Unlock: Analysis of Variance

One-way ANOVA decomposes the total sum of squares into a between-group component and a within-group component. Under iid normal data with equal group variances, the ratio of mean squares has an F distribution and gives an exact test of the equal-means null hypothesis. The Welch correction handles unequal variances. Two-way ANOVA partitions further into main effects and interaction. Post-hoc procedures (Tukey HSD, Bonferroni, Scheffe) correct for the multiple-comparison problem that naive pairwise t-tests ignore.