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organic carbon either by osmotrophy, myzotrophy, or phagotrophy. Some unicellular species of green algae, many golden algae, euglenids, dinoflagellates, and other algae have become heterotrophs (also called colorless or apochlorotic algae), sometimes parasitic, relying entirely on external energy sources and have limited or no photosynthetic apparatus. Some other heterotrophic organisms, such as the apicomplexans, are also derived from cells whose ancestors possessed plastids, but are not traditionally considered as algae. Algae have photosynthetic machinery ultimately derived from cyanobacteria that produce oxygen as a by-product of photosynthesis, unlike other photosynthetic bacteria such as purple and green sulfur bacteria. Fossilized filamentous algae
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Algae
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] |
8602
|
from the Vindhya basin have been dated back to 1.6 to 1.7 billion years ago. The singular "alga" is the Latin word for "seaweed" and retains that meaning in English. The etymology is obscure. Although some speculate that it is related to Latin "algēre", "be cold", no reason is known to associate seaweed with temperature. A more likely source is "alliga", "binding, entwining". The Ancient Greek word for seaweed was φῦκος ("phŷcos"), which could mean either the seaweed (probably red algae) or a red dye derived from it. The Latinization, "fūcus", meant primarily the cosmetic rouge. The etymology is uncertain,
|
Algae
|
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] |
8603
|
but a strong candidate has long been some word related to the Biblical פוך ("pūk"), "paint" (if not that word itself), a cosmetic eye-shadow used by the ancient Egyptians and other inhabitants of the eastern Mediterranean. It could be any color: black, red, green, or blue. Accordingly, the modern study of marine and freshwater algae is called either phycology or algology, depending on whether the Greek or Latin root is used. The name "Fucus" appears in a number of taxa. The algae contain chloroplasts that are similar in structure to cyanobacteria. Chloroplasts contain circular DNA like that in cyanobacteria and
|
Algae
|
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] |
8604
|
are interpreted as representing reduced endosymbiotic cyanobacteria. However, the exact origin of the chloroplasts is different among separate lineages of algae, reflecting their acquisition during different endosymbiotic events. The table below describes the composition of the three major groups of algae. Their lineage relationships are shown in the figure in the upper right. Many of these groups contain some members that are no longer photosynthetic. Some retain plastids, but not chloroplasts, while others have lost plastids entirely. Phylogeny based on plastid not nucleocytoplasmic genealogy: Linnaeus, in "Species Plantarum" (1753), the starting point for modern botanical nomenclature, recognized 14 genera of
|
Algae
|
[
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] |
8605
|
algae, of which only four are currently considered among algae. In "Systema Naturae", Linnaeus described the genera "Volvox" and "Corallina", and a species of "Acetabularia" (as "Madrepora"), among the animals. In 1768, Samuel Gottlieb Gmelin (1744–1774) published the "Historia Fucorum", the first work dedicated to marine algae and the first book on marine biology to use the then new binomial nomenclature of Linnaeus. It included elaborate illustrations of seaweed and marine algae on folded leaves. W.H.Harvey (1811—1866) and Lamouroux (1813) were the first to divide macroscopic algae into four divisions based on their pigmentation. This is the first use of
|
Algae
|
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0.2398974448442459,
0.4948883056640625,
-0.18220838904380798,
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0.23544272780418396,
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0.010089615359902382,
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0.5564876794815063,
0.6205757260322571
] |
8606
|
a biochemical criterion in plant systematics. Harvey's four divisions are: red algae (Rhodospermae), brown algae (Melanospermae), green algae (Chlorospermae), and Diatomaceae. At this time, microscopic algae were discovered and reported by a different group of workers (e.g., O. F. Müller and Ehrenberg) studying the Infusoria (microscopic organisms). Unlike macroalgae, which were clearly viewed as plants, microalgae were frequently considered animals because they are often motile. Even the nonmotile (coccoid) microalgae were sometimes merely seen as stages of the lifecycle of plants, macroalgae, or animals. Although used as a taxonomic category in some pre-Darwinian classifications, e.g., Linnaeus (1753), de Jussieu (1789),
|
Algae
|
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] |
8607
|
Horaninow (1843), Agassiz (1859), Wilson & Cassin (1864), in further classifications, the "algae" are seen as an artificial, polyphyletic group. Throughout the 20th century, most classifications treated the following groups as divisions or classes of algae: cyanophytes, rhodophytes, chrysophytes, xanthophytes, bacillariophytes, phaeophytes, pyrrhophytes (cryptophytes and dinophytes), euglenophytes, and chlorophytes. Later, many new groups were discovered (e.g., Bolidophyceae), and others were splintered from older groups: charophytes and glaucophytes (from chlorophytes), many heterokontophytes (e.g., synurophytes from chrysophytes, or eustigmatophytes from xanthophytes), haptophytes (from chrysophytes), and chlorarachniophytes (from xanthophytes). With the abandonment of plant-animal dichotomous classification, most groups of algae (sometimes all) were
|
Algae
|
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] |
8608
|
included in Protista, later also abandoned in favour of Eukaryota. However, as a legacy of the older plant life scheme, some groups that were also treated as protozoans in the past still have duplicated classifications (see ambiregnal protists). Some parasitic algae (e.g., the green algae "Prototheca" and "Helicosporidium", parasites of metazoans, or "Cephaleuros", parasites of plants) were originally classified as fungi, sporozoans, or protistans of "incertae sedis", while others (e.g., the green algae "Phyllosiphon" and "Rhodochytrium", parasites of plants, or the red algae "Pterocladiophila" and "Gelidiocolax mammillatus", parasites of other red algae, or the dinoflagellates "Oodinium", parasites of fish) had
|
Algae
|
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] |
8609
|
their relationship with algae conjectured early. In other cases, some groups were originally characterized as parasitic algae (e.g., "Chlorochytrium"), but later were seen as endophytic algae. Some filamentous bacteria (e.g., "Beggiatoa") were originally seen as algae. Furthermore, groups like the apicomplexans are also parasites derived from ancestors that possessed plastids, but are not included in any group traditionally seen as algae. The first land plants probably evolved from shallow freshwater charophyte algae much like "Chara" almost 500 million years ago. These probably had an isomorphic alternation of generations and were probably filamentous. Fossils of isolated land plant spores suggest land
|
Algae
|
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] |
8610
|
plants may have been around as long as 475 million years ago. A range of algal morphologies is exhibited, and convergence of features in unrelated groups is common. The only groups to exhibit three-dimensional multicellular thalli are the reds and browns, and some chlorophytes. Apical growth is constrained to subsets of these groups: the florideophyte reds, various browns, and the charophytes. The form of charophytes is quite different from those of reds and browns, because they have distinct nodes, separated by internode 'stems'; whorls of branches reminiscent of the horsetails occur at the nodes. Conceptacles are another polyphyletic trait; they
|
Algae
|
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] |
8611
|
appear in the coralline algae and the Hildenbrandiales, as well as the browns. Most of the simpler algae are unicellular flagellates or amoeboids, but colonial and nonmotile forms have developed independently among several of the groups. Some of the more common organizational levels, more than one of which may occur in the lifecycle of a species, are In three lines, even higher levels of organization have been reached, with full tissue differentiation. These are the brown algae,—some of which may reach 50 m in length (kelps)—the red algae, and the green algae. The most complex forms are found among the
|
Algae
|
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] |
8612
|
charophyte algae (see Charales and Charophyta), in a lineage that eventually led to the higher land plants. The innovation that defines these nonalgal plants is the presence of female reproductive organs with protective cell layers that protect the zygote and developing embryo. Hence, the land plants are referred to as the Embryophytes. Many algae, particularly members of the Characeae, have served as model experimental organisms to understand the mechanisms of the water permeability of membranes, osmoregulation, turgor regulation, salt tolerance, cytoplasmic streaming, and the generation of action potentials. Phytohormones are found not only in higher plants, but in algae, too.
|
Algae
|
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] |
8613
|
Some species of algae form symbiotic relationships with other organisms. In these symbioses, the algae supply photosynthates (organic substances) to the host organism providing protection to the algal cells. The host organism derives some or all of its energy requirements from the algae. Examples are: Lichens are defined by the International Association for Lichenology to be "an association of a fungus and a photosynthetic symbiont resulting in a stable vegetative body having a specific structure." The fungi, or mycobionts, are mainly from the Ascomycota with a few from the Basidiomycota. In nature they do not occur separate from lichens. It
|
Algae
|
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] |
8614
|
is unknown when they began to associate. One mycobiont associates with the same phycobiont species, rarely two, from the green algae, except that alternatively, the mycobiont may associate with a species of cyanobacteria (hence "photobiont" is the more accurate term). A photobiont may be associated with many different mycobionts or may live independently; accordingly, lichens are named and classified as fungal species. The association is termed a morphogenesis because the lichen has a form and capabilities not possessed by the symbiont species alone (they can be experimentally isolated). The photobiont possibly triggers otherwise latent genes in the mycobiont. Trentepohlia is
|
Algae
|
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] |
8615
|
an example of a common green alga genus worldwide that can grow on its own or be lichenised. Lichen thus share some of the habitat and often similar appearance with specialized species of algae ("aerophytes") growing on exposed surfaces such as tree trunks and rocks and sometimes discoloring them. Coral reefs are accumulated from the calcareous exoskeletons of marine invertebrates of the order Scleractinia (stony corals). These animals metabolize sugar and oxygen to obtain energy for their cell-building processes, including secretion of the exoskeleton, with water and carbon dioxide as byproducts. Dinoflagellates (algal protists) are often endosymbionts in the cells
|
Algae
|
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0.6298924088478088
] |
8616
|
of the coral-forming marine invertebrates, where they accelerate host-cell metabolism by generating sugar and oxygen immediately available through photosynthesis using incident light and the carbon dioxide produced by the host. Reef-building stony corals (hermatypic corals) require endosymbiotic algae from the genus "Symbiodinium" to be in a healthy condition. The loss of "Symbiodinium" from the host is known as coral bleaching, a condition which leads to the deterioration of a reef. Endosymbiontic green algae live close to the surface of some sponges, for example, breadcrumb sponges ("Halichondria panicea"). The alga is thus protected from predators; the sponge is provided with oxygen
|
Algae
|
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] |
8617
|
and sugars which can account for 50 to 80% of sponge growth in some species. Rhodophyta, Chlorophyta, and Heterokontophyta, the three main algal divisions, have lifecycles which show considerable variation and complexity. In general, an asexual phase exists where the seaweed's cells are diploid, a sexual phase where the cells are haploid, followed by fusion of the male and female gametes. Asexual reproduction permits efficient population increases, but less variation is possible. Commonly, in sexual reproduction of unicellular and colonial algae, two specialized, sexually compatible, haploid gametes make physical contact and fuse to form a zygote. To ensure a successful
|
Algae
|
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] |
8618
|
mating, the development and release of gametes is highly synchronized and regulated; pheromones may play a key role in these processes. Sexual reproduction allows for more variation and provides the benefit of efficient recombinational repair of DNA damages during meiosis, a key stage of the sexual cycle. However, sexual reproduction is more costly than asexual reproduction. Meiosis has been shown to occur in many different species of algae. The "Algal Collection of the US National Herbarium" (located in the National Museum of Natural History) consists of approximately 320,500 dried specimens, which, although not exhaustive (no exhaustive collection exists), gives an
|
Algae
|
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] |
8619
|
idea of the order of magnitude of the number of algal species (that number remains unknown). Estimates vary widely. For example, according to one standard textbook, in the British Isles the "UK Biodiversity Steering Group Report" estimated there to be 20,000 algal species in the UK. Another checklist reports only about 5,000 species. Regarding the difference of about 15,000 species, the text concludes: "It will require many detailed field surveys before it is possible to provide a reliable estimate of the total number of species ..." Regional and group estimates have been made, as well: and so on, but lacking
|
Algae
|
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] |
8620
|
any scientific basis or reliable sources, these numbers have no more credibility than the British ones mentioned above. Most estimates also omit microscopic algae, such as phytoplankton. The most recent estimate suggests 72,500 algal species worldwide. The distribution of algal species has been fairly well studied since the founding of phytogeography in the mid-19th century. Algae spread mainly by the dispersal of spores analogously to the dispersal of Plantae by seeds and spores. This dispersal can be accomplished by air, water, or other organisms. Due to this, spores can be found in a variety of environments: fresh and marine waters,
|
Algae
|
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0.41985654830932617
] |
8621
|
air, soil, and in or on other organisms. Whether a spore is to grow into an organism depends on the combination of the species and the environmental conditions where the spore lands. The spores of freshwater algae are dispersed mainly by running water and wind, as well as by living carriers. However, not all bodies of water can carry all species of algae, as the chemical composition of certain water bodies limits the algae that can survive within them. Marine spores are often spread by ocean currents. Ocean water presents many vastly different habitats based on temperature and nutrient availability,
|
Algae
|
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] |
8622
|
resulting in phytogeographic zones, regions, and provinces. To some degree, the distribution of algae is subject to floristic discontinuities caused by geographical features, such as Antarctica, long distances of ocean or general land masses. It is, therefore, possible to identify species occurring by locality, such as "Pacific algae" or "North Sea algae". When they occur out of their localities, hypothesizing a transport mechanism is usually possible, such as the hulls of ships. For example, "Ulva reticulata" and "U. fasciata" travelled from the mainland to Hawaii in this manner. Mapping is possible for select species only: "there are many valid examples
|
Algae
|
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] |
8623
|
of confined distribution patterns." For example, "Clathromorphum" is an arctic genus and is not mapped far south of there. However, scientists regard the overall data as insufficient due to the "difficulties of undertaking such studies." Algae are prominent in bodies of water, common in terrestrial environments, and are found in unusual environments, such as on snow and ice. Seaweeds grow mostly in shallow marine waters, under deep; however, some such as Navicula pennata have been recorded to a depth of . The various sorts of algae play significant roles in aquatic ecology. Microscopic forms that live suspended in the water
|
Algae
|
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] |
8624
|
column (phytoplankton) provide the food base for most marine food chains. In very high densities (algal blooms), these algae may discolor the water and outcompete, poison, or asphyxiate other life forms. Algae can be used as indicator organisms to monitor pollution in various aquatic systems. In many cases, algal metabolism is sensitive to various pollutants. Due to this, the species composition of algal populations may shift in the presence of chemical pollutants. To detect these changes, algae can be sampled from the environment and maintained in laboratories with relative ease. On the basis of their habitat, algae can be categorized
|
Algae
|
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] |
8625
|
as: aquatic (planktonic, benthic, marine, freshwater, lentic, lotic), terrestrial, aerial (subareial), lithophytic, halophytic (or euryhaline), psammon, thermophilic, cryophilic, epibiont (epiphytic, epizoic), endosymbiont (endophytic, endozoic), parasitic, calcifilic or lichenic (phycobiont). In classical Chinese, the word is used both for "algae" and (in the modest tradition of the imperial scholars) for "literary talent". The third island in Kunming Lake beside the Summer Palace in Beijing is known as the Zaojian Tang Dao, which thus simultaneously means "Island of the Algae-Viewing Hall" and "Island of the Hall for Reflecting on Literary Talent". Agar, a gelatinous substance derived from red algae, has a number
|
Algae
|
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] |
8626
|
of commercial uses. It is a good medium on which to grow bacteria and fungi, as most microorganisms cannot digest agar. Alginic acid, or alginate, is extracted from brown algae. Its uses range from gelling agents in food, to medical dressings. Alginic acid also has been used in the field of biotechnology as a biocompatible medium for cell encapsulation and cell immobilization. Molecular cuisine is also a user of the substance for its gelling properties, by which it becomes a delivery vehicle for flavours. Between 100,000 and 170,000 wet tons of "Macrocystis" are harvested annually in New Mexico for alginate
|
Algae
|
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] |
8627
|
extraction and abalone feed. To be competitive and independent from fluctuating support from (local) policy on the long run, biofuels should equal or beat the cost level of fossil fuels. Here, algae-based fuels hold great promise, directly related to the potential to produce more biomass per unit area in a year than any other form of biomass. The break-even point for algae-based biofuels is estimated to occur by 2025. For centuries, seaweed has been used as a fertilizer; George Owen of Henllys writing in the 16th century referring to drift weed in South Wales:This kind of ore they often gather
|
Algae
|
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] |
8628
|
and lay on great heapes, where it heteth and rotteth, and will have a strong and loathsome smell; when being so rotten they cast on the land, as they do their muck, and thereof springeth good corn, especially barley ... After spring-tydes or great rigs of the sea, they fetch it in sacks on horse backes, and carie the same three, four, or five miles, and cast it on the lande, which doth very much better the ground for corn and grass. Today, algae are used by humans in many ways; for example, as fertilizers, soil conditioners, and livestock feed.
|
Algae
|
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] |
8629
|
Aquatic and microscopic species are cultured in clear tanks or ponds and are either harvested or used to treat effluents pumped through the ponds. Algaculture on a large scale is an important type of aquaculture in some places. Maerl is commonly used as a soil conditioner. Naturally growing seaweeds are an important source of food, especially in Asia. They provide many vitamins including: A, B, B, B, niacin, and C, and are rich in iodine, potassium, iron, magnesium, and calcium. In addition, commercially cultivated microalgae, including both algae and cyanobacteria, are marketed as nutritional supplements, such as spirulina, "Chlorella" and
|
Algae
|
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] |
8630
|
the vitamin-C supplement from "Dunaliella", high in beta-carotene. Algae are national foods of many nations: China consumes more than 70 species, including "fat choy", a cyanobacterium considered a vegetable; Japan, over 20 species such as "nori" and "aonori"; Ireland, dulse; Chile, cochayuyo. Laver is used to make "laver bread" in Wales, where it is known as "bara lawr"; in Korea, "gim". It is also used along the west coast of North America from California to British Columbia, in Hawaii and by the Māori of New Zealand. Sea lettuce and badderlocks are salad ingredients in Scotland, Ireland, Greenland, and Iceland. Algae
|
Algae
|
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] |
8631
|
is being considered a potential solution for world hunger problem. The oils from some algae have high levels of unsaturated fatty acids. For example, "Parietochloris incisa" is very high in arachidonic acid, where it reaches up to 47% of the triglyceride pool. Some varieties of algae favored by vegetarianism and veganism contain the long-chain, essential omega-3 fatty acids, docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA). Fish oil contains the omega-3 fatty acids, but the original source is algae (microalgae in particular), which are eaten by marine life such as copepods and are passed up the food chain. Algae have emerged
|
Algae
|
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8632
|
in recent years as a popular source of omega-3 fatty acids for vegetarians who cannot get long-chain EPA and DHA from other vegetarian sources such as flaxseed oil, which only contains the short-chain alpha-linolenic acid (ALA). Agricultural Research Service scientists found that 60–90% of nitrogen runoff and 70–100% of phosphorus runoff can be captured from manure effluents using a horizontal algae scrubber, also called an algal turf scrubber (ATS). Scientists developed the ATS, which consists of shallow, 100-foot raceways of nylon netting where algae colonies can form, and studied its efficacy for three years. They found that algae can readily
|
Algae
|
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] |
8633
|
be used to reduce the nutrient runoff from agricultural fields and increase the quality of water flowing into rivers, streams, and oceans. Researchers collected and dried the nutrient-rich algae from the ATS and studied its potential as an organic fertilizer. They found that cucumber and corn seedlings grew just as well using ATS organic fertilizer as they did with commercial fertilizers. Algae scrubbers, using bubbling upflow or vertical waterfall versions, are now also being used to filter aquaria and ponds. Various polymers can be created from algae, which can be especially useful in the creation of bioplastics. These include hybrid
|
Algae
|
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] |
8634
|
plastics, cellulose based plastics, poly-lactic acid, and bio-polyethylene. Several companies have begun to produce algae polymers commercially, including for use in flip-flops and in surf boards. The alga "Stichococcus bacillaris" has been seen to colonize silicone resins used at archaeological sites; biodegrading the synthetic substance. The natural pigments (carotenoids and chlorophylls) produced by algae can be used as alternatives to chemical dyes and coloring agents. The presence of some individual algal pigments, together with specific pigment concentration ratios, are taxon-specific: analysis of their concentrations with various analytical methods, particularly high-performance liquid chromatography, can therefore offer deep insight into the taxonomic
|
Algae
|
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] |
8635
|
composition and relative abundance of natural algae populations in sea water samples. Carrageenan, from the red alga "Chondrus crispus", is used as a stabilizer in milk products. Algae Algae (; singular alga ) is an informal term for a large, diverse group of photosynthetic eukaryotic organisms that are not necessarily closely related, and is thus polyphyletic. Included organisms range from unicellular microalgae genera, such as "Chlorella" and the diatoms, to multicellular forms, such as the giant kelp, a large brown alga which may grow up to 50 m in length. Most are aquatic and autotrophic and lack many of the
|
Algae
|
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] |
8636
|
Analysis of variance Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether the population means of several groups are equal, and therefore generalizes the "t"-test to more than two groups. ANOVA is useful
|
"Analysis of variance"
|
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] |
8637
|
for comparing (testing) three or more group means for statistical significance. It is conceptually similar to multiple two-sample t-tests, but is more conservative, resulting in fewer type I errors, and is therefore suited to a wide range of practical problems. While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s. The development of least-squares methods by Laplace and Gauss circa 1800 provided an improved method of
|
"Analysis of variance"
|
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] |
8638
|
combining observations (over the existing practices then used in astronomy and geodesy). It also initiated much study of the contributions to sums of squares. Laplace knew how to estimate a variance from a residual (rather than a total) sum of squares. By 1827, Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides. Before 1800, astronomers had isolated observational errors resulting from reaction times (the "personal equation") and had developed methods of reducing the errors. The experimental methods used in the study of the personal equation were later accepted by the emerging field of psychology
|
"Analysis of variance"
|
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] |
8639
|
which developed strong (full factorial) experimental methods to which randomization and blinding were soon added. An eloquent non-mathematical explanation of the additive effects model was available in 1885. Ronald Fisher introduced the term variance and proposed its formal analysis in a 1918 article "The Correlation Between Relatives on the Supposition of Mendelian Inheritance". His first application of the analysis of variance was published in 1921. Analysis of variance became widely known after being included in Fisher's 1925 book "Statistical Methods for Research Workers". Randomization models were developed by several researchers. The first was published in Polish by Jerzy Neyman in
|
"Analysis of variance"
|
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] |
8640
|
1923. One of the attributes of ANOVA that ensured its early popularity was computational elegance. The structure of the additive model allows solution for the additive coefficients by simple algebra rather than by matrix calculations. In the era of mechanical calculators this simplicity was critical. The determination of statistical significance also required access to tables of the F function which were supplied by early statistics texts. The analysis of variance can be used as an exploratory tool to explain observations. A dog show provides an example. A dog show is not a random sampling of the breed: it is typically
|
"Analysis of variance"
|
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] |
8641
|
limited to dogs that are adult, pure-bred, and exemplary. A histogram of dog weights from a show might plausibly be rather complex, like the yellow-orange distribution shown in the illustrations. Suppose we wanted to predict the weight of a dog based on a certain set of characteristics of each dog. One way to do that is to "explain" the distribution of weights by dividing the dog population into groups based on those characteristics. A successful grouping will split dogs such that (a) each group has a low variance of dog weights (meaning the group is relatively homogeneous) and (b) the
|
"Analysis of variance"
|
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] |
8642
|
mean of each group is distinct (if two groups have the same mean, then it isn't reasonable to conclude that the groups are, in fact, separate in any meaningful way). In the illustrations to the right, groups are identified as "X", "X", etc. In the first illustration, the dogs are divided according to the product (interaction) of two binary groupings: young vs old, and short-haired vs long-haired (e.g., group 1 is young, short-haired dogs, group 2 is young, long-haired dogs, etc.). Since the distributions of dog weight within each of the groups (shown in blue) has a relatively large variance,
|
"Analysis of variance"
|
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] |
8643
|
and since the means are very similar across groups, grouping dogs by these characteristics does not produce an effective way to explain the variation in dog weights: knowing which group a dog is in doesn't allow us to predict its weight much better than simply knowing the dog is in a dog show. Thus, this grouping fails to explain the variation in the overall distribution (yellow-orange). An attempt to explain the weight distribution by grouping dogs as "pet vs working breed" and "less athletic vs more athletic" would probably be somewhat more successful (fair fit). The heaviest show dogs are
|
"Analysis of variance"
|
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] |
8644
|
likely to be big, strong, working breeds, while breeds kept as pets tend to be smaller and thus lighter. As shown by the second illustration, the distributions have variances that are considerably smaller than in the first case, and the means are more distinguishable. However, the significant overlap of distributions, for example, means that we cannot distinguish "X" and "X" reliably. Grouping dogs according to a coin flip might produce distributions that look similar. An attempt to explain weight by breed is likely to produce a very good fit. All Chihuahuas are light and all St Bernards are heavy. The
|
"Analysis of variance"
|
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] |
8645
|
difference in weights between Setters and Pointers does not justify separate breeds. The analysis of variance provides the formal tools to justify these intuitive judgments. A common use of the method is the analysis of experimental data or the development of models. The method has some advantages over correlation: not all of the data must be numeric and one result of the method is a judgment in the confidence in an explanatory relationship. ANOVA is a form of statistical hypothesis testing heavily used in the analysis of experimental data. A test result (calculated from the null hypothesis and the sample)
|
"Analysis of variance"
|
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] |
8646
|
is called statistically significant if it is deemed unlikely to have occurred by chance, "assuming the truth of the null hypothesis". A statistically significant result, when a probability (p-value) is less than a pre-specified threshold (significance level), justifies the rejection of the null hypothesis, but only if the a priori probability of the null hypothesis is not high. In the typical application of ANOVA, the null hypothesis is that all groups are random samples from the same population. For example, when studying the effect of different treatments on similar samples of patients, the null hypothesis would be that all treatments
|
"Analysis of variance"
|
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] |
8647
|
have the same effect (perhaps none). Rejecting the null hypothesis is taken to mean that the differences in observed effects between treatment groups are unlikely to be due to random chance. By construction, hypothesis testing limits the rate of Type I errors (false positives) to a significance level. Experimenters also wish to limit Type II errors (false negatives). The rate of Type II errors depends largely on sample size (the rate is larger for smaller samples), significance level (when the standard of proof is high, the chances of overlooking a discovery are also high) and effect size (a smaller effect
|
"Analysis of variance"
|
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] |
8648
|
size is more prone to Type II error). The terminology of ANOVA is largely from the statistical design of experiments. The experimenter adjusts factors and measures responses in an attempt to determine an effect. Factors are assigned to experimental units by a combination of randomization and blocking to ensure the validity of the results. Blinding keeps the weighing impartial. Responses show a variability that is partially the result of the effect and is partially random error. ANOVA is the synthesis of several ideas and it is used for multiple purposes. As a consequence, it is difficult to define concisely or
|
"Analysis of variance"
|
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] |
8649
|
precisely. "Classical" ANOVA for balanced data does three things at once: In short, ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the observed data. Additionally: As a result: ANOVA "has long enjoyed the status of being the most used (some would say abused) statistical technique in psychological research." ANOVA "is probably the most useful technique in the field of statistical inference." ANOVA is difficult to teach, particularly for complex experiments, with split-plot designs being notorious. In some cases the proper application of the method is best determined by problem pattern recognition followed
|
"Analysis of variance"
|
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] |
8650
|
by the consultation of a classic authoritative test. (Condensed from the "NIST Engineering Statistics Handbook": Section 5.7. A Glossary of DOE Terminology.) There are three classes of models used in the analysis of variance, and these are outlined here. The fixed-effects model (class I) of analysis of variance applies to situations in which the experimenter applies one or more treatments to the subjects of the experiment to see whether the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatment would generate in the population as a whole. Random-effects model (class
|
"Analysis of variance"
|
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] |
8651
|
II) is used when the treatments are not fixed. This occurs when the various factor levels are sampled from a larger population. Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments (a multi-variable generalization of simple differences) differ from the fixed-effects model. A mixed-effects model (class III) contains experimental factors of both fixed and random-effects types, with appropriately different interpretations and analysis for the two types. Example: Teaching experiments could be performed by a college or university department to find a good introductory textbook, with each text considered a treatment. The fixed-effects model
|
"Analysis of variance"
|
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] |
8652
|
would compare a list of candidate texts. The random-effects model would determine whether important differences exist among a list of randomly selected texts. The mixed-effects model would compare the (fixed) incumbent texts to randomly selected alternatives. Defining fixed and random effects has proven elusive, with competing definitions arguably leading toward a linguistic quagmire. The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when
|
"Analysis of variance"
|
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] |
8653
|
data is balanced across factors but much deeper understanding is needed for unbalanced data. The analysis of variance can be presented in terms of a linear model, which makes the following assumptions about the probability distribution of the responses: The separate assumptions of the textbook model imply that the errors are independently, identically, and normally distributed for fixed effects models, that is, that the errors (formula_1) are independent and In a randomized controlled experiment, the treatments are randomly assigned to experimental units, following the experimental protocol. This randomization is objective and declared before the experiment is carried out. The objective
|
"Analysis of variance"
|
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] |
8654
|
random-assignment is used to test the significance of the null hypothesis, following the ideas of C. S. Peirce and Ronald Fisher. This design-based analysis was discussed and developed by Francis J. Anscombe at Rothamsted Experimental Station and by Oscar Kempthorne at Iowa State University. Kempthorne and his students make an assumption of "unit treatment additivity", which is discussed in the books of Kempthorne and David R. Cox. In its simplest form, the assumption of unit-treatment additivity states that the observed response formula_3 from experimental unit formula_4 when receiving treatment formula_5 can be written as the sum of the unit's response
|
"Analysis of variance"
|
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] |
8655
|
formula_6 and the treatment-effect formula_7, that is The assumption of unit-treatment additivity implies that, for every treatment formula_5, the formula_5th treatment has exactly the same effect formula_11 on every experiment unit. The assumption of unit treatment additivity usually cannot be directly falsified, according to Cox and Kempthorne. However, many "consequences" of treatment-unit additivity can be falsified. For a randomized experiment, the assumption of unit-treatment additivity "implies" that the variance is constant for all treatments. Therefore, by contraposition, a necessary condition for unit-treatment additivity is that the variance is constant. The use of unit treatment additivity and randomization is similar to
|
"Analysis of variance"
|
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0.00379410688765347
] |
8656
|
the design-based inference that is standard in finite-population survey sampling. Kempthorne uses the randomization-distribution and the assumption of "unit treatment additivity" to produce a "derived linear model", very similar to the textbook model discussed previously. The test statistics of this derived linear model are closely approximated by the test statistics of an appropriate normal linear model, according to approximation theorems and simulation studies. However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations. In the randomization-based analysis, there is "no assumption" of a "normal" distribution and certainly "no assumption" of
|
"Analysis of variance"
|
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] |
8657
|
"independence". On the contrary, "the observations are dependent"! The randomization-based analysis has the disadvantage that its exposition involves tedious algebra and extensive time. Since the randomization-based analysis is complicated and is closely approximated by the approach using a normal linear model, most teachers emphasize the normal linear model approach. Few statisticians object to model-based analysis of balanced randomized experiments. However, when applied to data from non-randomized experiments or observational studies, model-based analysis lacks the warrant of randomization. For observational data, the derivation of confidence intervals must use "subjective" models, as emphasized by Ronald Fisher and his followers. In practice, the
|
"Analysis of variance"
|
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] |
8658
|
estimates of treatment-effects from observational studies generally are often inconsistent. In practice, "statistical models" and observational data are useful for suggesting hypotheses that should be treated very cautiously by the public. The normal-model based ANOVA analysis assumes the independence, normality and homogeneity of the variances of the residuals. The randomization-based analysis assumes only the homogeneity of the variances of the residuals (as a consequence of unit-treatment additivity) and uses the randomization procedure of the experiment. Both these analyses require homoscedasticity, as an assumption for the normal-model analysis and as a consequence of randomization and additivity for the randomization-based analysis. However,
|
"Analysis of variance"
|
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] |
8659
|
studies of processes that change variances rather than means (called dispersion effects) have been successfully conducted using ANOVA. There are "no" necessary assumptions for ANOVA in its full generality, but the "F"-test used for ANOVA hypothesis testing has assumptions and practical limitations which are of continuing interest. Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions. The property of unit-treatment additivity is not invariant under a "change of scale", so statisticians often use transformations to achieve unit-treatment additivity. If the response variable is expected to follow a parametric family of probability distributions,
|
"Analysis of variance"
|
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] |
8660
|
then the statistician may specify (in the protocol for the experiment or observational study) that the responses be transformed to stabilize the variance. Also, a statistician may specify that logarithmic transforms be applied to the responses, which are believed to follow a multiplicative model. According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition. ANOVA is used in the analysis of comparative experiments, those in which only the difference in outcomes is of interest. The statistical significance of the experiment is determined by a ratio of two variances. This ratio is
|
"Analysis of variance"
|
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-0.022295769304037094
] |
8661
|
independent of several possible alterations to the experimental observations: Adding a constant to all observations does not alter significance. Multiplying all observations by a constant does not alter significance. So ANOVA statistical significance result is independent of constant bias and scaling errors as well as the units used in expressing observations. In the era of mechanical calculation it was common to subtract a constant from all observations (when equivalent to dropping leading digits) to simplify data entry. This is an example of data coding. The calculations of ANOVA can be characterized as computing a number of means and variances, dividing
|
"Analysis of variance"
|
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] |
8662
|
two variances and comparing the ratio to a handbook value to determine statistical significance. Calculating a treatment effect is then trivial, "the effect of any treatment is estimated by taking the difference between the mean of the observations which receive the treatment and the general mean". ANOVA uses traditional standardized terminology. The definitional equation of sample variance is formula_12, where the divisor is called the degrees of freedom (DF), the summation is called the sum of squares (SS), the result is called the mean square (MS) and the squared terms are deviations from the sample mean. ANOVA estimates 3 sample
|
"Analysis of variance"
|
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] |
8663
|
variances: a total variance based on all the observation deviations from the grand mean, an error variance based on all the observation deviations from their appropriate treatment means, and a treatment variance. The treatment variance is based on the deviations of treatment means from the grand mean, the result being multiplied by the number of observations in each treatment to account for the difference between the variance of observations and the variance of means. The fundamental technique is a partitioning of the total sum of squares "SS" into components related to the effects used in the model. For example, the
|
"Analysis of variance"
|
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] |
8664
|
model for a simplified ANOVA with one type of treatment at different levels. The number of degrees of freedom "DF" can be partitioned in a similar way: one of these components (that for error) specifies a chi-squared distribution which describes the associated sum of squares, while the same is true for "treatments" if there is no treatment effect. See also Lack-of-fit sum of squares. The "F"-test is used for comparing the factors of the total deviation. For example, in one-way, or single-factor ANOVA, statistical significance is tested for by comparing the F test statistic where "MS" is mean square, formula_17
|
"Analysis of variance"
|
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] |
8665
|
= number of treatments and formula_18 = total number of cases to the "F"-distribution with formula_19, formula_20 degrees of freedom. Using the "F"-distribution is a natural candidate because the test statistic is the ratio of two scaled sums of squares each of which follows a scaled chi-squared distribution. The expected value of F is formula_21 (where n is the treatment sample size) which is 1 for no treatment effect. As values of F increase above 1, the evidence is increasingly inconsistent with the null hypothesis. Two apparent experimental methods of increasing F are increasing the sample size and reducing the
|
"Analysis of variance"
|
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] |
8666
|
error variance by tight experimental controls. There are two methods of concluding the ANOVA hypothesis test, both of which produce the same result: The ANOVA "F"-test is known to be nearly optimal in the sense of minimizing false negative errors for a fixed rate of false positive errors (i.e. maximizing power for a fixed significance level). For example, to test the hypothesis that various medical treatments have exactly the same effect, the "F"-test's "p"-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced. Such permutation tests characterize tests with maximum power against all
|
"Analysis of variance"
|
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] |
8667
|
alternative hypotheses, as observed by Rosenbaum. The ANOVA "F"-test (of the null-hypothesis that all treatments have exactly the same effect) is recommended as a practical test, because of its robustness against many alternative distributions. ANOVA consists of separable parts; partitioning sources of variance and hypothesis testing can be used individually. ANOVA is used to support other statistical tools. Regression is first used to fit more complex models to data, then ANOVA is used to compare models with the objective of selecting simple(r) models that adequately describe the data. "Such models could be fit without any reference to ANOVA, but ANOVA
|
"Analysis of variance"
|
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] |
8668
|
tools could then be used to make some sense of the fitted models, and to test hypotheses about batches of coefficients." "[W]e think of the analysis of variance as a way of understanding and structuring multilevel models—not as an alternative to regression but as a tool for summarizing complex high-dimensional inferences ..." The simplest experiment suitable for ANOVA analysis is the completely randomized experiment with a single factor. More complex experiments with a single factor involve constraints on randomization and include completely randomized blocks and Latin squares (and variants: Graeco-Latin squares, etc.). The more complex experiments share many of the
|
"Analysis of variance"
|
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] |
8669
|
complexities of multiple factors. A relatively complete discussion of the analysis (models, data summaries, ANOVA table) of the completely randomized experiment is available. ANOVA generalizes to the study of the effects of multiple factors. When the experiment includes observations at all combinations of levels of each factor, it is termed factorial. Factorial experiments are more efficient than a series of single factor experiments and the efficiency grows as the number of factors increases. Consequently, factorial designs are heavily used. The use of ANOVA to study the effects of multiple factors has a complication. In a 3-way ANOVA with factors x,
|
"Analysis of variance"
|
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] |
8670
|
y and z, the ANOVA model includes terms for the main effects (x, y, z) and terms for interactions (xy, xz, yz, xyz). All terms require hypothesis tests. The proliferation of interaction terms increases the risk that some hypothesis test will produce a false positive by chance. Fortunately, experience says that high order interactions are rare. The ability to detect interactions is a major advantage of multiple factor ANOVA. Testing one factor at a time hides interactions, but produces apparently inconsistent experimental results. Caution is advised when encountering interactions; Test interaction terms first and expand the analysis beyond ANOVA if
|
"Analysis of variance"
|
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0.07819364964962006,
-0.41472524404525757,
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0.052560582756996155
] |
8671
|
interactions are found. Texts vary in their recommendations regarding the continuation of the ANOVA procedure after encountering an interaction. Interactions complicate the interpretation of experimental data. Neither the calculations of significance nor the estimated treatment effects can be taken at face value. "A significant interaction will often mask the significance of main effects." Graphical methods are recommended to enhance understanding. Regression is often useful. A lengthy discussion of interactions is available in Cox (1958). Some interactions can be removed (by transformations) while others cannot. A variety of techniques are used with multiple factor ANOVA to reduce expense. One technique used
|
"Analysis of variance"
|
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] |
8672
|
in factorial designs is to minimize replication (possibly no replication with support of analytical trickery) and to combine groups when effects are found to be statistically (or practically) insignificant. An experiment with many insignificant factors may collapse into one with a few factors supported by many replications. Several fully worked numerical examples are available. A simple case uses one-way (a single factor) analysis. A more complex case uses two-way (two-factor) analysis. Some analysis is required in support of the "design" of the experiment while other analysis is performed after changes in the factors are formally found to produce statistically significant
|
"Analysis of variance"
|
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] |
8673
|
changes in the responses. Because experimentation is iterative, the results of one experiment alter plans for following experiments. In the design of an experiment, the number of experimental units is planned to satisfy the goals of the experiment. Experimentation is often sequential. Early experiments are often designed to provide mean-unbiased estimates of treatment effects and of experimental error. Later experiments are often designed to test a hypothesis that a treatment effect has an important magnitude; in this case, the number of experimental units is chosen so that the experiment is within budget and has adequate power, among other goals. Reporting
|
"Analysis of variance"
|
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] |
8674
|
sample size analysis is generally required in psychology. "Provide information on sample size and the process that led to sample size decisions." The analysis, which is written in the experimental protocol before the experiment is conducted, is examined in grant applications and administrative review boards. Besides the power analysis, there are less formal methods for selecting the number of experimental units. These include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation increase (above the residuals) and methods based on achieving a desired confident interval. Power analysis is often applied in
|
"Analysis of variance"
|
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] |
8675
|
the context of ANOVA in order to assess the probability of successfully rejecting the null hypothesis if we assume a certain ANOVA design, effect size in the population, sample size and significance level. Power analysis can assist in study design by determining what sample size would be required in order to have a reasonable chance of rejecting the null hypothesis when the alternative hypothesis is true. Several standardized measures of effect have been proposed for ANOVA to summarize the strength of the association between a predictor(s) and the dependent variable or the overall standardized difference of the complete model. Standardized
|
"Analysis of variance"
|
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8676
|
effect-size estimates facilitate comparison of findings across studies and disciplines. However, while standardized effect sizes are commonly used in much of the professional literature, a non-standardized measure of effect size that has immediately "meaningful" units may be preferable for reporting purposes. It is always appropriate to carefully consider outliers. They have a disproportionate impact on statistical conclusions and are often the result of errors. It is prudent to verify that the assumptions of ANOVA have been met. Residuals are examined or analyzed to confirm homoscedasticity and gross normality. Residuals should have the appearance of (zero mean normal distribution) noise when
|
"Analysis of variance"
|
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] |
8677
|
plotted as a function of anything including time and modeled data values. Trends hint at interactions among factors or among observations. One rule of thumb: "If the largest standard deviation is less than twice the smallest standard deviation, we can use methods based on the assumption of equal standard deviations and our results will still be approximately correct." A statistically significant effect in ANOVA is often followed up with one or more different follow-up tests. This can be done in order to assess which groups are different from which other groups or to test various other focused hypotheses. Follow-up tests
|
"Analysis of variance"
|
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] |
8678
|
are often distinguished in terms of whether they are planned (a priori) or post hoc. Planned tests are determined before looking at the data and post hoc tests are performed after looking at the data. Often one of the "treatments" is none, so the treatment group can act as a control. Dunnett's test (a modification of the t-test) tests whether each of the other treatment groups has the same mean as the control. Post hoc tests such as Tukey's range test most commonly compare every group mean with every other group mean and typically incorporate some method of controlling for
|
"Analysis of variance"
|
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] |
8679
|
Type I errors. Comparisons, which are most commonly planned, can be either simple or compound. Simple comparisons compare one group mean with one other group mean. Compound comparisons typically compare two sets of groups means where one set has two or more groups (e.g., compare average group means of group A, B and C with group D). Comparisons can also look at tests of trend, such as linear and quadratic relationships, when the independent variable involves ordered levels. Following ANOVA with pair-wise multiple-comparison tests has been criticized on several grounds. There are many such tests (10 in one table) and
|
"Analysis of variance"
|
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] |
8680
|
recommendations regarding their use are vague or conflicting. There are several types of ANOVA. Many statisticians base ANOVA on the design of the experiment, especially on the protocol that specifies the random assignment of treatments to subjects; the protocol's description of the assignment mechanism should include a specification of the structure of the treatments and of any blocking. It is also common to apply ANOVA to observational data using an appropriate statistical model. Some popular designs use the following types of ANOVA: Balanced experiments (those with an equal sample size for each treatment) are relatively easy to interpret; Unbalanced experiments
|
"Analysis of variance"
|
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8681
|
offer more complexity. For single-factor (one-way) ANOVA, the adjustment for unbalanced data is easy, but the unbalanced analysis lacks both robustness and power. For more complex designs the lack of balance leads to further complications. "The orthogonality property of main effects and interactions present in balanced data does not carry over to the unbalanced case. This means that the usual analysis of variance techniques do not apply. Consequently, the analysis of unbalanced factorials is much more difficult than that for balanced designs." In the general case, "The analysis of variance can also be applied to unbalanced data, but then the
|
"Analysis of variance"
|
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] |
8682
|
sums of squares, mean squares, and "F"-ratios will depend on the order in which the sources of variation are considered." The simplest techniques for handling unbalanced data restore balance by either throwing out data or by synthesizing missing data. More complex techniques use regression. ANOVA is (in part) a significance test. The American Psychological Association holds the view that simply reporting significance is insufficient and that reporting confidence bounds is preferred. While ANOVA is conservative (in maintaining a significance level) against multiple comparisons in one dimension, it is not conservative against comparisons in multiple dimensions. ANOVA is considered to be
|
"Analysis of variance"
|
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] |
8683
|
a special case of linear regression which in turn is a special case of the general linear model. All consider the observations to be the sum of a model (fit) and a residual (error) to be minimized. The Kruskal–Wallis test and the Friedman test are nonparametric tests, which do not rely on an assumption of normality. Below we make clear the connection between multi-way ANOVA and linear regression. Linearly re-order the data so that formula_22 observation is associated with a response formula_23 and factors formula_24 where formula_25 denotes the different factors and formula_26 is the total number of factors. In
|
"Analysis of variance"
|
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] |
8684
|
one-way ANOVA formula_27 and in two-way ANOVA formula_28. Furthermore, we assume the formula_29 factor has formula_30 levels, namely formula_31. Now, we can one-hot encode the factors into the formula_32 dimensional vector formula_33. The one-hot encoding function formula_34 is defined such that the formula_35 entry of formula_36 is formula_37 The vector formula_33 is the concatenation of all of the above vectors for all formula_39. Thus, formula_40. In order to obtain a fully general formula_26-way interaction ANOVA we must also concatenate every additional interaction term in the vector formula_33 and then add an intercept term. Let that vector be formula_43. With this
|
"Analysis of variance"
|
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] |
8685
|
notation in place, we now have the exact connection with linear regression. We simply regress response formula_23 against the vector formula_43. However, there is a concern about identifiability. In order to overcome such issues we assume that the sum of the parameters within each set of interactions is equal to zero. From here, one can use "F"-statistics or other methods to determine the relevance of the individual factors. We can consider the 2-way interaction example where we assume that the first factor has 2 levels and the second factor has 3 levels. Define formula_46 if formula_47 and formula_48 if formula_49,
|
"Analysis of variance"
|
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8686
|
i.e. formula_50 is the one-hot encoding of the first factor and formula_39 is the one-hot encoding of the second factor. With that, formula_52 where the last term is an intercept term. For a more concrete example suppose that formula_53 Then, formula_54 Analysis of variance Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is
|
"Analysis of variance"
|
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] |
8687
|
Alkane In organic chemistry, an alkane, or paraffin (a historical name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which all the carbon–carbon bonds are single. Alkanes have the general chemical formula CH. The alkanes range in complexity from the simplest case of methane (CH), where "n" = 1 (sometimes called the parent molecule), to arbitrarily large and complex molecules, like pentacontane (CH) or 6-ethyl-2-methyl-5-(1-methylethyl)octane, an isomer of tetradecane (CH) IUPAC defines alkanes as "acyclic branched or unbranched hydrocarbons having the
|
Alkane
|
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] |
8688
|
general formula , and therefore consisting entirely of hydrogen atoms and saturated carbon atoms". However, some sources use the term to denote "any" saturated hydrocarbon, including those that are either monocyclic (i.e. the cycloalkanes) or polycyclic, despite their having a different general formula (i.e. cycloalkanes are CH). In an alkane, each carbon atom is sp-hybridized with 4 sigma bonds (either C–C or C–H), and each hydrogen atom is joined to one of the carbon atoms (in a C–H bond). The longest series of linked carbon atoms in a molecule is known as its carbon skeleton or carbon backbone. The number
|
Alkane
|
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] |
8689
|
of carbon atoms may be thought of as the size of the alkane. One group of the higher alkanes are waxes, solids at standard ambient temperature and pressure (SATP), for which the number of carbons in the carbon backbone is greater than about 17. With their repeated –CH units, the alkanes constitute a homologous series of organic compounds in which the members differ in molecular mass by multiples of 14.03 u (the total mass of each such methylene-bridge unit, which comprises a single carbon atom of mass 12.01 u and two hydrogen atoms of mass ~1.01 u each). Alkanes are
|
Alkane
|
[
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] |
8690
|
not very reactive and have little biological activity. They can be viewed as molecular trees upon which can be hung the more active/reactive functional groups of biological molecules. The alkanes have two main commercial sources: petroleum (crude oil) and natural gas. An alkyl group, generally abbreviated with the symbol R, is a functional group that, like an alkane, consists solely of single-bonded carbon and hydrogen atoms connected acyclically—for example, a methyl or ethyl group. Saturated hydrocarbons are hydrocarbons having only single covalent bonds between their carbons. They can be: According to the definition by IUPAC, the former two are alkanes,
|
Alkane
|
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8691
|
whereas the third group is called cycloalkanes. Saturated hydrocarbons can also combine any of the linear, cyclic (e.g., polycyclic) and branching structures; the general formula is , where "k" is the number of independent loops. Alkanes are the acyclic (loopless) ones, corresponding to "k" = 0. Alkanes with more than three carbon atoms can be arranged in various different ways, forming structural isomers. The simplest isomer of an alkane is the one in which the carbon atoms are arranged in a single chain with no branches. This isomer is sometimes called the "n"-isomer ("n" for "normal", although it is not
|
Alkane
|
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] |
8692
|
necessarily the most common). However the chain of carbon atoms may also be branched at one or more points. The number of possible isomers increases rapidly with the number of carbon atoms. For example, for acyclic alkanes: Branched alkanes can be chiral. For example, 3-methylhexane and its higher homologues are chiral due to their stereogenic center at carbon atom number 3. In addition to the alkane isomers, the chain of carbon atoms may form one or more loops. Such compounds are called cycloalkanes. Stereoisomers and cyclic compounds are excluded when calculating the number of isomers above. The IUPAC nomenclature (systematic
|
Alkane
|
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] |
8693
|
way of naming compounds) for alkanes is based on identifying hydrocarbon chains. Unbranched, saturated hydrocarbon chains are named systematically with a Greek numerical prefix denoting the number of carbons and the suffix "-ane". In 1866, August Wilhelm von Hofmann suggested systematizing nomenclature by using the whole sequence of vowels a, e, i, o and u to create suffixes -ane, -ene, -ine (or -yne), -one, -une, for the hydrocarbons CH, CH, CH, CH, CH. Now, the first three name hydrocarbons with single, double and triple bonds; "-one" represents a ketone; "-ol" represents an alcohol or OH group; "-oxy-" means an ether
|
Alkane
|
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] |
8694
|
and refers to oxygen between two carbons, so that methoxymethane is the IUPAC name for dimethyl ether. It is difficult or impossible to find compounds with more than one IUPAC name. This is because shorter chains attached to longer chains are prefixes and the convention includes brackets. Numbers in the name, referring to which carbon a group is attached to, should be as low as possible so that 1- is implied and usually omitted from names of organic compounds with only one side-group. Symmetric compounds will have two ways of arriving at the same name. Straight-chain alkanes are sometimes indicated
|
Alkane
|
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] |
8695
|
by the prefix ""n"-" (for "normal") where a non-linear isomer exists. Although this is not strictly necessary, the usage is still common in cases where there is an important difference in properties between the straight-chain and branched-chain isomers, e.g., "n"-hexane or 2- or 3-methylpentane. Alternative names for this group are: linear paraffins or "n"-paraffins. The members of the series (in terms of number of carbon atoms) are named as follows: The first four names were derived from methanol, ether, propionic acid and butyric acid, respectively (hexadecane is also sometimes referred to as cetane). Alkanes with five or more carbon atoms
|
Alkane
|
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8696
|
are named by adding the suffix -ane to the appropriate numerical multiplier prefix with elision of any terminal vowel ("-a" or "-o") from the basic numerical term. Hence, pentane, CH; hexane, CH; heptane, CH; octane, CH; etc. The prefix is generally Greek, however alkanes with a carbon atom count ending in nine, for example nonane, use the Latin prefix non-. For a more complete list, see List of alkanes. Simple branched alkanes often have a common name using a prefix to distinguish them from linear alkanes, for example "n"-pentane, isopentane, and neopentane. IUPAC naming conventions can be used to produce
|
Alkane
|
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] |
8697
|
a systematic name. The key steps in the naming of more complicated branched alkanes are as follows: Though technically distinct from the alkanes, this class of hydrocarbons is referred to by some as the "cyclic alkanes." As their description implies, they contain one or more rings. Simple cycloalkanes have a prefix "cyclo-" to distinguish them from alkanes. Cycloalkanes are named as per their acyclic counterparts with respect to the number of carbon atoms in their backbones, e.g., cyclopentane (CH) is a cycloalkane with 5 carbon atoms just like pentane (CH), but they are joined up in a five-membered ring. In
|
Alkane
|
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] |
8698
|
a similar manner, propane and cyclopropane, butane and cyclobutane, etc. Substituted cycloalkanes are named similarly to substituted alkanes — the cycloalkane ring is stated, and the substituents are according to their position on the ring, with the numbering decided by the Cahn–Ingold–Prelog priority rules. The trivial (non-systematic) name for alkanes is "paraffins". Together, alkanes are known as the "paraffin series". Trivial names for compounds are usually historical artifacts. They were coined before the development of systematic names, and have been retained due to familiar usage in industry. Cycloalkanes are also called naphthenes. It is almost certain that the term "paraffin"
|
Alkane
|
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] |
8699
|
stems from the petrochemical industry. Branched-chain alkanes are called "isoparaffins". The use of the term "paraffin" is a general term and often does not distinguish between pure compounds and mixtures of isomers, i.e., compounds of the same chemical formula, e.g., pentane and isopentane. The following trivial names are retained in the IUPAC system: All alkanes are colorless. Alkanes with the lowest molecular weights are gasses, those of intermediate molecular weight are liquids, and the heaviest are waxy solids. Alkanes experience intermolecular van der Waals forces. Stronger intermolecular van der Waals forces give rise to greater boiling points of alkanes. There
|
Alkane
|
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] |
8700
|
are two determinants for the strength of the van der Waals forces: Under standard conditions, from CH to CH alkanes are gaseous; from CH to CH they are liquids; and after CH they are solids. As the boiling point of alkanes is primarily determined by weight, it should not be a surprise that the boiling point has almost a linear relationship with the size (molecular weight) of the molecule. As a rule of thumb, the boiling point rises 20–30 °C for each carbon added to the chain; this rule applies to other homologous series. A straight-chain alkane will have a
|
Alkane
|
[
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