Compute the within-group variance, also known as residual variance.This is why the method is called analysis of variance even though the main goal is to compare the group means.īriefly, the mathematical procedure behind the ANOVA test is as follow:
Thus, it’s possible to evaluate whether the differences between the group means are significant by comparing the two variance estimates. The idea behind the ANOVA test is very simple: if the average variation between groups is large enough compared to the average variation within groups, then you could conclude that at least one group mean is not equal to the others. The figure shows the variation between the means of the groups (panel A) and the variation within each group (panel B), also known as residual variance. The dashed line indicates the group mean. Other synonyms are: factorial ANOVA or three-way between-subjects ANOVA.Īssume that we have 3 groups to compare, as illustrated in the image below.
This chapter describes the different types of ANOVA for comparing independent groups, including: Although the name of the technique refers to variances, the main goal of ANOVA is to investigate differences in means. The ANOVA test (or Analysis of Variance) is used to compare the mean of multiple groups.