In statistics,<unk> <unk>  is a collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables.  The initial techniques of the<unk>  were developed by the statistician and geneticist R. A. Fisher in the 1920s and 1930s, and is sometimes known as Fisher's<unk>  or Fisher's<unk> , due to the use of Fisher's F-distribution as part of the test of statistical significance.
There are three conceptual classes of such models:
Fixed-effects model assumes that the data come from normal populations which may differ only in their means. (Model 1)
Random-effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy. (Model 2)
Mixed effects models describe situations where both fixed and random effects are present. (Model 3)
In practice, there are several types of<unk>  depending on the number of treatments and the way they are applied to the subjects in the experiment:
One-way<unk>  is used to test for differences among two or more independent groups. Typically, however, the One-way<unk>  is used to test for differences among three or more groups, with the two-group case relegated to the t-test (Gossett, 1908), which is a special case of the<unk> . The relation between<unk>  and t is given as
F = t squared.
One-way<unk>  for repeated measures is used when the subjects are subjected to repeated measures; this means that the same subjects are used for each treatment.  Note that this method can be subject to carryover effects.
Factorial<unk>  is used when the experimenter wants to study the effects of two or more treatment variables. The most commonly used type of factorial<unk>  is the 2×2 (read: two by two) design, where there are two independent variables and each variable has two levels or distinct values. Factorial<unk>  can also be multi-level such as 3×3, etc. or higher order such as 2×2×2, etc. but analyses with higher numbers of factors are rarely done because the calculations are lengthy and the results are hard to interpret.
When one wishes to test two or more independent groups subjecting the subjects to repeated measures, one may perform a factorial mixed-design<unk> , in which one factor is independent and the other is repeated measures.  This is a type of mixed effect model.
Multivariate<unk>  <unk>  is used when there is more than one dependent variable.
Analysis of variance
Analysis of covariance
Linear regression
Analysis of rhythmic variance
Likelihood-ratio test
Chi-square test
Kendall tau rank correlation coefficient
Binomial test