PERMANOVA

PERMANOVA, short for permutational multivariate analysis of variance, is a non-parametric method for testing whether the multivariate means (centroids) of predefined groups differ in a space defined by a distance or dissimilarity matrix. It extends the concept of ANOVA to multivariate data and is widely used in ecology, genomics, and related fields where response variables are numerous and not necessarily normally distributed. The approach relies on permutations rather than parametric assumptions, making it robust to non-normal data and to arbitrary distance measures.

The method begins by computing a distance or dissimilarity matrix from the multivariate data, using a measure such as Bray-Curtis, Euclidean, Jaccard, or others. A statistic, commonly an F-like ratio, assesses differences among group centroids by partitioning the total variation into components attributed to the groups versus within-group variation. The significance of the observed statistic is evaluated by repeatedly permuting group labels many times to build a null distribution; the p-value is the fraction of permutations yielding a statistic as large as or larger than the observed one.

PERMANOVA can accommodate complex experimental designs, including factorial and nested factors, covariates, and blocking structures by restricting permutations to appropriate strata. However, a key caveat is that a significant result indicates differences in group centroids, not necessarily in dispersion. Heterogeneity of dispersion among groups can inflate Type I error, so tests of dispersion (e.g., PERMDISP) are often recommended, and effect size can be reported as R-squared values.

Common implementations include the adonis and adonis2 functions in the R vegan package, as well as other software packages across ecological and statistical toolkits.