ANOVA is an acronym for analysis of variance, a statistical method that is used to infer if the mean value of a continuous variable is the same in different populations defined by nominal variables. The method is so named since it partitions the total variance into components stemming from different sources. Ratios of these variance components are then used for inference about the means. ANOVA can also be viewed from a model-based perspective whereby the variable of interest is the outcome variable and the nominal population indicators are the predictors. More analytical precision is achieved when such a model includes continuous variables that may not have been possible to control experimentally. Such a procedure is called ANCOVA, an acronym for analysis of covariance.
ANOVA and ANCOVA are among the foundational methods of statistics. Their flexible framework lends itself to a variety of experimental and nonexperimental settings and make it possible to simultaneously analyze multiple sources of variance. ANOVA is also commonly used to test groups of coefficients in regression analyses and summarize model fit.
This entry begins with a brief historical background followed by an introduction to ANOVA using an example of a simple experimental design, a discussion of the assumptions, and extensions to more complicated designs. The model-based perspective is then introduced followed by an explanation of ANCOVA. Extensions such as the nonparametric ANOVA and multivariate ANOVA are also included.