PERMANOVA, (permutational multivariate ANOVA), is a non-parametric alternative to MANOVA, or multivariate ANOVA test. It is appropriate with multiple sets of variables that do not meet the assumptions of MANOVA, namely multivariate normality. It is often used with data that is highly skewed, zero-inflated, ordinal, or qualitative, such as ecological community data, microbiome data, or genetic data.
It operates on a distance matrix constructed from any dissimilarity measure, and tests the null hypothesis that there are no differences in the relative magnitude (or presence/absence) of a set of variables among objects from different treatments or groups. P-values are calculated via permutation tests. PERMANOVA tests often accompany ordination plots from PCoA or NMDS.
This workshop will illustrate the theory behind the PERMANOVA test statistic, how to test this statistic for statistical significance given the experimental design. Implementation will be illustrated in the vegan package in R. This workshop is appropriate for someone who has taken a college-level statistics course that covered ANOVA.