MANOVA tests whether the joint vector of group means differs across two or more numeric dependent variables at once.
Running k separate univariate ANOVAs on k correlated DVs inflates the family-wise type-I rate and ignores the correlation among DVs. MANOVA gives a single multivariate test on the joint vector of means — control the family-wise rate at α once, then drill into univariate or contrast follow-ups if the omnibus is significant.
Four standard multivariate test statistics: Pillai (most robust to assumption violations; recommended default), Wilks Λ (most popular historically, equivalent to LRT under multivariate normality), Hotelling-Lawley (most powerful for tight alternative hypotheses), Roy's largest root (most powerful when one canonical dimension dominates, but unstable under violations).
MANOVA has stricter assumptions than univariate ANOVA: multivariate normality and homogeneity of the covariance matrices across groups (Box's M test). When Box's M is significant, prefer Pillai's trace; consider the alternative — robust MANOVA or a permutation MANOVA (PERMANOVA) on a Euclidean distance matrix.
≥ 2 DVs + one or two factors + optional A × B interaction + multivariate-test selector.
Per-term multivariate statistic + approx F + p + per-DV univariate ANOVA follow-up table.
Significant multivariate test followed by univariate ANOVAs identifies which DVs drive the effect. Differing significance patterns across the four statistics (Pillai vs Roy) indicate the structure is concentrated in fewer dimensions than the others assume.