# MANOVA

One-way MANOVA (Multivariate ANalysis Of VAriance) is the multivariate version of the univariate ANOVA, testing whether two or more groups (specified with a group column) have the same multivariate mean.

Two statistics are provided: Wilk's lambda with its associated Rao's *F* and the Pillai trace with its approximated *F*. Wilk's lambda is probably more commonly used, but the Pillai trace may be more robust.

*Number of constraints*: For correct calculation of the *p* values, the number of dependent variables (constraints) must be specified. It should normally be left at 0, but for Procrustes fitted landmark data use 4 (for 2D) or 6 (for 3D).

*Pairwise comparisons (post-hoc)*: If the MANOVA shows significant overall difference between groups, the analysis can proceed by pairwise comparisons. In PAST, the post-hoc analysis is simple, by pairwise Hotelling's tests. The following values can be displayed in the table:

- Hotelling's
*p*values, not corrected for multiple testing. Marked in pink if significant (*p*<0.05). - The same
*p*values, but significance (pink) assessed using the sequential Bonferroni scheme. - Bonferroni corrected
*p*values (multiplied by the number of pairwise comparisons). The Bonferroni correction gives very little power. - Squared Mahalanobis distances.

Note: These pairwise comparisons use the within-group covariance matrix pooled over all groups participating in the MANOVA. They may therefore give slightly other results than if only two of the groups are selected for analysis.

Missing data supported by column average substitution.