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ANOVA–Nested Models and Components of Variance

A nalysis of variance, or ANOVA, is one of the basic tools of statistics. Its purpose is to apportion the variability in a set of data between two or more sources. There are many different ANOVA models, and the choice of the appropriate one depends both on the structure of the data and on the purpose of the analysis. Sometimes this is done with the aim of testing whether there is any variability associated with a particular source, and thus testing whether a factor has any effect. Sometimes the aim is to estimate the amount of variability associated with each level of a hierarchical sampling structure, and it is this nested ANOVA that will be described here.