(d, 'cohen', 'pointbiserialr')
0.4000000000000001
| def convert_effsize(ef, input_type, output_type, nx=None, ny=None):
"""Conversion between effect sizes.
Parameters
----------
ef : float
Original effect size.
input_type : string
Effect size type of ef. Must be ``'cohen'`` or ``'pointbiserialr'``.
output_type : string
Desired effect size type. Available methods are:
* ``'cohen'``: Unbiased Cohen d
* ``'hedges'``: Hedges g
* ``'pointbiserialr'``: Point-biserial correlation
* ``'eta-square'``: Eta-square
* ``'odds-ratio'``: Odds ratio
* ``'AUC'``: Area Under the Curve
* ``'none'``: pass-through (return ``ef``)
nx, ny : int, optional
Length of vector x and y. Required to convert to Hedges g.
Returns
-------
ef : float
Desired converted effect size
See Also
--------
compute_effsize : Calculate effect size between two set of observations.
compute_effsize_from_t : Convert a T-statistic to an effect size.
Notes
-----
The formula to convert from a`point-biserial correlation
<https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient>`_ **r** to **d** is
given in [1]_:
.. math:: d = \\frac{2r_{pb}}{\\sqrt{1 - r_{pb}^2}}
The formula to convert **d** to a point-biserial correlation **r** is given in [2]_:
.. math::
r_{pb} = \\frac{d}{\\sqrt{d^2 + \\frac{(n_x + n_y)^2 - 2(n_x + n_y)}
{n_xn_y}}}
The formula to convert **d** to :math:`\\eta^2` is given in [3]_:
.. math:: \\eta^2 = \\frac{(0.5 d)^2}{1 + (0.5 d)^2}
The formula to convert **d** to an odds-ratio is given in [4]_:
.. math:: \\text{OR} = \\exp (\\frac{d \\pi}{\\sqrt{3}})
The formula to convert **d** to area under the curve is given in [5]_:
.. math:: \\text{AUC} = \\mathcal{N}_{cdf}(\\frac{d}{\\sqrt{2}})
References
----------
.. [1] Rosenthal, Robert. "Parametric measures of effect size."
The handbook of research synthesis 621 (1994): 231-244.
.. [2] McGrath, Robert E., and Gregory J. Meyer. "When effect sizes
disagree: the case of r and d." Psychological methods 11.4 (2006): 386.
.. [3] Cohen, Jacob. "Statistical power analysis for the behavioral
sciences. 2nd." (1988).
.. [4] Borenstein, Michael, et al. "Effect sizes for continuous data."
The handbook of research synthesis and meta-analysis 2 (2009): 221-235.
.. [5] Ruscio, John. "A probability-based measure of effect size:
Robustness to base rates and other factors." Psychological methods 1
3.1 (2008): 19.
Examples
--------
1. Convert from Cohen d to eta-square
>>> import pingouin as pg
>>> d = .45
>>> eta = pg.convert_effsize(d, 'cohen', 'eta-square')
>>> print(eta)
0.048185603807257595
2. Convert from Cohen d to Hegdes g (requires the sample sizes of each
group)
>>> pg.convert_effsize(.45, 'cohen', 'hedges', nx=10, ny=10)
0.4309859154929578
3. Convert a point-biserial correlation to Cohen d
>>> rpb = 0.40
>>> d = pg.convert_effsize(rpb, 'pointbiserialr', 'cohen')
>>> print(d)
0.8728715609439696
4. Reverse operation: convert Cohen d to a point-biserial correlation
>>> pg.convert_effsize(d, 'cohen', 'pointbiserialr')
0.4000000000000001
"""
it = input_type.lower()
ot = output_type.lower()
# Check input and output type
for inp in [it, ot]:
if not _check_eftype(inp):
err = f"Could not interpret input '{inp}'"
raise ValueError(err)
if it not in ["pointbiserialr", "cohen"]:
raise ValueError("Input type must be 'cohen' or 'pointbiserialr'")
# Pass-through option
if it == ot or ot == "none":
return ef
# Convert point-biserial r to Cohen d (Rosenthal 1994)
d = (2 * ef) / np.sqrt(1 - ef**2) if it == "pointbiserialr" else ef
# Then convert to the desired output type
if ot == "cohen":
return d
elif ot == "hedges":
if all(v is not None for v in [nx, ny]):
return d * (1 - (3 / (4 * (nx + ny) - 9)))
else:
# If shapes of x and y are not known, return cohen's d
warnings.warn(
"You need to pass nx and ny arguments to compute "
"Hedges g. Returning Cohen's d instead"
)
return d
elif ot == "pointbiserialr":
# McGrath and Meyer 2006
if all(v is not None for v in [nx, ny]):
a = ((nx + ny) ** 2 - 2 * (nx + ny)) / (nx * ny)
else:
a = 4
return d / np.sqrt(d**2 + a)
elif ot == "eta-square":
# Cohen 1988
return (d / 2) ** 2 / (1 + (d / 2) ** 2)
elif ot == "odds-ratio":
# Borenstein et al. 2009
return np.exp(d * np.pi / np.sqrt(3))
elif ot == "r":
# https://github.com/raphaelvallat/pingouin/issues/302
raise ValueError(
"Using effect size 'r' in `pingouin.convert_effsize` has been deprecated. "
"Please use 'pointbiserialr' instead."
)
else: # ['auc']
# Ruscio 2008
from scipy.stats import norm
return norm.cdf(d / np.sqrt(2))
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|
31,999 | pingouin.correlation | corr | (Robust) correlation between two variables.
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 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)
**kwargs : optional
Optional argument(s) passed to the lower-level correlation functions.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'n'``: Sample size (after removal of missing values)
* ``'outliers'``: number of outliers, only if a robust method was used
* ``'r'``: Correlation coefficient
* ``'CI95%'``: 95% parametric confidence intervals around :math:`r`
* ``'p-val'``: p-value
* ``'BF10'``: Bayes Factor of the alternative hypothesis (only for Pearson correlation)
* ``'power'``: achieved power of the test with an alpha of 0.05.
See also
--------
pairwise_corr : Pairwise correlation between columns of a pandas DataFrame
partial_corr : Partial correlation
rm_corr : Repeated measures correlation
Notes
-----
The `Pearson correlation coefficient
<https://en.wikipedia.org/wiki/Pearson_correlation_coefficient>`_
measures the linear relationship between two datasets. Strictly speaking,
Pearson's correlation requires that each dataset be normally distributed.
Correlations of -1 or +1 imply a perfect negative and positive linear
relationship, respectively, with 0 indicating the absence of association.
.. math::
r_{xy} = \frac{\sum_i(x_i - \bar{x})(y_i - \bar{y})}
{\sqrt{\sum_i(x_i - \bar{x})^2} \sqrt{\sum_i(y_i - \bar{y})^2}}
= \frac{\text{cov}(x, y)}{\sigma_x \sigma_y}
where :math:`\text{cov}` is the sample covariance and :math:`\sigma`
is the sample standard deviation.
If ``method='pearson'``, The Bayes Factor is calculated using the
:py:func:`pingouin.bayesfactor_pearson` function.
The `Spearman correlation coefficient
<https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient>`_
is a non-parametric measure of the monotonicity of the relationship between
two datasets. Unlike the Pearson correlation, the Spearman correlation does
not assume that both datasets are normally distributed. Correlations of -1
or +1 imply an exact negative and positive monotonic relationship,
respectively. Mathematically, the Spearman correlation coefficient is
defined as the Pearson correlation coefficient between the
`rank variables <https://en.wikipedia.org/wiki/Ranking>`_.
The `Kendall correlation coefficient
<https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient>`_
is a measure of the correspondence between two rankings. Values also range
from -1 (perfect disagreement) to 1 (perfect agreement), with 0 indicating
the absence of association. Consistent with
:py:func:`scipy.stats.kendalltau`, Pingouin returns the Tau-b coefficient,
which adjusts for ties:
.. math:: \tau_B = \frac{(P - Q)}{\sqrt{(P + Q + T) (P + Q + U)}}
where :math:`P` is the number of concordant pairs, :math:`Q` the number of
discordand pairs, :math:`T` the number of ties in x, and :math:`U`
the number of ties in y.
The `biweight midcorrelation
<https://en.wikipedia.org/wiki/Biweight_midcorrelation>`_ and
percentage bend correlation [1]_ are both robust methods that
protects against *univariate* outliers by down-weighting observations that
deviate too much from the median.
The Shepherd pi [2]_ correlation and skipped [3]_, [4]_ correlation are
both robust methods that returns the Spearman correlation coefficient after
removing *bivariate* outliers. Briefly, the Shepherd pi uses a
bootstrapping of the Mahalanobis distance to identify outliers, while the
skipped correlation is based on the minimum covariance determinant
(which requires scikit-learn). Note that these two methods are
significantly slower than the previous ones.
The confidence intervals for the correlation coefficient are estimated
using the Fisher transformation.
.. important:: Rows with missing values (NaN) are automatically removed.
References
----------
.. [1] Wilcox, R.R., 1994. The percentage bend correlation coefficient.
Psychometrika 59, 601–616. https://doi.org/10.1007/BF02294395
.. [2] Schwarzkopf, D.S., De Haas, B., Rees, G., 2012. Better ways to
improve standards in brain-behavior correlation analysis. Front.
Hum. Neurosci. 6, 200. https://doi.org/10.3389/fnhum.2012.00200
.. [3] Rousselet, G.A., Pernet, C.R., 2012. Improving standards in
brain-behavior correlation analyses. Front. Hum. Neurosci. 6, 119.
https://doi.org/10.3389/fnhum.2012.00119
.. [4] Pernet, C.R., Wilcox, R., Rousselet, G.A., 2012. Robust correlation
analyses: false positive and power validation using a new open
source matlab toolbox. Front. Psychol. 3, 606.
https://doi.org/10.3389/fpsyg.2012.00606
Examples
--------
1. Pearson correlation
>>> import numpy as np
>>> import pingouin as pg
>>> # Generate random correlated samples
>>> np.random.seed(123)
>>> mean, cov = [4, 6], [(1, .5), (.5, 1)]
>>> x, y = np.random.multivariate_normal(mean, cov, 30).T
>>> # Compute Pearson correlation
>>> pg.corr(x, y).round(3)
n r CI95% p-val BF10 power
pearson 30 0.491 [0.16, 0.72] 0.006 8.55 0.809
2. Pearson correlation with two outliers
>>> x[3], y[5] = 12, -8
>>> pg.corr(x, y).round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.439 0.302 0.121
3. Spearman correlation (robust to outliers)
>>> pg.corr(x, y, method="spearman").round(3)
n r CI95% p-val power
spearman 30 0.401 [0.05, 0.67] 0.028 0.61
4. Biweight midcorrelation (robust)
>>> pg.corr(x, y, method="bicor").round(3)
n r CI95% p-val power
bicor 30 0.393 [0.04, 0.66] 0.031 0.592
5. Percentage bend correlation (robust)
>>> pg.corr(x, y, method='percbend').round(3)
n r CI95% p-val power
percbend 30 0.389 [0.03, 0.66] 0.034 0.581
6. Shepherd's pi correlation (robust)
>>> pg.corr(x, y, method='shepherd').round(3)
n outliers r CI95% p-val power
shepherd 30 2 0.437 [0.08, 0.7] 0.02 0.662
7. Skipped spearman correlation (robust)
>>> pg.corr(x, y, method='skipped').round(3)
n outliers r CI95% p-val power
skipped 30 2 0.437 [0.08, 0.7] 0.02 0.662
8. One-tailed Pearson correlation
>>> pg.corr(x, y, alternative="greater", method='pearson').round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-0.17, 1.0] 0.22 0.467 0.194
>>> pg.corr(x, y, alternative="less", method='pearson').round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-1.0, 0.43] 0.78 0.137 0.008
9. Perfect correlation
>>> pg.corr(x, -x).round(3)
n r CI95% p-val BF10 power
pearson 30 -1.0 [-1.0, -1.0] 0.0 inf 1
10. Using columns of a pandas dataframe
>>> import pandas as pd
>>> data = pd.DataFrame({'x': x, 'y': y})
>>> pg.corr(data['x'], data['y']).round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.439 0.302 0.121
| def corr(x, y, alternative="two-sided", method="pearson", **kwargs):
"""(Robust) correlation between two variables.
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 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)
**kwargs : optional
Optional argument(s) passed to the lower-level correlation functions.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'n'``: Sample size (after removal of missing values)
* ``'outliers'``: number of outliers, only if a robust method was used
* ``'r'``: Correlation coefficient
* ``'CI95%'``: 95% parametric confidence intervals around :math:`r`
* ``'p-val'``: p-value
* ``'BF10'``: Bayes Factor of the alternative hypothesis (only for Pearson correlation)
* ``'power'``: achieved power of the test with an alpha of 0.05.
See also
--------
pairwise_corr : Pairwise correlation between columns of a pandas DataFrame
partial_corr : Partial correlation
rm_corr : Repeated measures correlation
Notes
-----
The `Pearson correlation coefficient
<https://en.wikipedia.org/wiki/Pearson_correlation_coefficient>`_
measures the linear relationship between two datasets. Strictly speaking,
Pearson's correlation requires that each dataset be normally distributed.
Correlations of -1 or +1 imply a perfect negative and positive linear
relationship, respectively, with 0 indicating the absence of association.
.. math::
r_{xy} = \\frac{\\sum_i(x_i - \\bar{x})(y_i - \\bar{y})}
{\\sqrt{\\sum_i(x_i - \\bar{x})^2} \\sqrt{\\sum_i(y_i - \\bar{y})^2}}
= \\frac{\\text{cov}(x, y)}{\\sigma_x \\sigma_y}
where :math:`\\text{cov}` is the sample covariance and :math:`\\sigma`
is the sample standard deviation.
If ``method='pearson'``, The Bayes Factor is calculated using the
:py:func:`pingouin.bayesfactor_pearson` function.
The `Spearman correlation coefficient
<https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient>`_
is a non-parametric measure of the monotonicity of the relationship between
two datasets. Unlike the Pearson correlation, the Spearman correlation does
not assume that both datasets are normally distributed. Correlations of -1
or +1 imply an exact negative and positive monotonic relationship,
respectively. Mathematically, the Spearman correlation coefficient is
defined as the Pearson correlation coefficient between the
`rank variables <https://en.wikipedia.org/wiki/Ranking>`_.
The `Kendall correlation coefficient
<https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient>`_
is a measure of the correspondence between two rankings. Values also range
from -1 (perfect disagreement) to 1 (perfect agreement), with 0 indicating
the absence of association. Consistent with
:py:func:`scipy.stats.kendalltau`, Pingouin returns the Tau-b coefficient,
which adjusts for ties:
.. math:: \\tau_B = \\frac{(P - Q)}{\\sqrt{(P + Q + T) (P + Q + U)}}
where :math:`P` is the number of concordant pairs, :math:`Q` the number of
discordand pairs, :math:`T` the number of ties in x, and :math:`U`
the number of ties in y.
The `biweight midcorrelation
<https://en.wikipedia.org/wiki/Biweight_midcorrelation>`_ and
percentage bend correlation [1]_ are both robust methods that
protects against *univariate* outliers by down-weighting observations that
deviate too much from the median.
The Shepherd pi [2]_ correlation and skipped [3]_, [4]_ correlation are
both robust methods that returns the Spearman correlation coefficient after
removing *bivariate* outliers. Briefly, the Shepherd pi uses a
bootstrapping of the Mahalanobis distance to identify outliers, while the
skipped correlation is based on the minimum covariance determinant
(which requires scikit-learn). Note that these two methods are
significantly slower than the previous ones.
The confidence intervals for the correlation coefficient are estimated
using the Fisher transformation.
.. important:: Rows with missing values (NaN) are automatically removed.
References
----------
.. [1] Wilcox, R.R., 1994. The percentage bend correlation coefficient.
Psychometrika 59, 601–616. https://doi.org/10.1007/BF02294395
.. [2] Schwarzkopf, D.S., De Haas, B., Rees, G., 2012. Better ways to
improve standards in brain-behavior correlation analysis. Front.
Hum. Neurosci. 6, 200. https://doi.org/10.3389/fnhum.2012.00200
.. [3] Rousselet, G.A., Pernet, C.R., 2012. Improving standards in
brain-behavior correlation analyses. Front. Hum. Neurosci. 6, 119.
https://doi.org/10.3389/fnhum.2012.00119
.. [4] Pernet, C.R., Wilcox, R., Rousselet, G.A., 2012. Robust correlation
analyses: false positive and power validation using a new open
source matlab toolbox. Front. Psychol. 3, 606.
https://doi.org/10.3389/fpsyg.2012.00606
Examples
--------
1. Pearson correlation
>>> import numpy as np
>>> import pingouin as pg
>>> # Generate random correlated samples
>>> np.random.seed(123)
>>> mean, cov = [4, 6], [(1, .5), (.5, 1)]
>>> x, y = np.random.multivariate_normal(mean, cov, 30).T
>>> # Compute Pearson correlation
>>> pg.corr(x, y).round(3)
n r CI95% p-val BF10 power
pearson 30 0.491 [0.16, 0.72] 0.006 8.55 0.809
2. Pearson correlation with two outliers
>>> x[3], y[5] = 12, -8
>>> pg.corr(x, y).round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-0.23, 0.48] 0.439 0.302 0.121
3. Spearman correlation (robust to outliers)
>>> pg.corr(x, y, method="spearman").round(3)
n r CI95% p-val power
spearman 30 0.401 [0.05, 0.67] 0.028 0.61
4. Biweight midcorrelation (robust)
>>> pg.corr(x, y, method="bicor").round(3)
n r CI95% p-val power
bicor 30 0.393 [0.04, 0.66] 0.031 0.592
5. Percentage bend correlation (robust)
>>> pg.corr(x, y, method='percbend').round(3)
n r CI95% p-val power
percbend 30 0.389 [0.03, 0.66] 0.034 0.581
6. Shepherd's pi correlation (robust)
>>> pg.corr(x, y, method='shepherd').round(3)
n outliers r CI95% p-val power
shepherd 30 2 0.437 [0.08, 0.7] 0.02 0.662
7. Skipped spearman correlation (robust)
>>> pg.corr(x, y, method='skipped').round(3)
n outliers r CI95% p-val power
skipped 30 2 0.437 [0.08, 0.7] 0.02 0.662
8. One-tailed Pearson correlation
>>> pg.corr(x, y, alternative="greater", method='pearson').round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-0.17, 1.0] 0.22 0.467 0.194
>>> pg.corr(x, y, alternative="less", method='pearson').round(3)
n r CI95% p-val BF10 power
pearson 30 0.147 [-1.0, 0.43] 0.78 0.137 0.008
9. Perfect correlation
| (x, y, alternative='two-sided', method='pearson', **kwargs) | [
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|
32,001 | pingouin.reliability | cronbach_alpha | Cronbach's alpha reliability measure.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Wide or long-format dataframe.
items : str
Column in ``data`` with the items names (long-format only).
scores : str
Column in ``data`` with the scores (long-format only).
subject : str
Column in ``data`` with the subject identifier (long-format only).
nan_policy : bool
If `'listwise'`, remove the entire rows that contain missing values
(= listwise deletion). If `'pairwise'` (default), only pairwise
missing values are removed when computing the covariance matrix.
For more details, please refer to the :py:meth:`pandas.DataFrame.cov`
method.
ci : float
Confidence interval (.95 = 95%)
Returns
-------
alpha : float
Cronbach's alpha
Notes
-----
This function works with both wide and long format dataframe. If you pass a
long-format dataframe, you must also pass the ``items``, ``scores`` and
``subj`` columns (in which case the data will be converted into wide
format using the :py:meth:`pandas.DataFrame.pivot` method).
Internal consistency is usually measured with Cronbach's alpha [1]_,
a statistic calculated from the pairwise correlations between items.
Internal consistency ranges between negative infinity and one.
Coefficient alpha will be negative whenever there is greater
within-subject variability than between-subject variability.
Cronbach's :math:`\alpha` is defined as
.. math::
\alpha ={k \over k-1}\left(1-{\sum_{{i=1}}^{k}\sigma_{{y_{i}}}^{2}
\over\sigma_{x}^{2}}\right)
where :math:`k` refers to the number of items, :math:`\sigma_{x}^{2}`
is the variance of the observed total scores, and
:math:`\sigma_{{y_{i}}}^{2}` the variance of component :math:`i` for
the current sample of subjects.
Another formula for Cronbach's :math:`\alpha` is
.. math::
\alpha = \frac{k \times \bar c}{\bar v + (k - 1) \times \bar c}
where :math:`\bar c` refers to the average of all covariances between
items and :math:`\bar v` to the average variance of each item.
95% confidence intervals are calculated using Feldt's method [2]_:
.. math::
c_L = 1 - (1 - \alpha) \cdot F_{(0.025, n-1, (n-1)(k-1))}
c_U = 1 - (1 - \alpha) \cdot F_{(0.975, n-1, (n-1)(k-1))}
where :math:`n` is the number of subjects and :math:`k` the number of
items.
Results have been tested against the `psych
<https://cran.r-project.org/web/packages/psych/psych.pdf>`_ R package.
References
----------
.. [1] http://www.real-statistics.com/reliability/cronbachs-alpha/
.. [2] Feldt, Leonard S., Woodruff, David J., & Salih, Fathi A. (1987).
Statistical inference for coefficient alpha. Applied Psychological
Measurement, 11(1):93-103.
Examples
--------
Binary wide-format dataframe (with missing values)
>>> import pingouin as pg
>>> data = pg.read_dataset('cronbach_wide_missing')
>>> # In R: psych:alpha(data, use="pairwise")
>>> pg.cronbach_alpha(data=data)
(0.732660835214447, array([0.435, 0.909]))
After listwise deletion of missing values (remove the entire rows)
>>> # In R: psych:alpha(data, use="complete.obs")
>>> pg.cronbach_alpha(data=data, nan_policy='listwise')
(0.8016949152542373, array([0.581, 0.933]))
After imputing the missing values with the median of each column
>>> pg.cronbach_alpha(data=data.fillna(data.median()))
(0.7380191693290734, array([0.447, 0.911]))
Likert-type long-format dataframe
>>> data = pg.read_dataset('cronbach_alpha')
>>> pg.cronbach_alpha(data=data, items='Items', scores='Scores',
... subject='Subj')
(0.5917188485995826, array([0.195, 0.84 ]))
| def cronbach_alpha(
data=None, items=None, scores=None, subject=None, nan_policy="pairwise", ci=0.95
):
"""Cronbach's alpha reliability measure.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Wide or long-format dataframe.
items : str
Column in ``data`` with the items names (long-format only).
scores : str
Column in ``data`` with the scores (long-format only).
subject : str
Column in ``data`` with the subject identifier (long-format only).
nan_policy : bool
If `'listwise'`, remove the entire rows that contain missing values
(= listwise deletion). If `'pairwise'` (default), only pairwise
missing values are removed when computing the covariance matrix.
For more details, please refer to the :py:meth:`pandas.DataFrame.cov`
method.
ci : float
Confidence interval (.95 = 95%)
Returns
-------
alpha : float
Cronbach's alpha
Notes
-----
This function works with both wide and long format dataframe. If you pass a
long-format dataframe, you must also pass the ``items``, ``scores`` and
``subj`` columns (in which case the data will be converted into wide
format using the :py:meth:`pandas.DataFrame.pivot` method).
Internal consistency is usually measured with Cronbach's alpha [1]_,
a statistic calculated from the pairwise correlations between items.
Internal consistency ranges between negative infinity and one.
Coefficient alpha will be negative whenever there is greater
within-subject variability than between-subject variability.
Cronbach's :math:`\\alpha` is defined as
.. math::
\\alpha ={k \\over k-1}\\left(1-{\\sum_{{i=1}}^{k}\\sigma_{{y_{i}}}^{2}
\\over\\sigma_{x}^{2}}\\right)
where :math:`k` refers to the number of items, :math:`\\sigma_{x}^{2}`
is the variance of the observed total scores, and
:math:`\\sigma_{{y_{i}}}^{2}` the variance of component :math:`i` for
the current sample of subjects.
Another formula for Cronbach's :math:`\\alpha` is
.. math::
\\alpha = \\frac{k \\times \\bar c}{\\bar v + (k - 1) \\times \\bar c}
where :math:`\\bar c` refers to the average of all covariances between
items and :math:`\\bar v` to the average variance of each item.
95% confidence intervals are calculated using Feldt's method [2]_:
.. math::
c_L = 1 - (1 - \\alpha) \\cdot F_{(0.025, n-1, (n-1)(k-1))}
c_U = 1 - (1 - \\alpha) \\cdot F_{(0.975, n-1, (n-1)(k-1))}
where :math:`n` is the number of subjects and :math:`k` the number of
items.
Results have been tested against the `psych
<https://cran.r-project.org/web/packages/psych/psych.pdf>`_ R package.
References
----------
.. [1] http://www.real-statistics.com/reliability/cronbachs-alpha/
.. [2] Feldt, Leonard S., Woodruff, David J., & Salih, Fathi A. (1987).
Statistical inference for coefficient alpha. Applied Psychological
Measurement, 11(1):93-103.
Examples
--------
Binary wide-format dataframe (with missing values)
>>> import pingouin as pg
>>> data = pg.read_dataset('cronbach_wide_missing')
>>> # In R: psych:alpha(data, use="pairwise")
>>> pg.cronbach_alpha(data=data)
(0.732660835214447, array([0.435, 0.909]))
After listwise deletion of missing values (remove the entire rows)
>>> # In R: psych:alpha(data, use="complete.obs")
>>> pg.cronbach_alpha(data=data, nan_policy='listwise')
(0.8016949152542373, array([0.581, 0.933]))
After imputing the missing values with the median of each column
>>> pg.cronbach_alpha(data=data.fillna(data.median()))
(0.7380191693290734, array([0.447, 0.911]))
Likert-type long-format dataframe
>>> data = pg.read_dataset('cronbach_alpha')
>>> pg.cronbach_alpha(data=data, items='Items', scores='Scores',
... subject='Subj')
(0.5917188485995826, array([0.195, 0.84 ]))
"""
# Safety check
assert isinstance(data, pd.DataFrame), "data must be a dataframe."
assert nan_policy in ["pairwise", "listwise"]
if all([v is not None for v in [items, scores, subject]]):
# Data in long-format: we first convert to a wide format
data = data.pivot(index=subject, values=scores, columns=items)
# From now we assume that data is in wide format
n, k = data.shape
assert k >= 2, "At least two items are required."
assert n >= 2, "At least two raters/subjects are required."
err = "All columns must be numeric."
assert all([data[c].dtype.kind in "bfiu" for c in data.columns]), err
if data.isna().any().any() and nan_policy == "listwise":
# In R = psych:alpha(data, use="complete.obs")
data = data.dropna(axis=0, how="any")
# Compute covariance matrix and Cronbach's alpha
C = data.cov(numeric_only=True)
cronbach = (k / (k - 1)) * (1 - np.trace(C) / C.sum().sum())
# which is equivalent to
# v = np.diag(C).mean()
# c = C.to_numpy()[np.tril_indices_from(C, k=-1)].mean()
# cronbach = (k * c) / (v + (k - 1) * c)
# Confidence intervals
alpha = 1 - ci
df1 = n - 1
df2 = df1 * (k - 1)
lower = 1 - (1 - cronbach) * f.isf(alpha / 2, df1, df2)
upper = 1 - (1 - cronbach) * f.isf(1 - alpha / 2, df1, df2)
return cronbach, np.round([lower, upper], 3)
| (data=None, items=None, scores=None, subject=None, nan_policy='pairwise', ci=0.95) | [
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|
32,003 | pingouin.contingency | dichotomous_crosstab |
Generates a 2x2 contingency table from a :py:class:`pandas.DataFrame` that
contains only dichotomous entries, which are converted to 0 or 1.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Pandas dataframe
x, y : string
Column names in ``data``.
Currently, Pingouin recognizes the following values as dichotomous
measurements:
* ``0``, ``0.0``, ``False``, ``'No'``, ``'N'``, ``'Absent'``, ``'False'``, ``'F'`` or ``'Negative'`` for negative cases;
* ``1``, ``1.0``, ``True``, ``'Yes'``, ``'Y'``, ``'Present'``, ``'True'``, ``'T'``, ``'Positive'`` or ``'P'``, for positive cases;
If strings are used, Pingouin will recognize them regardless of their
uppercase/lowercase combinations.
Returns
-------
crosstab : :py:class:`pandas.DataFrame`
The 2x2 crosstab. See :py:func:`pandas.crosstab` for more details.
Examples
--------
>>> import pandas as pd
>>> import pingouin as pg
>>> df = pd.DataFrame({'A': ['Yes', 'No', 'No'], 'B': [0., 1., 0.]})
>>> pg.dichotomous_crosstab(data=df, x='A', y='B')
B 0 1
A
0 1 1
1 1 0
| def dichotomous_crosstab(data, x, y):
"""
Generates a 2x2 contingency table from a :py:class:`pandas.DataFrame` that
contains only dichotomous entries, which are converted to 0 or 1.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Pandas dataframe
x, y : string
Column names in ``data``.
Currently, Pingouin recognizes the following values as dichotomous
measurements:
* ``0``, ``0.0``, ``False``, ``'No'``, ``'N'``, ``'Absent'``,\
``'False'``, ``'F'`` or ``'Negative'`` for negative cases;
* ``1``, ``1.0``, ``True``, ``'Yes'``, ``'Y'``, ``'Present'``,\
``'True'``, ``'T'``, ``'Positive'`` or ``'P'``, for positive cases;
If strings are used, Pingouin will recognize them regardless of their
uppercase/lowercase combinations.
Returns
-------
crosstab : :py:class:`pandas.DataFrame`
The 2x2 crosstab. See :py:func:`pandas.crosstab` for more details.
Examples
--------
>>> import pandas as pd
>>> import pingouin as pg
>>> df = pd.DataFrame({'A': ['Yes', 'No', 'No'], 'B': [0., 1., 0.]})
>>> pg.dichotomous_crosstab(data=df, x='A', y='B')
B 0 1
A
0 1 1
1 1 0
"""
crosstab = pd.crosstab(_dichotomize_series(data, x), _dichotomize_series(data, y))
shape = crosstab.shape
if shape != (2, 2):
if shape == (2, 1):
crosstab.loc[:, int(not bool(crosstab.columns[0]))] = [0, 0]
elif shape == (1, 2):
crosstab.loc[int(not bool(crosstab.index[0])), :] = [0, 0]
else: # shape = (1, 1) or shape = (>2, >2)
raise ValueError(
"Both series contain only one unique value. " "Cannot build 2x2 contingency table."
)
crosstab = crosstab.sort_index(axis=0).sort_index(axis=1)
return crosstab
| (data, x, y) | [
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|
32,004 | pingouin.correlation | distance_corr | Distance correlation between two arrays.
Statistical significance (p-value) is evaluated with a permutation test.
Parameters
----------
x, y : array_like
1D or 2D input arrays, shape (n_samples, n_features).
``x`` and ``y`` must have the same number of samples and must not
contain missing values.
alternative : str
Alternative of the test. Can be either "two-sided", "greater" (default) or "less".
To be consistent with the original R implementation, the default is to calculate the
one-sided "greater" p-value.
n_boot : int or None
Number of bootstrap to perform. If None, no bootstrapping is performed and the function
only returns the distance correlation (no p-value). Default is 1000 (thus giving a
precision of 0.001).
seed : int or None
Random state seed.
Returns
-------
dcor : float
Sample distance correlation (range from 0 to 1).
pval : float
P-value.
Notes
-----
From Wikipedia:
*Distance correlation is a measure of dependence between two paired
random vectors of arbitrary, not necessarily equal, dimension. The
distance correlation coefficient is zero if and only if the random
vectors are independent. Thus, distance correlation measures both
linear and nonlinear association between two random variables or
random vectors. This is in contrast to Pearson's correlation, which can
only detect linear association between two random variables.*
The distance correlation of two random variables is obtained by
dividing their distance covariance by the product of their distance
standard deviations:
.. math::
\text{dCor}(X, Y) = \frac{\text{dCov}(X, Y)}
{\sqrt{\text{dVar}(X) \cdot \text{dVar}(Y)}}
where :math:`\text{dCov}(X, Y)` is the square root of the arithmetic
average of the product of the double-centered pairwise Euclidean distance
matrices.
Note that by contrast to Pearson's correlation, the distance correlation
cannot be negative, i.e :math:`0 \leq \text{dCor} \leq 1`.
Results have been tested against the
`energy <https://cran.r-project.org/web/packages/energy/energy.pdf>`_
R package.
References
----------
* https://en.wikipedia.org/wiki/Distance_correlation
* Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007).
Measuring and testing dependence by correlation of distances.
The annals of statistics, 35(6), 2769-2794.
* https://gist.github.com/satra/aa3d19a12b74e9ab7941
* https://gist.github.com/wladston/c931b1495184fbb99bec
Examples
--------
1. With two 1D vectors
>>> from pingouin import distance_corr
>>> a = [1, 2, 3, 4, 5]
>>> b = [1, 2, 9, 4, 4]
>>> dcor, pval = distance_corr(a, b, seed=9)
>>> print(round(dcor, 3), pval)
0.763 0.312
2. With two 2D arrays and no p-value
>>> import numpy as np
>>> np.random.seed(123)
>>> from pingouin import distance_corr
>>> a = np.random.random((10, 10))
>>> b = np.random.random((10, 10))
>>> round(distance_corr(a, b, n_boot=None), 3)
0.88
| def distance_corr(x, y, alternative="greater", n_boot=1000, seed=None):
"""Distance correlation between two arrays.
Statistical significance (p-value) is evaluated with a permutation test.
Parameters
----------
x, y : array_like
1D or 2D input arrays, shape (n_samples, n_features).
``x`` and ``y`` must have the same number of samples and must not
contain missing values.
alternative : str
Alternative of the test. Can be either "two-sided", "greater" (default) or "less".
To be consistent with the original R implementation, the default is to calculate the
one-sided "greater" p-value.
n_boot : int or None
Number of bootstrap to perform. If None, no bootstrapping is performed and the function
only returns the distance correlation (no p-value). Default is 1000 (thus giving a
precision of 0.001).
seed : int or None
Random state seed.
Returns
-------
dcor : float
Sample distance correlation (range from 0 to 1).
pval : float
P-value.
Notes
-----
From Wikipedia:
*Distance correlation is a measure of dependence between two paired
random vectors of arbitrary, not necessarily equal, dimension. The
distance correlation coefficient is zero if and only if the random
vectors are independent. Thus, distance correlation measures both
linear and nonlinear association between two random variables or
random vectors. This is in contrast to Pearson's correlation, which can
only detect linear association between two random variables.*
The distance correlation of two random variables is obtained by
dividing their distance covariance by the product of their distance
standard deviations:
.. math::
\\text{dCor}(X, Y) = \\frac{\\text{dCov}(X, Y)}
{\\sqrt{\\text{dVar}(X) \\cdot \\text{dVar}(Y)}}
where :math:`\\text{dCov}(X, Y)` is the square root of the arithmetic
average of the product of the double-centered pairwise Euclidean distance
matrices.
Note that by contrast to Pearson's correlation, the distance correlation
cannot be negative, i.e :math:`0 \\leq \\text{dCor} \\leq 1`.
Results have been tested against the
`energy <https://cran.r-project.org/web/packages/energy/energy.pdf>`_
R package.
References
----------
* https://en.wikipedia.org/wiki/Distance_correlation
* Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007).
Measuring and testing dependence by correlation of distances.
The annals of statistics, 35(6), 2769-2794.
* https://gist.github.com/satra/aa3d19a12b74e9ab7941
* https://gist.github.com/wladston/c931b1495184fbb99bec
Examples
--------
1. With two 1D vectors
>>> from pingouin import distance_corr
>>> a = [1, 2, 3, 4, 5]
>>> b = [1, 2, 9, 4, 4]
>>> dcor, pval = distance_corr(a, b, seed=9)
>>> print(round(dcor, 3), pval)
0.763 0.312
2. With two 2D arrays and no p-value
>>> import numpy as np
>>> np.random.seed(123)
>>> from pingouin import distance_corr
>>> a = np.random.random((10, 10))
>>> b = np.random.random((10, 10))
>>> round(distance_corr(a, b, n_boot=None), 3)
0.88
"""
assert alternative in [
"two-sided",
"greater",
"less",
], "Alternative must be one of 'two-sided' (default), 'greater' or 'less'."
x = np.asarray(x)
y = np.asarray(y)
# Check for NaN values
if any([np.isnan(np.min(x)), np.isnan(np.min(y))]):
raise ValueError("Input arrays must not contain NaN values.")
if x.ndim == 1:
x = x[:, None]
if y.ndim == 1:
y = y[:, None]
assert x.shape[0] == y.shape[0], "x and y must have same number of samples"
# Extract number of samples
n = x.shape[0]
n2 = n**2
# Process first array to avoid redundancy when performing bootstrap
a = squareform(pdist(x, metric="euclidean"))
A = a - a.mean(axis=0)[None, :] - a.mean(axis=1)[:, None] + a.mean()
dcov2_xx = np.vdot(A, A) / n2
# Process second array and compute final distance correlation
dcor = _dcorr(y, n2, A, dcov2_xx)
# Compute one-sided p-value using a bootstrap procedure
if n_boot is not None and n_boot > 1:
# Define random seed and permutation
rng = np.random.RandomState(seed)
bootsam = rng.random_sample((n_boot, n)).argsort(axis=1)
bootstat = np.empty(n_boot)
for i in range(n_boot):
bootstat[i] = _dcorr(y[bootsam[i, :]], n2, A, dcov2_xx)
pval = _perm_pval(bootstat, dcor, alternative=alternative)
return dcor, pval
else:
return dcor
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|
32,007 | pingouin.distribution | epsilon | Epsilon adjustement factor for repeated measures.
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).
correction : string
Specify the epsilon version:
* ``'gg'``: Greenhouse-Geisser
* ``'hf'``: Huynh-Feldt
* ``'lb'``: Lower bound
Returns
-------
eps : float
Epsilon adjustement factor.
See Also
--------
sphericity : Mauchly and JNS test for sphericity.
homoscedasticity : Test equality of variance.
Notes
-----
The lower bound epsilon is:
.. math:: lb = \frac{1}{\text{dof}},
where the degrees of freedom :math:`\text{dof}` is the number of groups
:math:`k` minus 1 for one-way design and :math:`(k_1 - 1)(k_2 - 1)`
for two-way design
The Greenhouse-Geisser epsilon is given by:
.. math::
\epsilon_{GG} = \frac{k^2(\overline{\text{diag}(S)} -
\overline{S})^2}{(k-1)(\sum_{i=1}^{k}\sum_{j=1}^{k}s_{ij}^2 -
2k\sum_{j=1}^{k}\overline{s_i}^2 + k^2\overline{S}^2)}
where :math:`S` is the covariance matrix, :math:`\overline{S}` the
grandmean of S and :math:`\overline{\text{diag}(S)}` the mean of all the
elements on the diagonal of S (i.e. mean of the variances).
The Huynh-Feldt epsilon is given by:
.. math::
\epsilon_{HF} = \frac{n(k-1)\epsilon_{GG}-2}{(k-1)
(n-1-(k-1)\epsilon_{GG})}
where :math:`n` is the number of observations.
Missing values are automatically removed from data (listwise deletion).
Examples
--------
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]})
>>> gg = pg.epsilon(data, correction='gg')
>>> hf = pg.epsilon(data, correction='hf')
>>> lb = pg.epsilon(data, correction='lb')
>>> print("%.2f %.2f %.2f" % (lb, gg, hf))
0.50 0.56 0.62
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 calculate the epsilon of the *Time* within-subject factor
>>> pg.epsilon(data, dv='Performance', subject='Subject',
... within='Time')
1.0
Since *Time* has only two levels (Pre and Post), the sphericity assumption
is necessarily met, and therefore the epsilon adjustement factor is 1.
The *Metric* factor, however, has three levels:
>>> round(pg.epsilon(data, dv='Performance', subject='Subject',
... within=['Metric']), 3)
0.969
The epsilon value is very close to 1, meaning that there is no major
violation of sphericity.
Now, let's calculate the epsilon for the interaction between the two
repeated measures factor:
>>> round(pg.epsilon(data, dv='Performance', subject='Subject',
... within=['Time', 'Metric']), 3)
0.727
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
>>> round(pg.epsilon(piv), 3)
0.727
which gives the same epsilon value as the long-format dataframe.
| def epsilon(data, dv=None, within=None, subject=None, correction="gg"):
"""Epsilon adjustement factor for repeated measures.
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).
correction : string
Specify the epsilon version:
* ``'gg'``: Greenhouse-Geisser
* ``'hf'``: Huynh-Feldt
* ``'lb'``: Lower bound
Returns
-------
eps : float
Epsilon adjustement factor.
See Also
--------
sphericity : Mauchly and JNS test for sphericity.
homoscedasticity : Test equality of variance.
Notes
-----
The lower bound epsilon is:
.. math:: lb = \\frac{1}{\\text{dof}},
where the degrees of freedom :math:`\\text{dof}` is the number of groups
:math:`k` minus 1 for one-way design and :math:`(k_1 - 1)(k_2 - 1)`
for two-way design
The Greenhouse-Geisser epsilon is given by:
.. math::
\\epsilon_{GG} = \\frac{k^2(\\overline{\\text{diag}(S)} -
\\overline{S})^2}{(k-1)(\\sum_{i=1}^{k}\\sum_{j=1}^{k}s_{ij}^2 -
2k\\sum_{j=1}^{k}\\overline{s_i}^2 + k^2\\overline{S}^2)}
where :math:`S` is the covariance matrix, :math:`\\overline{S}` the
grandmean of S and :math:`\\overline{\\text{diag}(S)}` the mean of all the
elements on the diagonal of S (i.e. mean of the variances).
The Huynh-Feldt epsilon is given by:
.. math::
\\epsilon_{HF} = \\frac{n(k-1)\\epsilon_{GG}-2}{(k-1)
(n-1-(k-1)\\epsilon_{GG})}
where :math:`n` is the number of observations.
Missing values are automatically removed from data (listwise deletion).
Examples
--------
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]})
>>> gg = pg.epsilon(data, correction='gg')
>>> hf = pg.epsilon(data, correction='hf')
>>> lb = pg.epsilon(data, correction='lb')
>>> print("%.2f %.2f %.2f" % (lb, gg, hf))
0.50 0.56 0.62
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 calculate the epsilon of the *Time* within-subject factor
>>> pg.epsilon(data, dv='Performance', subject='Subject',
... within='Time')
1.0
Since *Time* has only two levels (Pre and Post), the sphericity assumption
is necessarily met, and therefore the epsilon adjustement factor is 1.
The *Metric* factor, however, has three levels:
>>> round(pg.epsilon(data, dv='Performance', subject='Subject',
... within=['Metric']), 3)
0.969
The epsilon value is very close to 1, meaning that there is no major
violation of sphericity.
Now, let's calculate the epsilon for the interaction between the two
repeated measures factor:
>>> round(pg.epsilon(data, dv='Performance', subject='Subject',
... within=['Time', 'Metric']), 3)
0.727
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
>>> round(pg.epsilon(piv), 3)
0.727
which gives the same epsilon value 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.
# Drop rows with missing values
data = data.dropna()
# Support for two-way factor of shape (2, N)
data = _check_multilevel_rm(data, func="epsilon")
# Covariance matrix
S = data.cov(numeric_only=True)
n, k = data.shape
# Epsilon is always 1 with only two repeated measures.
if k <= 2:
return 1.0
# Degrees of freedom
if S.columns.nlevels == 1:
# One-way design
dof = k - 1
else:
# Two-way design (>2, >2)
ka, kb = S.columns.levshape
dof = (ka - 1) * (kb - 1)
# Lower bound
if correction == "lb":
return 1 / dof
# Greenhouse-Geisser
# Method 1. Sums of squares. (see real-statistics.com)
mean_var = np.diag(S).mean()
S_mean = S.mean().mean()
ss_mat = (S**2).sum().sum()
ss_rows = (S.mean(1) ** 2).sum().sum()
num = (k * (mean_var - S_mean)) ** 2
den = (k - 1) * (ss_mat - 2 * k * ss_rows + k**2 * S_mean**2)
eps = np.min([num / den, 1])
# Method 2. Eigenvalues.
# Sv = S.to_numpy()
# S_pop = Sv - Sv.mean(0)[:, None] - Sv.mean(1)[None, :] + Sv.mean()
# eig = np.linalg.eigvalsh(S_pop)
# eig = eig[eig > 0.1]
# V = eig.sum()**2 / np.sum(eig**2)
# eps = np.min([V / dof, 1])
# Huynh-Feldt
if correction == "hf":
num = n * dof * eps - 2
den = dof * (n - 1 - dof * eps)
eps = np.min([num / den, 1])
return eps
| (data, dv=None, within=None, subject=None, correction='gg') | [
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|
32,009 | pingouin.nonparametric | friedman | Friedman test for repeated measurements.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Both wide and long-format dataframe are supported for this test.
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-subject factor (only required if ``data`` is in
long format). Two or more within-factor are not currently supported.
subject : string
Name of column containing the subject/rater identifier (only required if ``data`` is in
long format).
method : string
Statistical test to perform. Must be ``'chisq'`` (chi-square test) or ``'f'`` (F test).
See notes below for explanation.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W'``: Kendall's coefficient of concordance, corrected for ties
If ``method='chisq'``
* ``'Q'``: The Friedman chi-square statistic, corrected for ties
* ``'dof'``: degrees of freedom
* ``'p-unc'``: Uncorrected p-value of the chi squared test
If ``method='f'``
* ``'F'``: The Friedman F statistic, corrected for ties
* ``'dof1'``: degrees of freedom of the numerator
* ``'dof2'``: degrees of freedom of the denominator
* ``'p-unc'``: Uncorrected p-value of the F test
Notes
-----
The Friedman test is used for non-parametric (rank-based) one-way repeated measures ANOVA.
It is equivalent to the test of significance of Kendalls's
coefficient of concordance (Kendall's W). Most commonly a Q statistic,
which has asymptotical chi-squared distribution, is computed and used for
testing. However, the chi-squared test tend to be overly conservative for small numbers
of samples and/or repeated measures, in which case a F-test is more adequate [1]_.
Data can be in wide or 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.
References
----------
.. [1] Marozzi, M. (2014). Testing for concordance between several
criteria. Journal of Statistical Computation and Simulation,
84(9), 1843–1850. https://doi.org/10.1080/00949655.2013.766189
.. [2] https://www.real-statistics.com/anova-repeated-measures/friedman-test/
Examples
--------
Compute the Friedman test for repeated measurements, using a wide-format dataframe
>>> import pandas as pd
>>> import pingouin as pg
>>> df = pd.DataFrame({
... 'white': {0: 10, 1: 8, 2: 7, 3: 9, 4: 7, 5: 4, 6: 5, 7: 6, 8: 5, 9: 10, 10: 4, 11: 7},
... 'red': {0: 7, 1: 5, 2: 8, 3: 6, 4: 5, 5: 7, 6: 9, 7: 6, 8: 4, 9: 6, 10: 7, 11: 3},
... 'rose': {0: 8, 1: 5, 2: 6, 3: 4, 4: 7, 5: 5, 6: 3, 7: 7, 8: 6, 9: 4, 10: 4, 11: 3}})
>>> pg.friedman(df)
Source W ddof1 Q p-unc
Friedman Within 0.083333 2 2.0 0.367879
Compare with SciPy
>>> from scipy.stats import friedmanchisquare
>>> friedmanchisquare(*df.to_numpy().T)
FriedmanchisquareResult(statistic=1.9999999999999893, pvalue=0.3678794411714444)
Using a long-format dataframe
>>> df_long = df.melt(ignore_index=False).reset_index()
>>> pg.friedman(data=df_long, dv="value", within="variable", subject="index")
Source W ddof1 Q p-unc
Friedman variable 0.083333 2 2.0 0.367879
Using the F-test method
>>> pg.friedman(df, method="f")
Source W ddof1 ddof2 F p-unc
Friedman Within 0.083333 1.833333 20.166667 1.0 0.378959
| def friedman(data=None, dv=None, within=None, subject=None, method="chisq"):
"""Friedman test for repeated measurements.
Parameters
----------
data : :py:class:`pandas.DataFrame`
DataFrame. Both wide and long-format dataframe are supported for this test.
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-subject factor (only required if ``data`` is in
long format). Two or more within-factor are not currently supported.
subject : string
Name of column containing the subject/rater identifier (only required if ``data`` is in
long format).
method : string
Statistical test to perform. Must be ``'chisq'`` (chi-square test) or ``'f'`` (F test).
See notes below for explanation.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W'``: Kendall's coefficient of concordance, corrected for ties
If ``method='chisq'``
* ``'Q'``: The Friedman chi-square statistic, corrected for ties
* ``'dof'``: degrees of freedom
* ``'p-unc'``: Uncorrected p-value of the chi squared test
If ``method='f'``
* ``'F'``: The Friedman F statistic, corrected for ties
* ``'dof1'``: degrees of freedom of the numerator
* ``'dof2'``: degrees of freedom of the denominator
* ``'p-unc'``: Uncorrected p-value of the F test
Notes
-----
The Friedman test is used for non-parametric (rank-based) one-way repeated measures ANOVA.
It is equivalent to the test of significance of Kendalls's
coefficient of concordance (Kendall's W). Most commonly a Q statistic,
which has asymptotical chi-squared distribution, is computed and used for
testing. However, the chi-squared test tend to be overly conservative for small numbers
of samples and/or repeated measures, in which case a F-test is more adequate [1]_.
Data can be in wide or 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.
References
----------
.. [1] Marozzi, M. (2014). Testing for concordance between several
criteria. Journal of Statistical Computation and Simulation,
84(9), 1843–1850. https://doi.org/10.1080/00949655.2013.766189
.. [2] https://www.real-statistics.com/anova-repeated-measures/friedman-test/
Examples
--------
Compute the Friedman test for repeated measurements, using a wide-format dataframe
>>> import pandas as pd
>>> import pingouin as pg
>>> df = pd.DataFrame({
... 'white': {0: 10, 1: 8, 2: 7, 3: 9, 4: 7, 5: 4, 6: 5, 7: 6, 8: 5, 9: 10, 10: 4, 11: 7},
... 'red': {0: 7, 1: 5, 2: 8, 3: 6, 4: 5, 5: 7, 6: 9, 7: 6, 8: 4, 9: 6, 10: 7, 11: 3},
... 'rose': {0: 8, 1: 5, 2: 6, 3: 4, 4: 7, 5: 5, 6: 3, 7: 7, 8: 6, 9: 4, 10: 4, 11: 3}})
>>> pg.friedman(df)
Source W ddof1 Q p-unc
Friedman Within 0.083333 2 2.0 0.367879
Compare with SciPy
>>> from scipy.stats import friedmanchisquare
>>> friedmanchisquare(*df.to_numpy().T)
FriedmanchisquareResult(statistic=1.9999999999999893, pvalue=0.3678794411714444)
Using a long-format dataframe
>>> df_long = df.melt(ignore_index=False).reset_index()
>>> pg.friedman(data=df_long, dv="value", within="variable", subject="index")
Source W ddof1 Q p-unc
Friedman variable 0.083333 2 2.0 0.367879
Using the F-test method
>>> pg.friedman(df, method="f")
Source W ddof1 ddof2 F p-unc
Friedman Within 0.083333 1.833333 20.166667 1.0 0.378959
"""
# 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().dropna() # Listwise deletion of missing values
assert data.shape[0] > 2, "Data must have at least 3 non-missing rows."
assert data.shape[1] > 1, "Data must contain at least two columns."
data["Subj"] = np.arange(data.shape[0])
data = data.melt(id_vars="Subj", var_name="Within", value_name="DV")
subject, within, dv = "Subj", "Within", "DV"
# Check dataframe
data = _check_dataframe(dv=dv, within=within, data=data, subject=subject, effects="within")
assert not data[within].isnull().any(), "Cannot have missing values in `within`."
assert not data[subject].isnull().any(), "Cannot have missing values in `subject`."
# Pivot the table to a wide-format dataframe. 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()
# Extract data in numpy array and calculate ranks
X = data_piv.to_numpy()
n, k = X.shape
ranked = scipy.stats.rankdata(X, axis=1)
ssbn = (ranked.sum(axis=0) ** 2).sum()
# Correction for ties
ties = 0
for i in range(n):
replist, repnum = scipy.stats.find_repeats(X[i])
for t in repnum:
ties += t * (t * t - 1)
# Compute Kendall's W corrected for ties
W = (12 * ssbn - 3 * n**2 * k * (k + 1) ** 2) / (n**2 * k * (k - 1) * (k + 1) - n * ties)
if method == "chisq":
# Compute the Q statistic
Q = n * (k - 1) * W
# Approximate the p-value
ddof1 = k - 1
p_unc = scipy.stats.chi2.sf(Q, ddof1)
# Create output dataframe
stats = pd.DataFrame(
{"Source": within, "W": W, "ddof1": ddof1, "Q": Q, "p-unc": p_unc}, index=["Friedman"]
)
elif method == "f":
# Compute the F statistic
F = W * (n - 1) / (1 - W)
# Approximate the p-value
ddof1 = k - 1 - 2 / n
ddof2 = (n - 1) * ddof1
p_unc = scipy.stats.f.sf(F, ddof1, ddof2)
# Create output dataframe
stats = pd.DataFrame(
{"Source": within, "W": W, "ddof1": ddof1, "ddof2": ddof2, "F": F, "p-unc": p_unc},
index=["Friedman"],
)
return _postprocess_dataframe(stats)
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|
32,010 | pingouin.distribution | gzscore | Geometric standard (Z) score.
Parameters
----------
x : array_like
Array of raw values.
axis : int or None, optional
Axis along which to operate. Default is 0. If None, compute over
the whole array `x`.
ddof : int, optional
Degrees of freedom correction in the calculation of the
standard deviation. Default is 1.
nan_policy : {'propagate', 'raise', 'omit'}, optional
Defines how to handle when input contains nan. 'propagate' returns nan,
'raise' throws an error, 'omit' performs the calculations ignoring nan
values. Default is 'propagate'. Note that when the value is 'omit',
nans in the input also propagate to the output, but they do not affect
the geometric z scores computed for the non-nan values.
Returns
-------
gzscore : array_like
Array of geometric z-scores (same shape as x).
Notes
-----
Geometric Z-scores are better measures of dispersion than arithmetic
z-scores when the sample data come from a log-normally distributed
population [1]_.
Given the raw scores :math:`x`, the geometric mean :math:`\mu_g` and
the geometric standard deviation :math:`\sigma_g`,
the standard score is given by the formula:
.. math:: z = \frac{log(x) - log(\mu_g)}{log(\sigma_g)}
References
----------
.. [1] https://en.wikipedia.org/wiki/Geometric_standard_deviation
Examples
--------
Standardize a lognormal-distributed vector:
>>> import numpy as np
>>> from pingouin import gzscore
>>> np.random.seed(123)
>>> raw = np.random.lognormal(size=100)
>>> z = gzscore(raw)
>>> print(round(z.mean(), 3), round(z.std(), 3))
-0.0 0.995
| def gzscore(x, *, axis=0, ddof=1, nan_policy="propagate"):
"""Geometric standard (Z) score.
Parameters
----------
x : array_like
Array of raw values.
axis : int or None, optional
Axis along which to operate. Default is 0. If None, compute over
the whole array `x`.
ddof : int, optional
Degrees of freedom correction in the calculation of the
standard deviation. Default is 1.
nan_policy : {'propagate', 'raise', 'omit'}, optional
Defines how to handle when input contains nan. 'propagate' returns nan,
'raise' throws an error, 'omit' performs the calculations ignoring nan
values. Default is 'propagate'. Note that when the value is 'omit',
nans in the input also propagate to the output, but they do not affect
the geometric z scores computed for the non-nan values.
Returns
-------
gzscore : array_like
Array of geometric z-scores (same shape as x).
Notes
-----
Geometric Z-scores are better measures of dispersion than arithmetic
z-scores when the sample data come from a log-normally distributed
population [1]_.
Given the raw scores :math:`x`, the geometric mean :math:`\\mu_g` and
the geometric standard deviation :math:`\\sigma_g`,
the standard score is given by the formula:
.. math:: z = \\frac{log(x) - log(\\mu_g)}{log(\\sigma_g)}
References
----------
.. [1] https://en.wikipedia.org/wiki/Geometric_standard_deviation
Examples
--------
Standardize a lognormal-distributed vector:
>>> import numpy as np
>>> from pingouin import gzscore
>>> np.random.seed(123)
>>> raw = np.random.lognormal(size=100)
>>> z = gzscore(raw)
>>> print(round(z.mean(), 3), round(z.std(), 3))
-0.0 0.995
"""
warnings.warn(
"gzscore is deprecated and will be removed in pingouin 0.7.0;"
" use scipy.stats.gzscore instead."
)
x = np.asanyarray(x)
log = np.ma.log if isinstance(x, np.ma.MaskedArray) else np.log
z = scipy.stats.zscore(log(x), axis=axis, ddof=ddof, nan_policy=nan_policy)
return z
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|
32,011 | pingouin.nonparametric | harrelldavis | Harrell-Davis robust estimate of the :math:`q^{th}` quantile(s) of the
data.
.. versionadded:: 0.2.9
Parameters
----------
x : array_like
Data, must be a one or two-dimensional vector.
quantile : float or array_like
Quantile or sequence of quantiles to compute, must be between 0 and 1.
Default is ``0.5``.
axis : int
Axis along which the MAD is computed. Default is the last axis (-1).
Can be either 0, 1 or -1.
Returns
-------
y : float or array_like
The estimated quantile(s). If ``quantile`` is a single quantile, will
return a float, otherwise will compute each quantile separately and
returns an array of floats.
Notes
-----
The Harrell-Davis method [1]_ estimates the :math:`q^{th}` quantile by a
linear combination of the order statistics. Results have been tested
against a Matlab implementation [2]_. Note that this method is also
used to measure the confidence intervals of the difference between
quantiles of two groups, as implemented in the shift function [3]_.
See Also
--------
plot_shift
References
----------
.. [1] Frank E. Harrell, C. E. Davis, A new distribution-free quantile
estimator, Biometrika, Volume 69, Issue 3, December 1982, Pages
635–640, https://doi.org/10.1093/biomet/69.3.635
.. [2] https://github.com/GRousselet/matlab_stats/blob/master/hd.m
.. [3] 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.
https://doi.org/doi:10.1111/ejn.13610
Examples
--------
Estimate the 0.5 quantile (i.e median) of 100 observation picked from a
normal distribution with zero mean and unit variance.
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.normal(0, 1, 100)
>>> round(pg.harrelldavis(x, quantile=0.5), 4)
-0.0499
Several quantiles at once
>>> pg.harrelldavis(x, quantile=[0.25, 0.5, 0.75])
array([-0.84133224, -0.04991657, 0.95897233])
On the last axis of a 2D vector (default)
>>> np.random.seed(123)
>>> x = np.random.normal(0, 1, (10, 100))
>>> pg.harrelldavis(x, quantile=[0.25, 0.5, 0.75])
array([[-0.84133224, -0.52346777, -0.81801193, -0.74611216, -0.64928321,
-0.48565262, -0.64332799, -0.8178394 , -0.70058282, -0.73088088],
[-0.04991657, 0.02932655, -0.08905073, -0.1860034 , 0.06970415,
0.15129817, 0.00430958, -0.13784786, -0.08648077, -0.14407123],
[ 0.95897233, 0.49543002, 0.57712236, 0.48620599, 0.85899005,
0.7903462 , 0.76558585, 0.62528436, 0.60421847, 0.52620286]])
On the first axis
>>> pg.harrelldavis(x, quantile=[0.5], axis=0).shape
(100,)
| def harrelldavis(x, quantile=0.5, axis=-1):
"""Harrell-Davis robust estimate of the :math:`q^{th}` quantile(s) of the
data.
.. versionadded:: 0.2.9
Parameters
----------
x : array_like
Data, must be a one or two-dimensional vector.
quantile : float or array_like
Quantile or sequence of quantiles to compute, must be between 0 and 1.
Default is ``0.5``.
axis : int
Axis along which the MAD is computed. Default is the last axis (-1).
Can be either 0, 1 or -1.
Returns
-------
y : float or array_like
The estimated quantile(s). If ``quantile`` is a single quantile, will
return a float, otherwise will compute each quantile separately and
returns an array of floats.
Notes
-----
The Harrell-Davis method [1]_ estimates the :math:`q^{th}` quantile by a
linear combination of the order statistics. Results have been tested
against a Matlab implementation [2]_. Note that this method is also
used to measure the confidence intervals of the difference between
quantiles of two groups, as implemented in the shift function [3]_.
See Also
--------
plot_shift
References
----------
.. [1] Frank E. Harrell, C. E. Davis, A new distribution-free quantile
estimator, Biometrika, Volume 69, Issue 3, December 1982, Pages
635–640, https://doi.org/10.1093/biomet/69.3.635
.. [2] https://github.com/GRousselet/matlab_stats/blob/master/hd.m
.. [3] 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.
https://doi.org/doi:10.1111/ejn.13610
Examples
--------
Estimate the 0.5 quantile (i.e median) of 100 observation picked from a
normal distribution with zero mean and unit variance.
>>> import numpy as np
>>> import pingouin as pg
>>> np.random.seed(123)
>>> x = np.random.normal(0, 1, 100)
>>> round(pg.harrelldavis(x, quantile=0.5), 4)
-0.0499
Several quantiles at once
>>> pg.harrelldavis(x, quantile=[0.25, 0.5, 0.75])
array([-0.84133224, -0.04991657, 0.95897233])
On the last axis of a 2D vector (default)
>>> np.random.seed(123)
>>> x = np.random.normal(0, 1, (10, 100))
>>> pg.harrelldavis(x, quantile=[0.25, 0.5, 0.75])
array([[-0.84133224, -0.52346777, -0.81801193, -0.74611216, -0.64928321,
-0.48565262, -0.64332799, -0.8178394 , -0.70058282, -0.73088088],
[-0.04991657, 0.02932655, -0.08905073, -0.1860034 , 0.06970415,
0.15129817, 0.00430958, -0.13784786, -0.08648077, -0.14407123],
[ 0.95897233, 0.49543002, 0.57712236, 0.48620599, 0.85899005,
0.7903462 , 0.76558585, 0.62528436, 0.60421847, 0.52620286]])
On the first axis
>>> pg.harrelldavis(x, quantile=[0.5], axis=0).shape
(100,)
"""
x = np.asarray(x)
assert x.ndim <= 2, "Only 1D or 2D array are supported for this function."
assert axis in [0, 1, -1], "Axis must be 0, 1 or -1."
# Sort the input array
x = np.sort(x, axis=axis)
n = x.shape[axis]
vec = np.arange(n)
if isinstance(quantile, float):
quantile = [quantile]
y = []
for q in quantile:
# Harrell-Davis estimate of the qth quantile
m1 = (n + 1) * q
m2 = (n + 1) * (1 - q)
w = scipy.stats.beta.cdf((vec + 1) / n, m1, m2) - scipy.stats.beta.cdf((vec) / n, m1, m2)
if axis != 0:
y.append((w * x).sum(axis))
else:
y.append((w[..., None] * x).sum(axis)) # Store results
if len(y) == 1:
y = y[0] # Return a float instead of a list if n quantile is 1
else:
y = np.array(y)
return y
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|
32,012 | pingouin.distribution | homoscedasticity | Test equality of variance.
Parameters
----------
data : :py:class:`pandas.DataFrame`, list or dict
Iterable. Can be either a list / dictionnary of iterables
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
Statistical test. `'levene'` (default) performs the Levene test
using :py:func:`scipy.stats.levene`, and `'bartlett'` performs the
Bartlett test using :py:func:`scipy.stats.bartlett`.
The former is more robust to departure from normality.
alpha : float
Significance level.
**kwargs : optional
Optional argument(s) passed to the lower-level :py:func:`scipy.stats.levene` function.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W/T'``: Test statistic ('W' for Levene, 'T' for Bartlett)
* ``'pval'``: p-value
* ``'equal_var'``: True if ``data`` has equal variance
See Also
--------
normality : Univariate normality test.
sphericity : Mauchly's test for sphericity.
Notes
-----
The **Bartlett** :math:`T` statistic [1]_ is defined as:
.. math::
T = \frac{(N-k) \ln{s^{2}_{p}} - \sum_{i=1}^{k}(N_{i} - 1)
\ln{s^{2}_{i}}}{1 + (1/(3(k-1)))((\sum_{i=1}^{k}{1/(N_{i} - 1))}
- 1/(N-k))}
where :math:`s_i^2` is the variance of the :math:`i^{th}` group,
:math:`N` is the total sample size, :math:`N_i` is the sample size of the
:math:`i^{th}` group, :math:`k` is the number of groups,
and :math:`s_p^2` is the pooled variance.
The pooled variance is a weighted average of the group variances and is
defined as:
.. math:: s^{2}_{p} = \sum_{i=1}^{k}(N_{i} - 1)s^{2}_{i}/(N-k)
The p-value is then computed using a chi-square distribution:
.. math:: T \sim \chi^2(k-1)
The **Levene** :math:`W` statistic [2]_ is defined as:
.. math::
W = \frac{(N-k)} {(k-1)}
\frac{\sum_{i=1}^{k}N_{i}(\overline{Z}_{i.}-\overline{Z})^{2} }
{\sum_{i=1}^{k}\sum_{j=1}^{N_i}(Z_{ij}-\overline{Z}_{i.})^{2} }
where :math:`Z_{ij} = |Y_{ij} - \text{median}({Y}_{i.})|`,
:math:`\overline{Z}_{i.}` are the group means of :math:`Z_{ij}` and
:math:`\overline{Z}` is the grand mean of :math:`Z_{ij}`.
The p-value is then computed using a F-distribution:
.. math:: W \sim F(k-1, N-k)
.. warning:: Missing values are not supported for this function.
Make sure to remove them before using the
:py:meth:`pandas.DataFrame.dropna` or :py:func:`pingouin.remove_na`
functions.
References
----------
.. [1] Bartlett, M. S. (1937). Properties of sufficiency and statistical
tests. Proc. R. Soc. Lond. A, 160(901), 268-282.
.. [2] Brown, M. B., & Forsythe, A. B. (1974). Robust tests for the
equality of variances. Journal of the American Statistical
Association, 69(346), 364-367.
Examples
--------
1. Levene test on a wide-format dataframe
>>> import numpy as np
>>> import pingouin as pg
>>> data = pg.read_dataset('mediation')
>>> pg.homoscedasticity(data[['X', 'Y', 'M']])
W pval equal_var
levene 1.173518 0.310707 True
2. Same data but using a long-format dataframe
>>> data_long = data[['X', 'Y', 'M']].melt()
>>> pg.homoscedasticity(data_long, dv="value", group="variable")
W pval equal_var
levene 1.173518 0.310707 True
3. Same but using a mean center
>>> pg.homoscedasticity(data_long, dv="value", group="variable", center="mean")
W pval equal_var
levene 1.572239 0.209303 True
4. Bartlett test using a list of iterables
>>> data = [[4, 8, 9, 20, 14], np.array([5, 8, 15, 45, 12])]
>>> pg.homoscedasticity(data, method="bartlett", alpha=.05)
T pval equal_var
bartlett 2.873569 0.090045 True
| def homoscedasticity(data, dv=None, group=None, method="levene", alpha=0.05, **kwargs):
"""Test equality of variance.
Parameters
----------
data : :py:class:`pandas.DataFrame`, list or dict
Iterable. Can be either a list / dictionnary of iterables
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
Statistical test. `'levene'` (default) performs the Levene test
using :py:func:`scipy.stats.levene`, and `'bartlett'` performs the
Bartlett test using :py:func:`scipy.stats.bartlett`.
The former is more robust to departure from normality.
alpha : float
Significance level.
**kwargs : optional
Optional argument(s) passed to the lower-level :py:func:`scipy.stats.levene` function.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'W/T'``: Test statistic ('W' for Levene, 'T' for Bartlett)
* ``'pval'``: p-value
* ``'equal_var'``: True if ``data`` has equal variance
See Also
--------
normality : Univariate normality test.
sphericity : Mauchly's test for sphericity.
Notes
-----
The **Bartlett** :math:`T` statistic [1]_ is defined as:
.. math::
T = \\frac{(N-k) \\ln{s^{2}_{p}} - \\sum_{i=1}^{k}(N_{i} - 1)
\\ln{s^{2}_{i}}}{1 + (1/(3(k-1)))((\\sum_{i=1}^{k}{1/(N_{i} - 1))}
- 1/(N-k))}
where :math:`s_i^2` is the variance of the :math:`i^{th}` group,
:math:`N` is the total sample size, :math:`N_i` is the sample size of the
:math:`i^{th}` group, :math:`k` is the number of groups,
and :math:`s_p^2` is the pooled variance.
The pooled variance is a weighted average of the group variances and is
defined as:
.. math:: s^{2}_{p} = \\sum_{i=1}^{k}(N_{i} - 1)s^{2}_{i}/(N-k)
The p-value is then computed using a chi-square distribution:
.. math:: T \\sim \\chi^2(k-1)
The **Levene** :math:`W` statistic [2]_ is defined as:
.. math::
W = \\frac{(N-k)} {(k-1)}
\\frac{\\sum_{i=1}^{k}N_{i}(\\overline{Z}_{i.}-\\overline{Z})^{2} }
{\\sum_{i=1}^{k}\\sum_{j=1}^{N_i}(Z_{ij}-\\overline{Z}_{i.})^{2} }
where :math:`Z_{ij} = |Y_{ij} - \\text{median}({Y}_{i.})|`,
:math:`\\overline{Z}_{i.}` are the group means of :math:`Z_{ij}` and
:math:`\\overline{Z}` is the grand mean of :math:`Z_{ij}`.
The p-value is then computed using a F-distribution:
.. math:: W \\sim F(k-1, N-k)
.. warning:: Missing values are not supported for this function.
Make sure to remove them before using the
:py:meth:`pandas.DataFrame.dropna` or :py:func:`pingouin.remove_na`
functions.
References
----------
.. [1] Bartlett, M. S. (1937). Properties of sufficiency and statistical
tests. Proc. R. Soc. Lond. A, 160(901), 268-282.
.. [2] Brown, M. B., & Forsythe, A. B. (1974). Robust tests for the
equality of variances. Journal of the American Statistical
Association, 69(346), 364-367.
Examples
--------
1. Levene test on a wide-format dataframe
>>> import numpy as np
>>> import pingouin as pg
>>> data = pg.read_dataset('mediation')
>>> pg.homoscedasticity(data[['X', 'Y', 'M']])
W pval equal_var
levene 1.173518 0.310707 True
2. Same data but using a long-format dataframe
>>> data_long = data[['X', 'Y', 'M']].melt()
>>> pg.homoscedasticity(data_long, dv="value", group="variable")
W pval equal_var
levene 1.173518 0.310707 True
3. Same but using a mean center
>>> pg.homoscedasticity(data_long, dv="value", group="variable", center="mean")
W pval equal_var
levene 1.572239 0.209303 True
4. Bartlett test using a list of iterables
>>> data = [[4, 8, 9, 20, 14], np.array([5, 8, 15, 45, 12])]
>>> pg.homoscedasticity(data, method="bartlett", alpha=.05)
T pval equal_var
bartlett 2.873569 0.090045 True
"""
assert isinstance(data, (pd.DataFrame, list, dict))
assert method.lower() in ["levene", "bartlett"]
func = getattr(scipy.stats, method)
if isinstance(data, pd.DataFrame):
# Data is a Pandas DataFrame
if dv is None and group is None:
# Wide-format
# Get numeric data only
numdata = data._get_numeric_data()
assert numdata.shape[1] > 1, "Data must have at least two columns."
statistic, p = func(*numdata.to_numpy().T, **kwargs)
else:
# Long-format
assert group in data.columns
assert dv in data.columns
grp = data.groupby(group, observed=True)[dv]
assert grp.ngroups > 1, "Data must have at least two columns."
statistic, p = func(*grp.apply(list), **kwargs)
elif isinstance(data, list):
# Check that list contains other list or np.ndarray
assert all(isinstance(el, (list, np.ndarray)) for el in data)
assert len(data) > 1, "Data must have at least two iterables."
statistic, p = func(*data, **kwargs)
else:
# Data is a dict
assert all(isinstance(el, (list, np.ndarray)) for el in data.values())
assert len(data) > 1, "Data must have at least two iterables."
statistic, p = func(*data.values(), **kwargs)
equal_var = True if p > alpha else False
stat_name = "W" if method.lower() == "levene" else "T"
stats = pd.DataFrame({stat_name: statistic, "pval": p, "equal_var": equal_var}, index=[method])
return _postprocess_dataframe(stats)
| (data, dv=None, group=None, method='levene', alpha=0.05, **kwargs) | [
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|
32,013 | pingouin.reliability | intraclass_corr | Intraclass correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Long-format dataframe. Data must be fully balanced.
targets : string
Name of column in ``data`` containing the targets.
raters : string
Name of column in ``data`` containing the raters.
ratings : string
Name of column in ``data`` containing the ratings.
nan_policy : str
Defines how to handle when input contains missing values (nan).
`'raise'` (default) throws an error, `'omit'` performs the calculations
after deleting target(s) with one or more missing values (= listwise
deletion).
.. versionadded:: 0.3.0
Returns
-------
stats : :py:class:`pandas.DataFrame`
Output dataframe:
* ``'Type'``: ICC type
* ``'Description'``: description of the ICC
* ``'ICC'``: intraclass correlation
* ``'F'``: F statistic
* ``'df1'``: numerator degree of freedom
* ``'df2'``: denominator degree of freedom
* ``'pval'``: p-value
* ``'CI95%'``: 95% confidence intervals around the ICC
Notes
-----
The intraclass correlation (ICC, [1]_) assesses the reliability of ratings
by comparing the variability of different ratings of the same subject to
the total variation across all ratings and all subjects.
Shrout and Fleiss (1979) [2]_ describe six cases of reliability of ratings
done by :math:`k` raters on :math:`n` targets. Pingouin returns all six
cases with corresponding F and p-values, as well as 95% confidence
intervals.
From the documentation of the ICC function in the `psych
<https://cran.r-project.org/web/packages/psych/psych.pdf>`_ R package:
- **ICC1**: Each target is rated by a different rater and the raters are
selected at random. This is a one-way ANOVA fixed effects model.
- **ICC2**: A random sample of :math:`k` raters rate each target. The
measure is one of absolute agreement in the ratings. ICC1 is sensitive
to differences in means between raters and is a measure of absolute
agreement.
- **ICC3**: A fixed set of :math:`k` raters rate each target. There is no
generalization to a larger population of raters. ICC2 and ICC3 remove
mean differences between raters, but are sensitive to interactions.
The difference between ICC2 and ICC3 is whether raters are seen as fixed
or random effects.
Then, for each of these cases, the reliability can either be estimated for
a single rating or for the average of :math:`k` ratings. The 1 rating case
is equivalent to the average intercorrelation, while the :math:`k` rating
case is equivalent to the Spearman Brown adjusted reliability.
**ICC1k**, **ICC2k**, **ICC3K** reflect the means of :math:`k` raters.
This function has been tested against the ICC function of the R psych
package. Note however that contrarily to the R implementation, the
current implementation does not use linear mixed effect but regular ANOVA,
which means that it only works with complete-case data (no missing values).
References
----------
.. [1] http://www.real-statistics.com/reliability/intraclass-correlation/
.. [2] Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations:
uses in assessing rater reliability. Psychological bulletin, 86(2),
420.
Examples
--------
ICCs of wine quality assessed by 4 judges.
>>> import pingouin as pg
>>> data = pg.read_dataset('icc')
>>> icc = pg.intraclass_corr(data=data, targets='Wine', raters='Judge',
... ratings='Scores').round(3)
>>> icc.set_index("Type")
Description ICC F df1 df2 pval CI95%
Type
ICC1 Single raters absolute 0.728 11.680 7 24 0.0 [0.43, 0.93]
ICC2 Single random raters 0.728 11.787 7 21 0.0 [0.43, 0.93]
ICC3 Single fixed raters 0.729 11.787 7 21 0.0 [0.43, 0.93]
ICC1k Average raters absolute 0.914 11.680 7 24 0.0 [0.75, 0.98]
ICC2k Average random raters 0.914 11.787 7 21 0.0 [0.75, 0.98]
ICC3k Average fixed raters 0.915 11.787 7 21 0.0 [0.75, 0.98]
| def intraclass_corr(data=None, targets=None, raters=None, ratings=None, nan_policy="raise"):
"""Intraclass correlation.
Parameters
----------
data : :py:class:`pandas.DataFrame`
Long-format dataframe. Data must be fully balanced.
targets : string
Name of column in ``data`` containing the targets.
raters : string
Name of column in ``data`` containing the raters.
ratings : string
Name of column in ``data`` containing the ratings.
nan_policy : str
Defines how to handle when input contains missing values (nan).
`'raise'` (default) throws an error, `'omit'` performs the calculations
after deleting target(s) with one or more missing values (= listwise
deletion).
.. versionadded:: 0.3.0
Returns
-------
stats : :py:class:`pandas.DataFrame`
Output dataframe:
* ``'Type'``: ICC type
* ``'Description'``: description of the ICC
* ``'ICC'``: intraclass correlation
* ``'F'``: F statistic
* ``'df1'``: numerator degree of freedom
* ``'df2'``: denominator degree of freedom
* ``'pval'``: p-value
* ``'CI95%'``: 95% confidence intervals around the ICC
Notes
-----
The intraclass correlation (ICC, [1]_) assesses the reliability of ratings
by comparing the variability of different ratings of the same subject to
the total variation across all ratings and all subjects.
Shrout and Fleiss (1979) [2]_ describe six cases of reliability of ratings
done by :math:`k` raters on :math:`n` targets. Pingouin returns all six
cases with corresponding F and p-values, as well as 95% confidence
intervals.
From the documentation of the ICC function in the `psych
<https://cran.r-project.org/web/packages/psych/psych.pdf>`_ R package:
- **ICC1**: Each target is rated by a different rater and the raters are
selected at random. This is a one-way ANOVA fixed effects model.
- **ICC2**: A random sample of :math:`k` raters rate each target. The
measure is one of absolute agreement in the ratings. ICC1 is sensitive
to differences in means between raters and is a measure of absolute
agreement.
- **ICC3**: A fixed set of :math:`k` raters rate each target. There is no
generalization to a larger population of raters. ICC2 and ICC3 remove
mean differences between raters, but are sensitive to interactions.
The difference between ICC2 and ICC3 is whether raters are seen as fixed
or random effects.
Then, for each of these cases, the reliability can either be estimated for
a single rating or for the average of :math:`k` ratings. The 1 rating case
is equivalent to the average intercorrelation, while the :math:`k` rating
case is equivalent to the Spearman Brown adjusted reliability.
**ICC1k**, **ICC2k**, **ICC3K** reflect the means of :math:`k` raters.
This function has been tested against the ICC function of the R psych
package. Note however that contrarily to the R implementation, the
current implementation does not use linear mixed effect but regular ANOVA,
which means that it only works with complete-case data (no missing values).
References
----------
.. [1] http://www.real-statistics.com/reliability/intraclass-correlation/
.. [2] Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations:
uses in assessing rater reliability. Psychological bulletin, 86(2),
420.
Examples
--------
ICCs of wine quality assessed by 4 judges.
>>> import pingouin as pg
>>> data = pg.read_dataset('icc')
>>> icc = pg.intraclass_corr(data=data, targets='Wine', raters='Judge',
... ratings='Scores').round(3)
>>> icc.set_index("Type")
Description ICC F df1 df2 pval CI95%
Type
ICC1 Single raters absolute 0.728 11.680 7 24 0.0 [0.43, 0.93]
ICC2 Single random raters 0.728 11.787 7 21 0.0 [0.43, 0.93]
ICC3 Single fixed raters 0.729 11.787 7 21 0.0 [0.43, 0.93]
ICC1k Average raters absolute 0.914 11.680 7 24 0.0 [0.75, 0.98]
ICC2k Average random raters 0.914 11.787 7 21 0.0 [0.75, 0.98]
ICC3k Average fixed raters 0.915 11.787 7 21 0.0 [0.75, 0.98]
"""
from pingouin import anova
# Safety check
assert isinstance(data, pd.DataFrame), "data must be a dataframe."
assert all([v is not None for v in [targets, raters, ratings]])
assert all([v in data.columns for v in [targets, raters, ratings]])
assert nan_policy in ["omit", "raise"]
# Convert data to wide-format
data = data.pivot_table(index=targets, columns=raters, values=ratings, observed=True)
# Listwise deletion of missing values
nan_present = data.isna().any().any()
if nan_present:
if nan_policy == "omit":
data = data.dropna(axis=0, how="any")
else:
raise ValueError(
"Either missing values are present in data or "
"data are unbalanced. Please remove them "
"manually or use nan_policy='omit'."
)
# Back to long-format
# data_wide = data.copy() # Optional, for PCA
data = data.reset_index().melt(id_vars=targets, value_name=ratings)
# Check that ratings is a numeric variable
assert data[ratings].dtype.kind in "bfiu", "Ratings must be numeric."
# Check that data are fully balanced
# This behavior is ensured by the long-to-wide-to-long transformation
# Unbalanced data will result in rows with missing values.
# assert data.groupby(raters)[ratings].count().nunique() == 1
# Extract sizes
k = data[raters].nunique()
n = data[targets].nunique()
# Two-way ANOVA
with np.errstate(invalid="ignore"):
# For max precision, make sure rounding is disabled
old_options = options.copy()
options["round"] = None
aov = anova(data=data, dv=ratings, between=[targets, raters], ss_type=2)
options.update(old_options) # restore options
# Extract mean squares
msb = aov.at[0, "MS"]
msw = (aov.at[1, "SS"] + aov.at[2, "SS"]) / (aov.at[1, "DF"] + aov.at[2, "DF"])
msj = aov.at[1, "MS"]
mse = aov.at[2, "MS"]
# Calculate ICCs
icc1 = (msb - msw) / (msb + (k - 1) * msw)
icc2 = (msb - mse) / (msb + (k - 1) * mse + k * (msj - mse) / n)
icc3 = (msb - mse) / (msb + (k - 1) * mse)
icc1k = (msb - msw) / msb
icc2k = (msb - mse) / (msb + (msj - mse) / n)
icc3k = (msb - mse) / msb
# Calculate F, df, and p-values
f1k = msb / msw
df1 = n - 1
df1kd = n * (k - 1)
p1k = f.sf(f1k, df1, df1kd)
f2k = f3k = msb / mse
df2kd = (n - 1) * (k - 1)
p2k = f.sf(f2k, df1, df2kd)
# Create output dataframe
stats = {
"Type": ["ICC1", "ICC2", "ICC3", "ICC1k", "ICC2k", "ICC3k"],
"Description": [
"Single raters absolute",
"Single random raters",
"Single fixed raters",
"Average raters absolute",
"Average random raters",
"Average fixed raters",
],
"ICC": [icc1, icc2, icc3, icc1k, icc2k, icc3k],
"F": [f1k, f2k, f2k, f1k, f2k, f2k],
"df1": n - 1,
"df2": [df1kd, df2kd, df2kd, df1kd, df2kd, df2kd],
"pval": [p1k, p2k, p2k, p1k, p2k, p2k],
}
stats = pd.DataFrame(stats)
# Calculate confidence intervals
alpha = 0.05
# Case 1 and 3
f1l = f1k / f.ppf(1 - alpha / 2, df1, df1kd)
f1u = f1k * f.ppf(1 - alpha / 2, df1kd, df1)
l1 = (f1l - 1) / (f1l + (k - 1))
u1 = (f1u - 1) / (f1u + (k - 1))
f3l = f3k / f.ppf(1 - alpha / 2, df1, df2kd)
f3u = f3k * f.ppf(1 - alpha / 2, df2kd, df1)
l3 = (f3l - 1) / (f3l + (k - 1))
u3 = (f3u - 1) / (f3u + (k - 1))
# Case 2
fj = msj / mse
vn = df2kd * (k * icc2 * fj + n * (1 + (k - 1) * icc2) - k * icc2) ** 2
vd = df1 * k**2 * icc2**2 * fj**2 + (n * (1 + (k - 1) * icc2) - k * icc2) ** 2
v = vn / vd
f2u = f.ppf | (data=None, targets=None, raters=None, ratings=None, nan_policy='raise') | [
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|
32,014 | pingouin.nonparametric | kruskal | Kruskal-Wallis H-test for independent samples.
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.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'H'``: The Kruskal-Wallis H statistic, corrected for ties
* ``'p-unc'``: Uncorrected p-value
* ``'dof'``: degrees of freedom
Notes
-----
The Kruskal-Wallis H-test tests the null hypothesis that the population
median of all of the groups are equal. It is a non-parametric version of
ANOVA. The test works on 2 or more independent samples, which may have
different sizes.
Due to the assumption that H has a chi square distribution, the number of
samples in each group must not be too small. A typical rule is that each
sample must have at least 5 measurements.
NaN values are automatically removed.
Examples
--------
Compute the Kruskal-Wallis H-test for independent samples.
>>> from pingouin import kruskal, read_dataset
>>> df = read_dataset('anova')
>>> kruskal(data=df, dv='Pain threshold', between='Hair color')
Source ddof1 H p-unc
Kruskal Hair color 3 10.58863 0.014172
| def kruskal(data=None, dv=None, between=None, detailed=False):
"""Kruskal-Wallis H-test for independent samples.
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.
Returns
-------
stats : :py:class:`pandas.DataFrame`
* ``'H'``: The Kruskal-Wallis H statistic, corrected for ties
* ``'p-unc'``: Uncorrected p-value
* ``'dof'``: degrees of freedom
Notes
-----
The Kruskal-Wallis H-test tests the null hypothesis that the population
median of all of the groups are equal. It is a non-parametric version of
ANOVA. The test works on 2 or more independent samples, which may have
different sizes.
Due to the assumption that H has a chi square distribution, the number of
samples in each group must not be too small. A typical rule is that each
sample must have at least 5 measurements.
NaN values are automatically removed.
Examples
--------
Compute the Kruskal-Wallis H-test for independent samples.
>>> from pingouin import kruskal, read_dataset
>>> df = read_dataset('anova')
>>> kruskal(data=df, dv='Pain threshold', between='Hair color')
Source ddof1 H p-unc
Kruskal Hair color 3 10.58863 0.014172
"""
# Check data
data = _check_dataframe(dv=dv, between=between, data=data, effects="between")
# Remove NaN values
data = data[[dv, between]].dropna()
# Reset index (avoid duplicate axis error)
data = data.reset_index(drop=True)
# Extract number of groups and total sample size
n_groups = data[between].nunique()
n = data[dv].size
# Rank data, dealing with ties appropriately
data["rank"] = scipy.stats.rankdata(data[dv])
# Find the total of rank per groups
grp = data.groupby(between, observed=True)["rank"]
sum_rk_grp = grp.sum().to_numpy()
n_per_grp = grp.count().to_numpy()
# Calculate chi-square statistic (H)
H = (12 / (n * (n + 1)) * np.sum(sum_rk_grp**2 / n_per_grp)) - 3 * (n + 1)
# Correct for ties
H /= scipy.stats.tiecorrect(data["rank"].to_numpy())
# Calculate DOF and p-value
ddof1 = n_groups - 1
p_unc = scipy.stats.chi2.sf(H, ddof1)
# Create output dataframe
stats = pd.DataFrame(
{
"Source": between,
"ddof1": ddof1,
"H": H,
"p-unc": p_unc,
},
index=["Kruskal"],
)
return _postprocess_dataframe(stats)
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|
32,015 | pingouin.regression | linear_regression | (Multiple) Linear regression.
Parameters
----------
X : array_like
Predictor(s), of shape *(n_samples, n_features)* or *(n_samples)*.
y : array_like
Dependent variable, of shape *(n_samples)*.
add_intercept : bool
If False, assume that the data are already centered. If True, add a
constant term to the model. In this case, the first value in the
output dict is the intercept of the model.
.. note:: It is generally recommended to include a constant term
(intercept) to the model to limit the bias and force the residual
mean to equal zero. The intercept coefficient and p-values
are however rarely meaningful.
weights : array_like
An optional vector of sample weights to be used in the fitting
process, of shape *(n_samples)*. Missing or negative weights are not
allowed. If not null, a weighted least squares is calculated.
.. versionadded:: 0.3.5
coef_only : bool
If True, return only the regression coefficients.
alpha : float
Alpha value used for the confidence intervals.
:math:`\text{CI} = [\alpha / 2 ; 1 - \alpha / 2]`
as_dataframe : bool
If True, returns a pandas DataFrame. If False, returns a dictionnary.
remove_na : bool
If True, apply a listwise deletion of missing values (i.e. the entire
row is removed). Default is False, which will raise an error if missing
values are present in either the predictor(s) or dependent
variable.
relimp : bool
If True, returns the relative importance (= contribution) of
predictors. This is irrelevant when the predictors are uncorrelated:
the total :math:`R^2` of the model is simply the sum of each univariate
regression :math:`R^2`-values. However, this does not apply when
predictors are correlated. Instead, the total :math:`R^2` of the model
is partitioned by averaging over all combinations of predictors,
as done in the `relaimpo
<https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf>`_
R package (``calc.relimp(type="lmg")``).
.. warning:: The computation time roughly doubles for each
additional predictor and therefore this can be extremely slow for
models with more than 12-15 predictors.
.. versionadded:: 0.3.0
Returns
-------
stats : :py:class:`pandas.DataFrame` or dict
Linear regression summary:
* ``'names'``: name of variable(s) in the model (e.g. x1, x2...)
* ``'coef'``: regression coefficients
* ``'se'``: standard errors
* ``'T'``: T-values
* ``'pval'``: p-values
* ``'r2'``: coefficient of determination (:math:`R^2`)
* ``'adj_r2'``: adjusted :math:`R^2`
* ``'CI[2.5%]'``: lower confidence intervals
* ``'CI[97.5%]'``: upper confidence intervals
* ``'relimp'``: relative contribution of each predictor to the final :math:`R^2` (only if ``relimp=True``).
* ``'relimp_perc'``: percent relative contribution
In addition, the output dataframe comes with hidden attributes such as
the residuals, and degrees of freedom of the model and residuals, which
can be accessed as follow, respectively:
>>> lm = pg.linear_regression() # doctest: +SKIP
>>> lm.residuals_, lm.df_model_, lm.df_resid_ # doctest: +SKIP
Note that to follow scikit-learn convention, these hidden atributes end
with an "_". When ``as_dataframe=False`` however, these attributes
are no longer hidden and can be accessed as any other keys in the
output dictionary.
>>> lm = pg.linear_regression() # doctest: +SKIP
>>> lm['residuals'], lm['df_model'], lm['df_resid'] # doctest: +SKIP
When ``as_dataframe=False`` the dictionary also contains the
processed ``X`` and ``y`` arrays (i.e, with NaNs removed if
``remove_na=True``) and the model's predicted values ``pred``.
>>> lm['X'], lm['y'], lm['pred'] # doctest: +SKIP
For a weighted least squares fit, the weighted ``Xw`` and ``yw``
arrays are included in the dictionary.
>>> lm['Xw'], lm['yw'] # doctest: +SKIP
See also
--------
logistic_regression, mediation_analysis, corr
Notes
-----
The :math:`\beta` coefficients are estimated using an ordinary least
squares (OLS) regression, as implemented in the
:py:func:`scipy.linalg.lstsq` function. The OLS method minimizes
the sum of squared residuals, and leads to a closed-form expression for
the estimated :math:`\beta`:
.. math:: \hat{\beta} = (X^TX)^{-1} X^Ty
It is generally recommended to include a constant term (intercept) to the
model to limit the bias and force the residual mean to equal zero.
Note that intercept coefficient and p-values are however rarely meaningful.
The standard error of the estimates is a measure of the accuracy of the
prediction defined as:
.. math:: \sigma = \sqrt{\text{MSE} \cdot (X^TX)^{-1}}
where :math:`\text{MSE}` is the mean squared error,
.. math::
\text{MSE} = \frac{SS_{\text{resid}}}{n - p - 1}
= \frac{\sum{(\text{true} - \text{pred})^2}}{n - p - 1}
:math:`p` is the total number of predictor variables in the model
(excluding the intercept) and :math:`n` is the sample size.
Using the :math:`\beta` coefficients and the standard errors,
the T-values can be obtained:
.. math:: T = \frac{\beta}{\sigma}
and the p-values approximated using a T-distribution with
:math:`n - p - 1` degrees of freedom.
The coefficient of determination (:math:`R^2`) is defined as:
.. math:: R^2 = 1 - (\frac{SS_{\text{resid}}}{SS_{\text{total}}})
The adjusted :math:`R^2` is defined as:
.. math:: \overline{R}^2 = 1 - (1 - R^2) \frac{n - 1}{n - p - 1}
The relative importance (``relimp``) column is a partitioning of the
total :math:`R^2` of the model into individual :math:`R^2` contribution.
This is calculated by taking the average over average contributions in
models of different sizes. For more details, please refer to
`Groemping et al. 2006 <http://dx.doi.org/10.18637/jss.v017.i01>`_
and the R package `relaimpo
<https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf>`_.
Note that Pingouin will automatically remove any duplicate columns
from :math:`X`, as well as any column with only one unique value
(constant), excluding the intercept.
Results have been compared against sklearn, R, statsmodels and JASP.
Examples
--------
1. Simple linear regression using columns of a pandas dataframe
In this first example, we'll use the tips dataset to see how well we
can predict the waiter's tip (in dollars) based on the total bill (also
in dollars).
>>> import numpy as np
>>> import pingouin as pg
>>> df = pg.read_dataset('tips')
>>> # Let's predict the tip ($) based on the total bill (also in $)
>>> lm = pg.linear_regression(df['total_bill'], df['tip'])
>>> lm.round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 0.92 0.16 5.76 0.0 0.46 0.45 0.61 1.23
1 total_bill 0.11 0.01 14.26 0.0 0.46 0.45 0.09 0.12
It comes as no surprise that total bill is indeed a significant predictor
of the waiter's tip (T=14.26, p<0.05). The :math:`R^2` of the model is 0.46
and the adjusted :math:`R^2` is 0.45, which means that our model roughly
explains ~45% of the total variance in the tip amount.
2. Multiple linear regression
We can also have more than one predictor and run a multiple linear
regression. Below, we add the party size as a second predictor of tip.
>>> # We'll add a second predictor: the party size
>>> lm = pg.linear_regression(df[['total_bill', 'size']], df['tip'])
>>> lm.round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 0.67 0.19 3.46 0.00 0.47 0.46 0.29 1.05
1 total_bill 0.09 0.01 10.17 0.00 0.47 0.46 0.07 0.11
2 size 0.19 0.09 2.26 0.02 0.47 0.46 0.02 0.36
The party size is also a significant predictor of tip (T=2.26, p=0.02).
Note that adding this new predictor however only improved the :math:`R^2`
of our model by ~1%.
This function also works with numpy arrays:
>>> X = df[['total_bill', 'size']].to_numpy()
>>> y = df['tip'].to_numpy()
>>> pg.linear_regression(X, y).round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 0.67 0.19 3.46 0.00 0.47 0.46 0.29 1.05
1 x1 0.09 0.01 10.17 0.00 0.47 0.46 0.07 0.11
2 x2 0.19 0.09 2.26 0.02 0.47 0.46 0.02 0.36
3. Get the residuals
>>> # For clarity, only display the first 9 values
>>> np.round(lm.residuals_, 2)[:9]
array([-1.62, -0.55, 0.31, 0.06, -0.11, 0.93, 0.13, -0.81, -0.49])
Using pandas, we can show a summary of the distribution of the residuals:
>>> import pandas as pd
>>> pd.Series(lm.residuals_).describe().round(2)
count 244.00
mean -0.00
std 1.01
min -2.93
25% -0.55
50% -0.09
75% 0.51
max 4.04
dtype: float64
5. No intercept and return only the regression coefficients
Sometimes it may be useful to remove the constant term from the regression,
or to only return the regression coefficients without calculating the
standard errors or p-values. This latter can potentially save you a lot of
time if you need to calculate hundreds of regression and only care about
the coefficients!
>>> pg.linear_regression(X, y, add_intercept=False, coef_only=True)
array([0.1007119 , 0.36209717])
6. Return a dictionnary instead of a dataframe
>>> lm_dict = pg.linear_regression(X, y, as_dataframe=False)
>>> lm_dict.keys()
dict_keys(['names', 'coef', 'se', 'T', 'pval', 'r2', 'adj_r2', 'CI[2.5%]',
'CI[97.5%]', 'df_model', 'df_resid', 'residuals', 'X', 'y',
'pred'])
7. Remove missing values
>>> X[4, 1] = np.nan
>>> y[7] = np.nan
>>> pg.linear_regression(X, y, remove_na=True, coef_only=True)
array([0.65749955, 0.09262059, 0.19927529])
8. Get the relative importance of predictors
>>> lm = pg.linear_regression(X, y, remove_na=True, relimp=True)
>>> lm[['names', 'relimp', 'relimp_perc']]
names relimp relimp_perc
0 Intercept NaN NaN
1 x1 0.342503 73.045583
2 x2 0.126386 26.954417
The ``relimp`` column is a partitioning of the total :math:`R^2` of the
model into individual contribution. Therefore, it sums to the :math:`R^2`
of the full model. The ``relimp_perc`` is normalized to sum to 100%. See
`Groemping 2006 <https://www.jstatsoft.org/article/view/v017i01>`_
for more details.
>>> lm[['relimp', 'relimp_perc']].sum()
relimp 0.468889
relimp_perc 100.000000
dtype: float64
9. Weighted linear regression
>>> X = [1, 2, 3, 4, 5, 6]
>>> y = [10, 22, 11, 13, 13, 16]
>>> w = [1, 0.1, 1, 1, 0.5, 1] # Array of weights. Must be >= 0.
>>> lm = pg.linear_regression(X, y, weights=w)
>>> lm.round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 9.00 2.03 4.42 0.01 0.51 0.39 3.35 14.64
1 x1 1.04 0.50 2.06 0.11 0.51 0.39 -0.36 2.44
| def linear_regression(
X,
y,
add_intercept=True,
weights=None,
coef_only=False,
alpha=0.05,
as_dataframe=True,
remove_na=False,
relimp=False,
):
"""(Multiple) Linear regression.
Parameters
----------
X : array_like
Predictor(s), of shape *(n_samples, n_features)* or *(n_samples)*.
y : array_like
Dependent variable, of shape *(n_samples)*.
add_intercept : bool
If False, assume that the data are already centered. If True, add a
constant term to the model. In this case, the first value in the
output dict is the intercept of the model.
.. note:: It is generally recommended to include a constant term
(intercept) to the model to limit the bias and force the residual
mean to equal zero. The intercept coefficient and p-values
are however rarely meaningful.
weights : array_like
An optional vector of sample weights to be used in the fitting
process, of shape *(n_samples)*. Missing or negative weights are not
allowed. If not null, a weighted least squares is calculated.
.. versionadded:: 0.3.5
coef_only : bool
If True, return only the regression coefficients.
alpha : float
Alpha value used for the confidence intervals.
:math:`\\text{CI} = [\\alpha / 2 ; 1 - \\alpha / 2]`
as_dataframe : bool
If True, returns a pandas DataFrame. If False, returns a dictionnary.
remove_na : bool
If True, apply a listwise deletion of missing values (i.e. the entire
row is removed). Default is False, which will raise an error if missing
values are present in either the predictor(s) or dependent
variable.
relimp : bool
If True, returns the relative importance (= contribution) of
predictors. This is irrelevant when the predictors are uncorrelated:
the total :math:`R^2` of the model is simply the sum of each univariate
regression :math:`R^2`-values. However, this does not apply when
predictors are correlated. Instead, the total :math:`R^2` of the model
is partitioned by averaging over all combinations of predictors,
as done in the `relaimpo
<https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf>`_
R package (``calc.relimp(type="lmg")``).
.. warning:: The computation time roughly doubles for each
additional predictor and therefore this can be extremely slow for
models with more than 12-15 predictors.
.. versionadded:: 0.3.0
Returns
-------
stats : :py:class:`pandas.DataFrame` or dict
Linear regression summary:
* ``'names'``: name of variable(s) in the model (e.g. x1, x2...)
* ``'coef'``: regression coefficients
* ``'se'``: standard errors
* ``'T'``: T-values
* ``'pval'``: p-values
* ``'r2'``: coefficient of determination (:math:`R^2`)
* ``'adj_r2'``: adjusted :math:`R^2`
* ``'CI[2.5%]'``: lower confidence intervals
* ``'CI[97.5%]'``: upper confidence intervals
* ``'relimp'``: relative contribution of each predictor to the final\
:math:`R^2` (only if ``relimp=True``).
* ``'relimp_perc'``: percent relative contribution
In addition, the output dataframe comes with hidden attributes such as
the residuals, and degrees of freedom of the model and residuals, which
can be accessed as follow, respectively:
>>> lm = pg.linear_regression() # doctest: +SKIP
>>> lm.residuals_, lm.df_model_, lm.df_resid_ # doctest: +SKIP
Note that to follow scikit-learn convention, these hidden atributes end
with an "_". When ``as_dataframe=False`` however, these attributes
are no longer hidden and can be accessed as any other keys in the
output dictionary.
>>> lm = pg.linear_regression() # doctest: +SKIP
>>> lm['residuals'], lm['df_model'], lm['df_resid'] # doctest: +SKIP
When ``as_dataframe=False`` the dictionary also contains the
processed ``X`` and ``y`` arrays (i.e, with NaNs removed if
``remove_na=True``) and the model's predicted values ``pred``.
>>> lm['X'], lm['y'], lm['pred'] # doctest: +SKIP
For a weighted least squares fit, the weighted ``Xw`` and ``yw``
arrays are included in the dictionary.
>>> lm['Xw'], lm['yw'] # doctest: +SKIP
See also
--------
logistic_regression, mediation_analysis, corr
Notes
-----
The :math:`\\beta` coefficients are estimated using an ordinary least
squares (OLS) regression, as implemented in the
:py:func:`scipy.linalg.lstsq` function. The OLS method minimizes
the sum of squared residuals, and leads to a closed-form expression for
the estimated :math:`\\beta`:
.. math:: \\hat{\\beta} = (X^TX)^{-1} X^Ty
It is generally recommended to include a constant term (intercept) to the
model to limit the bias and force the residual mean to equal zero.
Note that intercept coefficient and p-values are however rarely meaningful.
The standard error of the estimates is a measure of the accuracy of the
prediction defined as:
.. math:: \\sigma = \\sqrt{\\text{MSE} \\cdot (X^TX)^{-1}}
where :math:`\\text{MSE}` is the mean squared error,
.. math::
\\text{MSE} = \\frac{SS_{\\text{resid}}}{n - p - 1}
= \\frac{\\sum{(\\text{true} - \\text{pred})^2}}{n - p - 1}
:math:`p` is the total number of predictor variables in the model
(excluding the intercept) and :math:`n` is the sample size.
Using the :math:`\\beta` coefficients and the standard errors,
the T-values can be obtained:
.. math:: T = \\frac{\\beta}{\\sigma}
and the p-values approximated using a T-distribution with
:math:`n - p - 1` degrees of freedom.
The coefficient of determination (:math:`R^2`) is defined as:
.. math:: R^2 = 1 - (\\frac{SS_{\\text{resid}}}{SS_{\\text{total}}})
The adjusted :math:`R^2` is defined as:
.. math:: \\overline{R}^2 = 1 - (1 - R^2) \\frac{n - 1}{n - p - 1}
The relative importance (``relimp``) column is a partitioning of the
total :math:`R^2` of the model into individual :math:`R^2` contribution.
This is calculated by taking the average over average contributions in
models of different sizes. For more details, please refer to
`Groemping et al. 2006 <http://dx.doi.org/10.18637/jss.v017.i01>`_
and the R package `relaimpo
<https://cran.r-project.org/web/packages/relaimpo/relaimpo.pdf>`_.
Note that Pingouin will automatically remove any duplicate columns
from :math:`X`, as well as any column with only one unique value
(constant), excluding the intercept.
Results have been compared against sklearn, R, statsmodels and JASP.
Examples
--------
1. Simple linear regression using columns of a pandas dataframe
In this first example, we'll use the tips dataset to see how well we
can predict the waiter's tip (in dollars) based on the total bill (also
in dollars).
>>> import numpy as np
>>> import pingouin as pg
>>> df = pg.read_dataset('tips')
>>> # Let's predict the tip ($) based on the total bill (also in $)
>>> lm = pg.linear_regression(df['total_bill'], df['tip'])
>>> lm.round(2)
names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%]
0 Intercept 0.92 0.16 5.76 0.0 0.46 0.45 0.61 1.23
1 total_bill 0.11 0.01 14.26 0.0 0.46 0.45 0.09 0.12
It comes as no surprise that total bill is indeed a significant predictor
of the waiter's tip (T=14.26, p<0.05). The :math:`R^2` of the model is 0.46
and the adjusted :math:`R^2` is 0.45, which means that our model roughly
explains ~45% of the total variance in the tip amount.
2. Multiple linear regression
We can also have more than one predictor and run a multiple linear
regression. Below, we add the party size as a second predictor of tip.
>>> # We'll add a second | (X, y, add_intercept=True, weights=None, coef_only=False, alpha=0.05, as_dataframe=True, remove_na=False, relimp=False) | [
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|
32,016 | pingouin.datasets | list_dataset | List available example datasets.
Returns
-------
datasets : :py:class:`pandas.DataFrame`
A dataframe with the name, description and reference of all the
datasets included in Pingouin.
Examples
--------
>>> import pingouin as pg
>>> all_datasets = pg.list_dataset()
>>> all_datasets.index.tolist()
['ancova',
'anova',
'anova2',
'anova2_unbalanced',
'anova3',
'anova3_unbalanced',
'blandaltman',
'chi2_independence',
'chi2_mcnemar',
'circular',
'cochran',
'cronbach_alpha',
'cronbach_wide_missing',
'icc',
'mediation',
'mixed_anova',
'mixed_anova_unbalanced',
'multivariate',
'pairwise_corr',
'pairwise_tests',
'pairwise_tests_missing',
'partial_corr',
'penguins',
'rm_anova',
'rm_anova_wide',
'rm_anova2',
'rm_corr',
'rm_missing',
'tips']
| def list_dataset():
"""List available example datasets.
Returns
-------
datasets : :py:class:`pandas.DataFrame`
A dataframe with the name, description and reference of all the
datasets included in Pingouin.
Examples
--------
>>> import pingouin as pg
>>> all_datasets = pg.list_dataset()
>>> all_datasets.index.tolist()
['ancova',
'anova',
'anova2',
'anova2_unbalanced',
'anova3',
'anova3_unbalanced',
'blandaltman',
'chi2_independence',
'chi2_mcnemar',
'circular',
'cochran',
'cronbach_alpha',
'cronbach_wide_missing',
'icc',
'mediation',
'mixed_anova',
'mixed_anova_unbalanced',
'multivariate',
'pairwise_corr',
'pairwise_tests',
'pairwise_tests_missing',
'partial_corr',
'penguins',
'rm_anova',
'rm_anova_wide',
'rm_anova2',
'rm_corr',
'rm_missing',
'tips']
"""
return dts.set_index("dataset")
| () | [
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|
32,017 | pingouin.regression | logistic_regression | (Multiple) Binary logistic regression.
Parameters
----------
X : array_like
Predictor(s), of shape *(n_samples, n_features)* or *(n_samples)*.
y : array_like
Dependent variable, of shape *(n_samples)*.
``y`` must be binary, i.e. only contains 0 or 1. Multinomial logistic
regression is not supported.
coef_only : bool
If True, return only the regression coefficients.
alpha : float
Alpha value used for the confidence intervals.
:math:`\text{CI} = [\alpha / 2 ; 1 - \alpha / 2]`
as_dataframe : bool
If True, returns a pandas DataFrame. If False, returns a dictionnary.
remove_na : bool
If True, apply a listwise deletion of missing values (i.e. the entire
row is removed). Default is False, which will raise an error if missing
values are present in either the predictor(s) or dependent
variable.
**kwargs : optional
Optional arguments passed to
:py:class:`sklearn.linear_model.LogisticRegression` (see Notes).
Returns
-------
stats : :py:class:`pandas.DataFrame` or dict
Logistic regression summary:
* ``'names'``: name of variable(s) in the model (e.g. x1, x2...)
* ``'coef'``: regression coefficients (log-odds)
* ``'se'``: standard error
* ``'z'``: z-scores
* ``'pval'``: two-tailed p-values
* ``'CI[2.5%]'``: lower confidence interval
* ``'CI[97.5%]'``: upper confidence interval
See also
--------
linear_regression
Notes
-----
.. caution:: This function is a wrapper around the
:py:class:`sklearn.linear_model.LogisticRegression` class. However,
Pingouin internally disables the L2 regularization and changes the
default solver to 'newton-cg' to obtain results that are similar to R and
statsmodels.
Logistic regression assumes that the log-odds (the logarithm of the
odds) for the value labeled "1" in the response variable is a linear
combination of the predictor variables. The log-odds are given by the
`logit <https://en.wikipedia.org/wiki/Logit>`_ function,
which map a probability :math:`p` of the response variable being "1"
from :math:`[0, 1)` to :math:`(-\infty, +\infty)`.
.. math:: \text{logit}(p) = \ln \frac{p}{1 - p} = \beta_0 + \beta X
The odds of the response variable being "1" can be obtained by
exponentiating the log-odds:
.. math:: \frac{p}{1 - p} = e^{\beta_0 + \beta X}
and the probability of the response variable being "1" is given by the
`logistic function <https://en.wikipedia.org/wiki/Logistic_function>`_:
.. math:: p = \frac{1}{1 + e^{-(\beta_0 + \beta X})}
The first coefficient is always the constant term (intercept) of
the model. Pingouin will automatically add the intercept
to your predictor(s) matrix, therefore, :math:`X` should not include a
constant term. Pingouin will remove any constant term (e.g column with only
one unique value), or duplicate columns from :math:`X`.
The calculation of the p-values and confidence interval is adapted from a
`code by Rob Speare
<https://gist.github.com/rspeare/77061e6e317896be29c6de9a85db301d>`_.
Results have been compared against statsmodels, R, and JASP.
Examples
--------
1. Simple binary logistic regression.
In this first example, we'll use the
`penguins dataset <https://github.com/allisonhorst/palmerpenguins>`_
to see how well we can predict the sex of penguins based on their
bodies mass.
>>> import numpy as np
>>> import pandas as pd
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> # Let's first convert the target variable from string to boolean:
>>> df['male'] = (df['sex'] == 'male').astype(int) # male: 1, female: 0
>>> # Since there are missing values in our outcome variable, we need to
>>> # set `remove_na=True` otherwise regression will fail.
>>> lom = pg.logistic_regression(df['body_mass_g'], df['male'],
... remove_na=True)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -5.16 0.71 -7.24 0.0 -6.56 -3.77
1 body_mass_g 0.00 0.00 7.24 0.0 0.00 0.00
Body mass is a significant predictor of sex (p<0.001). Here, it
could be useful to rescale our predictor variable from *g* to *kg*
(e.g divide by 1000) in order to get more intuitive coefficients and
confidence intervals:
>>> df['body_mass_kg'] = df['body_mass_g'] / 1000
>>> lom = pg.logistic_regression(df['body_mass_kg'], df['male'],
... remove_na=True)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -5.16 0.71 -7.24 0.0 -6.56 -3.77
1 body_mass_kg 1.23 0.17 7.24 0.0 0.89 1.56
2. Multiple binary logistic regression
We'll now add the species as a categorical predictor in our model. To do
so, we first need to dummy-code our categorical variable, dropping the
first level of our categorical variable (species = Adelie) which will be
used as the reference level:
>>> df = pd.get_dummies(df, columns=['species'], dtype=float, drop_first=True)
>>> X = df[['body_mass_kg', 'species_Chinstrap', 'species_Gentoo']]
>>> y = df['male']
>>> lom = pg.logistic_regression(X, y, remove_na=True)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -26.24 2.84 -9.24 0.00 -31.81 -20.67
1 body_mass_kg 7.10 0.77 9.23 0.00 5.59 8.61
2 species_Chinstrap -0.13 0.42 -0.31 0.75 -0.96 0.69
3 species_Gentoo -9.72 1.12 -8.65 0.00 -11.92 -7.52
3. Using NumPy aray and returning only the coefficients
>>> pg.logistic_regression(X.to_numpy(), y.to_numpy(), coef_only=True,
... remove_na=True)
array([-26.23906892, 7.09826571, -0.13180626, -9.71718529])
4. Passing custom parameters to sklearn
>>> lom = pg.logistic_regression(X, y, solver='sag', max_iter=10000,
... random_state=42, remove_na=True)
>>> print(lom['coef'].to_numpy())
[-25.98248153 7.02881472 -0.13119779 -9.62247569]
**How to interpret the log-odds coefficients?**
We'll use the `Wikipedia example
<https://en.wikipedia.org/wiki/Logistic_regression#Probability_of_passing_an_exam_versus_hours_of_study>`_
of the probability of passing an exam
versus the hours of study:
*A group of 20 students spends between 0 and 6 hours studying for an
exam. How does the number of hours spent studying affect the
probability of the student passing the exam?*
>>> # First, let's create the dataframe
>>> Hours = [0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 1.75, 2.00, 2.25, 2.50,
... 2.75, 3.00, 3.25, 3.50, 4.00, 4.25, 4.50, 4.75, 5.00, 5.50]
>>> Pass = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]
>>> df = pd.DataFrame({'HoursStudy': Hours, 'PassExam': Pass})
>>> # And then run the logistic regression
>>> lr = pg.logistic_regression(df['HoursStudy'], df['PassExam']).round(3)
>>> lr
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -4.078 1.761 -2.316 0.021 -7.529 -0.626
1 HoursStudy 1.505 0.629 2.393 0.017 0.272 2.737
The ``Intercept`` coefficient (-4.078) is the log-odds of ``PassExam=1``
when ``HoursStudy=0``. The odds ratio can be obtained by exponentiating
the log-odds:
>>> np.exp(-4.078)
0.016941314421496552
i.e. :math:`0.017:1`. Conversely the odds of failing the exam are
:math:`(1/0.017) \approx 59:1`.
The probability can then be obtained with the following equation
.. math:: p = \frac{1}{1 + e^{-(-4.078 + 0 * 1.505)}}
>>> 1 / (1 + np.exp(-(-4.078)))
0.016659087580814722
The ``HoursStudy`` coefficient (1.505) means that for each additional hour
of study, the log-odds of passing the exam increase by 1.505, and the odds
are multipled by :math:`e^{1.505} \approx 4.50`.
For example, a student who studies 2 hours has a probability of passing
the exam of 25%:
>>> 1 / (1 + np.exp(-(-4.078 + 2 * 1.505)))
0.2557836148964987
The table below shows the probability of passing the exam for several
values of ``HoursStudy``:
+----------------+----------+----------------+------------------+
| Hours of Study | Log-odds | Odds | Probability |
+================+==========+================+==================+
| 0 | −4.08 | 0.017 ≈ 1:59 | 0.017 |
+----------------+----------+----------------+------------------+
| 1 | −2.57 | 0.076 ≈ 1:13 | 0.07 |
+----------------+----------+----------------+------------------+
| 2 | −1.07 | 0.34 ≈ 1:3 | 0.26 |
+----------------+----------+----------------+------------------+
| 3 | 0.44 | 1.55 | 0.61 |
+----------------+----------+----------------+------------------+
| 4 | 1.94 | 6.96 | 0.87 |
+----------------+----------+----------------+------------------+
| 5 | 3.45 | 31.4 | 0.97 |
+----------------+----------+----------------+------------------+
| 6 | 4.96 | 141.4 | 0.99 |
+----------------+----------+----------------+------------------+
| def logistic_regression(
X, y, coef_only=False, alpha=0.05, as_dataframe=True, remove_na=False, **kwargs
):
"""(Multiple) Binary logistic regression.
Parameters
----------
X : array_like
Predictor(s), of shape *(n_samples, n_features)* or *(n_samples)*.
y : array_like
Dependent variable, of shape *(n_samples)*.
``y`` must be binary, i.e. only contains 0 or 1. Multinomial logistic
regression is not supported.
coef_only : bool
If True, return only the regression coefficients.
alpha : float
Alpha value used for the confidence intervals.
:math:`\\text{CI} = [\\alpha / 2 ; 1 - \\alpha / 2]`
as_dataframe : bool
If True, returns a pandas DataFrame. If False, returns a dictionnary.
remove_na : bool
If True, apply a listwise deletion of missing values (i.e. the entire
row is removed). Default is False, which will raise an error if missing
values are present in either the predictor(s) or dependent
variable.
**kwargs : optional
Optional arguments passed to
:py:class:`sklearn.linear_model.LogisticRegression` (see Notes).
Returns
-------
stats : :py:class:`pandas.DataFrame` or dict
Logistic regression summary:
* ``'names'``: name of variable(s) in the model (e.g. x1, x2...)
* ``'coef'``: regression coefficients (log-odds)
* ``'se'``: standard error
* ``'z'``: z-scores
* ``'pval'``: two-tailed p-values
* ``'CI[2.5%]'``: lower confidence interval
* ``'CI[97.5%]'``: upper confidence interval
See also
--------
linear_regression
Notes
-----
.. caution:: This function is a wrapper around the
:py:class:`sklearn.linear_model.LogisticRegression` class. However,
Pingouin internally disables the L2 regularization and changes the
default solver to 'newton-cg' to obtain results that are similar to R and
statsmodels.
Logistic regression assumes that the log-odds (the logarithm of the
odds) for the value labeled "1" in the response variable is a linear
combination of the predictor variables. The log-odds are given by the
`logit <https://en.wikipedia.org/wiki/Logit>`_ function,
which map a probability :math:`p` of the response variable being "1"
from :math:`[0, 1)` to :math:`(-\\infty, +\\infty)`.
.. math:: \\text{logit}(p) = \\ln \\frac{p}{1 - p} = \\beta_0 + \\beta X
The odds of the response variable being "1" can be obtained by
exponentiating the log-odds:
.. math:: \\frac{p}{1 - p} = e^{\\beta_0 + \\beta X}
and the probability of the response variable being "1" is given by the
`logistic function <https://en.wikipedia.org/wiki/Logistic_function>`_:
.. math:: p = \\frac{1}{1 + e^{-(\\beta_0 + \\beta X})}
The first coefficient is always the constant term (intercept) of
the model. Pingouin will automatically add the intercept
to your predictor(s) matrix, therefore, :math:`X` should not include a
constant term. Pingouin will remove any constant term (e.g column with only
one unique value), or duplicate columns from :math:`X`.
The calculation of the p-values and confidence interval is adapted from a
`code by Rob Speare
<https://gist.github.com/rspeare/77061e6e317896be29c6de9a85db301d>`_.
Results have been compared against statsmodels, R, and JASP.
Examples
--------
1. Simple binary logistic regression.
In this first example, we'll use the
`penguins dataset <https://github.com/allisonhorst/palmerpenguins>`_
to see how well we can predict the sex of penguins based on their
bodies mass.
>>> import numpy as np
>>> import pandas as pd
>>> import pingouin as pg
>>> df = pg.read_dataset('penguins')
>>> # Let's first convert the target variable from string to boolean:
>>> df['male'] = (df['sex'] == 'male').astype(int) # male: 1, female: 0
>>> # Since there are missing values in our outcome variable, we need to
>>> # set `remove_na=True` otherwise regression will fail.
>>> lom = pg.logistic_regression(df['body_mass_g'], df['male'],
... remove_na=True)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -5.16 0.71 -7.24 0.0 -6.56 -3.77
1 body_mass_g 0.00 0.00 7.24 0.0 0.00 0.00
Body mass is a significant predictor of sex (p<0.001). Here, it
could be useful to rescale our predictor variable from *g* to *kg*
(e.g divide by 1000) in order to get more intuitive coefficients and
confidence intervals:
>>> df['body_mass_kg'] = df['body_mass_g'] / 1000
>>> lom = pg.logistic_regression(df['body_mass_kg'], df['male'],
... remove_na=True)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -5.16 0.71 -7.24 0.0 -6.56 -3.77
1 body_mass_kg 1.23 0.17 7.24 0.0 0.89 1.56
2. Multiple binary logistic regression
We'll now add the species as a categorical predictor in our model. To do
so, we first need to dummy-code our categorical variable, dropping the
first level of our categorical variable (species = Adelie) which will be
used as the reference level:
>>> df = pd.get_dummies(df, columns=['species'], dtype=float, drop_first=True)
>>> X = df[['body_mass_kg', 'species_Chinstrap', 'species_Gentoo']]
>>> y = df['male']
>>> lom = pg.logistic_regression(X, y, remove_na=True)
>>> lom.round(2)
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -26.24 2.84 -9.24 0.00 -31.81 -20.67
1 body_mass_kg 7.10 0.77 9.23 0.00 5.59 8.61
2 species_Chinstrap -0.13 0.42 -0.31 0.75 -0.96 0.69
3 species_Gentoo -9.72 1.12 -8.65 0.00 -11.92 -7.52
3. Using NumPy aray and returning only the coefficients
>>> pg.logistic_regression(X.to_numpy(), y.to_numpy(), coef_only=True,
... remove_na=True)
array([-26.23906892, 7.09826571, -0.13180626, -9.71718529])
4. Passing custom parameters to sklearn
>>> lom = pg.logistic_regression(X, y, solver='sag', max_iter=10000,
... random_state=42, remove_na=True)
>>> print(lom['coef'].to_numpy())
[-25.98248153 7.02881472 -0.13119779 -9.62247569]
**How to interpret the log-odds coefficients?**
We'll use the `Wikipedia example
<https://en.wikipedia.org/wiki/Logistic_regression#Probability_of_passing_an_exam_versus_hours_of_study>`_
of the probability of passing an exam
versus the hours of study:
*A group of 20 students spends between 0 and 6 hours studying for an
exam. How does the number of hours spent studying affect the
probability of the student passing the exam?*
>>> # First, let's create the dataframe
>>> Hours = [0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 1.75, 2.00, 2.25, 2.50,
... 2.75, 3.00, 3.25, 3.50, 4.00, 4.25, 4.50, 4.75, 5.00, 5.50]
>>> Pass = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]
>>> df = pd.DataFrame({'HoursStudy': Hours, 'PassExam': Pass})
>>> # And then run the logistic regression
>>> lr = pg.logistic_regression(df['HoursStudy'], df['PassExam']).round(3)
>>> lr
names coef se z pval CI[2.5%] CI[97.5%]
0 Intercept -4.078 1.761 -2.316 0.021 -7.529 -0.626
1 HoursStudy 1.505 0.629 2.393 0.017 0.272 2.737
The ``Intercept`` coefficient (-4.078) is the log-odds of ``PassExam=1``
when ``HoursStudy=0``. The odds ratio can be obtained by exponentiating
the log-odds:
>>> np.exp(-4.078)
0.016941314421496552
i.e. :math:`0.017:1`. Conversely the odds of failing the exam are
:math:`(1/0.017) \\approx 59:1`.
The probability can then be obtained with the following equation
.. math:: p = \\frac{1}{1 + e^{-(-4.078 + 0 * 1.505)}}
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|
32,018 | pingouin.nonparametric | mad |
Median Absolute Deviation (MAD) along given axis of an array.
Parameters
----------
a : array-like
Input array.
normalize : boolean.
If True, scale by a normalization constant :math:`c \approx 0.67`
to ensure consistency with the standard deviation for normally
distributed data.
axis : int or None, optional
Axis along which the MAD is computed. Default is 0.
Can also be None to compute the MAD over the entire array.
Returns
-------
mad : float
mad = median(abs(a - median(a))) / c
See also
--------
madmedianrule, numpy.std
Notes
-----
The `median absolute deviation
<https://en.wikipedia.org/wiki/Median_absolute_deviation>`_ (MAD) computes
the median over the absolute deviations from the median. It is a measure of
dispersion similar to the standard deviation, but is more robust to
outliers.
SciPy 1.3 and higher includes a similar function:
:py:func:`scipy.stats.median_abs_deviation`.
Please note that missing values are automatically removed.
Examples
--------
>>> from pingouin import mad
>>> a = [1.2, 5.4, 3.2, 7.8, 2.5]
>>> mad(a)
2.965204437011204
>>> mad(a, normalize=False)
2.0
2D arrays with missing values (axis handling example)
>>> import numpy as np
>>> np.random.seed(123)
>>> w = np.random.normal(size=(5, 10))
>>> w[3, 2] = np.nan
>>> mad(w) # Axis = 0 (default) = iterate over the columns
array([0.60304023, 2.35057834, 0.90350696, 1.28599837, 1.16024152,
0.38653752, 1.92564066, 1.2480913 , 0.42580373, 1.69814622])
>>> mad(w, axis=1) # Axis = 1 = iterate over the rows
array([1.32639022, 1.19295036, 1.41198672, 0.78020689, 1.01531254])
>>> mad(w, axis=None) # Axis = None = over the entire array
1.1607762457644006
Compare with Scipy >= 1.3
>>> from scipy.stats import median_abs_deviation
>>> median_abs_deviation(w, scale='normal', axis=None, nan_policy='omit')
1.1607762457644006
| def mad(a, normalize=True, axis=0):
"""
Median Absolute Deviation (MAD) along given axis of an array.
Parameters
----------
a : array-like
Input array.
normalize : boolean.
If True, scale by a normalization constant :math:`c \\approx 0.67`
to ensure consistency with the standard deviation for normally
distributed data.
axis : int or None, optional
Axis along which the MAD is computed. Default is 0.
Can also be None to compute the MAD over the entire array.
Returns
-------
mad : float
mad = median(abs(a - median(a))) / c
See also
--------
madmedianrule, numpy.std
Notes
-----
The `median absolute deviation
<https://en.wikipedia.org/wiki/Median_absolute_deviation>`_ (MAD) computes
the median over the absolute deviations from the median. It is a measure of
dispersion similar to the standard deviation, but is more robust to
outliers.
SciPy 1.3 and higher includes a similar function:
:py:func:`scipy.stats.median_abs_deviation`.
Please note that missing values are automatically removed.
Examples
--------
>>> from pingouin import mad
>>> a = [1.2, 5.4, 3.2, 7.8, 2.5]
>>> mad(a)
2.965204437011204
>>> mad(a, normalize=False)
2.0
2D arrays with missing values (axis handling example)
>>> import numpy as np
>>> np.random.seed(123)
>>> w = np.random.normal(size=(5, 10))
>>> w[3, 2] = np.nan
>>> mad(w) # Axis = 0 (default) = iterate over the columns
array([0.60304023, 2.35057834, 0.90350696, 1.28599837, 1.16024152,
0.38653752, 1.92564066, 1.2480913 , 0.42580373, 1.69814622])
>>> mad(w, axis=1) # Axis = 1 = iterate over the rows
array([1.32639022, 1.19295036, 1.41198672, 0.78020689, 1.01531254])
>>> mad(w, axis=None) # Axis = None = over the entire array
1.1607762457644006
Compare with Scipy >= 1.3
>>> from scipy.stats import median_abs_deviation
>>> median_abs_deviation(w, scale='normal', axis=None, nan_policy='omit')
1.1607762457644006
"""
a = np.asarray(a)
if axis is None:
# Calculate the MAD over the entire array
a = np.ravel(a)
axis = 0
c = scipy.stats.norm.ppf(3 / 4.0) if normalize else 1
center = np.apply_over_axes(np.nanmedian, a, axis)
return np.nanmedian((np.fabs(a - center)) / c, axis=axis)
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|
32,019 | pingouin.nonparametric | madmedianrule | Robust outlier detection based on the MAD-median rule.
Parameters
----------
a : array-like
Input array. Must be one-dimensional.
Returns
-------
outliers: boolean (same shape as a)
Boolean array indicating whether each sample is an outlier (True) or
not (False).
See also
--------
mad
Notes
-----
The MAD-median-rule ([1]_, [2]_) will refer to declaring :math:`X_i`
an outlier if
.. math::
\frac{\left | X_i - M \right |}{\text{MAD}_{\text{norm}}} > K,
where :math:`M` is the median of :math:`X`,
:math:`\text{MAD}_{\text{norm}}` the normalized median absolute deviation
of :math:`X`, and :math:`K` is the square
root of the .975 quantile of a :math:`X^2` distribution with one degree
of freedom, which is roughly equal to 2.24.
References
----------
.. [1] Hall, P., Welsh, A.H., 1985. Limit theorems for the median
deviation. Ann. Inst. Stat. Math. 37, 27–36.
https://doi.org/10.1007/BF02481078
.. [2] Wilcox, R. R. Introduction to Robust Estimation and Hypothesis
Testing. (Academic Press, 2011).
Examples
--------
>>> import pingouin as pg
>>> a = [-1.09, 1., 0.28, -1.51, -0.58, 6.61, -2.43, -0.43]
>>> pg.madmedianrule(a)
array([False, False, False, False, False, True, False, False])
| def madmedianrule(a):
"""Robust outlier detection based on the MAD-median rule.
Parameters
----------
a : array-like
Input array. Must be one-dimensional.
Returns
-------
outliers: boolean (same shape as a)
Boolean array indicating whether each sample is an outlier (True) or
not (False).
See also
--------
mad
Notes
-----
The MAD-median-rule ([1]_, [2]_) will refer to declaring :math:`X_i`
an outlier if
.. math::
\\frac{\\left | X_i - M \\right |}{\\text{MAD}_{\\text{norm}}} > K,
where :math:`M` is the median of :math:`X`,
:math:`\\text{MAD}_{\\text{norm}}` the normalized median absolute deviation
of :math:`X`, and :math:`K` is the square
root of the .975 quantile of a :math:`X^2` distribution with one degree
of freedom, which is roughly equal to 2.24.
References
----------
.. [1] Hall, P., Welsh, A.H., 1985. Limit theorems for the median
deviation. Ann. Inst. Stat. Math. 37, 27–36.
https://doi.org/10.1007/BF02481078
.. [2] Wilcox, R. R. Introduction to Robust Estimation and Hypothesis
Testing. (Academic Press, 2011).
Examples
--------
>>> import pingouin as pg
>>> a = [-1.09, 1., 0.28, -1.51, -0.58, 6.61, -2.43, -0.43]
>>> pg.madmedianrule(a)
array([False, False, False, False, False, True, False, False])
"""
a = np.asarray(a)
assert a.ndim == 1, "Only 1D array / list are supported for this function."
k = np.sqrt(scipy.stats.chi2.ppf(0.975, 1))
return (np.fabs(a - np.median(a)) / mad(a)) > k
| (a) | [
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|
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