PERMANOVA

PERMANOVA from a distance matrix

PERMANOVA tests whether groups differ in multivariate space without assuming multivariate normality. Magic Stat runs it from a dissimilarity matrix — Euclidean in the mean-comparison dialog, any of the common ecological measures in the ecology module — and reports pseudo-F, R² and a permutation p.

The honest part

What PERMANOVA tests, and what it does not

PERMANOVA — permutational multivariate analysis of variance, also called Adonis — partitions the total sum of squared distances between samples into a between-group and a within-group part, and tests the ratio with permutations. The test statistic is a pseudo-F, and the effect size is R²: the share of multivariate variation the grouping explains.

It is used so widely because it makes no normality assumption and works from any dissimilarity measure. It is misused just as widely because a significant result can mean a difference in group location, a difference in group dispersion, or both — and PERMANOVA does not distinguish them. If dispersion could differ between groups, a test of homogeneity of dispersion (such as PERMDISP) is needed alongside, and the ecology module runs that test too.

The choice of dissimilarity is not cosmetic: Bray–Curtis for abundance, Jaccard or Sorensen for presence/absence, Euclidean for standardised continuous variables. Changing the measure changes the question.

PERMANOVA is a test, not a picture. It is normally reported next to an ordination — PCoA or NMDS — computed from the same dissimilarity measure, so that the figure and the test describe the same thing.

What it does

What Magic Stat gives you for PERMANOVA

How it works

Groups and a dissimilarity to a p-value

  1. Load the data. samples in rows, the variables in columns, and a categorical column holding the groups.
  2. Pick the entry point. the MANOVA/PERMANOVA tab of the mean-comparison tests for Euclidean data, or the ecology module's beta-diversity section for a chosen dissimilarity.
  3. Choose the dissimilarity and the permutations. match the measure to the data; Bray–Curtis and 999 permutations are the usual starting points.
  4. Run it. Magic Stat partitions the sum of squared distances and builds the null distribution by reshuffling the group labels.
  5. Read and export. pseudo-F, R² and p in the results table; the report entry and, where requested, a dissimilarity heatmap.
Options

The settings, in the dialog

Dissimilarity measures (ecology module): Bray–Curtis · Euclidean · Manhattan · Canberra · Jaccard · Sorensen · Horn–Morisita. The mean-comparison dialog runs PERMANOVA on Euclidean distances.

Permutations: a spinner in the ecology module (99 to 9999, default 999); the mean-comparison dialog uses its standard number. Missing values are dropped from the selected columns before the distance matrix is built.

Frequently asked

PERMANOVA questions, answered honestly

PERMANOVA or MANOVA?

MANOVA assumes multivariate normal responses and uses parametric test statistics. PERMANOVA makes no such assumption and works from distances. If your variables are roughly normal and on comparable scales, MANOVA has more power; otherwise PERMANOVA is the safer test. The same dialog reports both.

Do I need to check dispersion?

Yes, whenever a significant result could plausibly come from groups differing in spread rather than in position. Run a homogeneity-of-dispersion test — the ecology module has one — and report it next to the PERMANOVA. A significant PERMANOVA with unequal dispersion is a result that needs care in the wording.

Which dissimilarity should I use?

Match it to the data and state it: Bray–Curtis for abundance, Jaccard or Sorensen for presence/absence, Euclidean for standardised continuous variables. The ordination you report should use the same measure.

How many permutations?

More is better within reason; 999 is the common convention and the default here. With very few samples the minimum achievable p is bounded by the number of permutations, which is worth stating in the methods.

Is my data uploaded somewhere?

No — the analysis runs locally. The only automatic signal is an anonymous installation counter with no data in it.

NMDS analysis → PCoA analysis → Cluster analysis →