Analysis of variance

Analysis of variance (ANOVA) is a statistical procedure for summarizing a classical linear model—a decomposition of sum of squares into a component for each source of variation in the model—along with an associated test (the F-test) of the hypothesis that any given source of variation in the model is zero. When applied to generalized linear models, multilevel models, and other extensions of classical regression, ANOVA can be extended in two different directions. First, the F-test can be used (in an asymptotic or approximate fashion) to compare nested models, to test the hypothesis that the simpler of the models is sufficient to explain the data. Second, the idea of variance decomposition can be interpreted as inference for the variances of batches of parameters (sources of variation) in multilevel regressions.