Editing Analysis of variance (section)

==Study designs==
There are several types of ANOVA. Many statisticians base ANOVA on the [[experimental design|design of the experiment]],<ref>Cochran & Cox (1957, p 9, "The general rule [is] that the way in which the experiment is conducted determines not only whether inferences can be made, but also the calculations required to make them.")</ref> 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 (statistics)|blocking]]. It is also common to apply ANOVA to observational data using an appropriate statistical model.<ref>{{Cite web |title=ANOVA Design |url=https://bluebox.creighton.edu/demo/modules/en-boundless-old/www.boundless.com/statistics/textbooks/boundless-statistics-textbook/estimation-and-hypothesis-testing-12/one-way-anova-57/anova-design-283-2741/ |access-date=2023-01-23 |website=bluebox.creighton.edu}}</ref>

Some popular designs use the following types of ANOVA:
*[[One-way ANOVA]] is used to test for differences among two or more [[statistical independence|independent]] groups (means), e.g. different levels of urea application in a crop, or different levels of antibiotic action on several different bacterial species,<ref>{{Cite web|url=http://www.biomedicalstatistics.info/en/multiplegroups/one-way-anova.html|archive-url=https://web.archive.org/web/20141107211953/http://www.biomedicalstatistics.info/en/multiplegroups/one-way-anova.html|url-status=dead|title=One-way/single factor ANOVA|archive-date=7 November 2014}}</ref> or different levels of effect of some medicine on groups of patients. However, should these groups not be independent, and there is an order in the groups (such as mild, moderate and severe disease), or in the dose of a drug (such as 5&nbsp;mg/mL, 10&nbsp;mg/mL, 20&nbsp;mg/mL) given to the same group of patients, then a [[linear trend estimation]] should be used. Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a [[t-test]].<ref>{{Cite journal | doi = 10.1093/biomet/6.1.1 | title = The Probable Error of a Mean | journal = Biometrika | volume = 6 | pages = 1–25 | year = 1908 | url = http://dml.cz/bitstream/handle/10338.dmlcz/143545/ActaOlom_52-2013-2_12.pdf | hdl = 10338.dmlcz/143545 }}</ref> When there are only two means to compare, the [[t-test]] and the ANOVA [[F-test|''F''-test]] are equivalent; the relation between ANOVA and ''t'' is given by {{math|1=''F'' = ''t''<sup>2</sup>}}.
*[[Factorial experiment|Factorial]] ANOVA is used when there is more than one factor.
*[[Repeated measures]] ANOVA is used when the same subjects are used for each factor (e.g., in a [[longitudinal study]]).
*[[Multivariate analysis of variance]] (MANOVA) is used when there is more than one [[dependent variable|response variable]].