Definition

ANOVA (Analysis of Variance)

A test of whether three or more group means differ, by comparing variation between groups to variation within them.

ANOVA generalizes the t-test: one overall F-test asks whether any group differs, avoiding the inflated false-positive rate of many pairwise t-tests. A significant F is followed by post-hoc tests (like Tukey’s HSD) to locate which pairs differ.

Factorial ANOVA adds multiple factors and their interactions; repeated-measures ANOVA handles the same participants across conditions. Assumptions mirror the t-test (normal-ish residuals, similar variances); Kruskal–Wallis is the rank-based fallback.