Analysis of variance (ANOVA) is a statistical procedure that attempts to determine the amount of variation in a variable y that is explained by a variable, or set of variables, X. It does so by decomposing a group of measurements into its components of systematic variation and random variation (or measurement error).

A simple, one-way ANOVA compares the variation in a variable y within groups, to the variation between groups, where one defines the groups by a single variable. It is equivalent to a simple linear regression with indicator variables for each group. An ANOVA procedure estimates the following model: y = β X + e, where e is the random error term, y is the endogenous, or dependent, variable, X is the exogenous, or independent, ...