Permutational Multivariate Analysis of Variance ( PERMANOVA )

Abstract Permutational multivariate analysis of variance (PERMANOVA) is a geometric partitioning of variation across a multivariate data cloud, defined explicitly in the space of a chosen dissimilarity measure, in response to one or more factors in an analysis of variance design. Statistical inferences are made in a distribution‐free setting using permutational algorithms. The PERMANOVA framework is readily extended to accommodate random effects, hierarchical models, mixed models, quantitative covariates, repeated measures, unbalanced and/or asymmetrical designs, and, most recently, heterogeneous dispersions among groups. Plots to accompany PERMANOVA models include ordinations of either fitted or residualized distance matrices, including multivariate analogues to main effects and interaction plots, to visualize results.