# One-way PerMANOVA

PerMANOVA (Permutational MANOVA, also known as NPMANOVA) is a non-parametric test of significant difference between two or more groups, based on any distance measure (Anderson 2001). PerMANOVA is normally used for ecological taxa-in-samples data, where groups of samples are to be compared, but may also be used as a general non-parametric MANOVA.

Items go in rows, variates in columns, and groups should be specified with a group column.

PerMANOVA calculates an *F* value in analogy with ANOVA. In fact, for univariate data sets and the Euclidean distance measure, PerMANOVA is equivalent to ANOVA and gives the same *F* value. See the Past manual for mathematical details.

The significance is computed by permutation of group membership, with 9,999 replicates (can be changed by the user).

#### Repeated measures

A repeated measures (blocked) ANOVA is carried out with the “Repeated measures” box is ticked. In this case, each group must have the same number of rows, and all the rows in each group must be consecutive. The first row in each group is then assumed to belong to the first subject (block), the second row in each group belongs to the second subject, etc. The calculations are analogous to the univariate repeated measures ANOVA.

The permutations for the *p* value are carried out only within subjects.

#### Pairwise tests

Pairwise PerMANOVAs between all pairs of groups are provided as a post-hoc test. Significant comparisons (at *p*<0.05) are shown in pink. The Bonferroni correction shown in the upper triangle of the matrix multiplies the *p* values with the number of comparisons. This correction is very conservative (produces large *p* values).

Missing data supported by pairwise deletion.

#### Reference

Anderson, M.J. 2001. A new method for non-parametric multivariate analysis of variance. *Austral Ecology* 26:32-46.