permutest.betadisper {vegan} R Documentation

## Permutation test of multivariate homogeneity of groups dispersions (variances)

### Description

Implements a permutation-based test of multivariate homogeneity of group dispersions (variances) for the results of a call to `betadisper`.

### Usage

```## S3 method for class 'betadisper':
permutest(x, pairwise = FALSE,
control = permControl(nperm = 999), ...)
```

### Arguments

 `x` an object of class `"betadisper"`, the result of a call to `betadisper`. `pairwise` logical; perform pairwise comparisons of group means? `control` a list of control values for the permutations to replace the default values returned by the function `permControl` `...` Arguments passed to other methods.

### Details

To test if one or more groups is more variable than the others, ANOVA of the distances to group centroids can be performed and parametric theory used to interpret the significance of F. An alternative is to use a permutation test. `permutest.betadisper` permutes model residuals to generate a permutation distribution of F under the Null hypothesis of no difference in dispersion between groups.

Pairwise comparisons of group mean dispersions can be performed by setting argument `pairwise` to `TRUE`. A classical t test is performed on the pairwise group dispersions. This is combined with a permutation test based on the t statistic calculated on pairwise group dispersions. An alternative to the classical comparison of group dispersions, is to calculate Tukey's Honest Significant Differences between groups, via `TukeyHSD.betadisper`.

### Value

`permutest.betadisper` returns a list of class `"permutest.betadisper"` with the following components:

 `tab` the ANOVA table which is an object inheriting from class `"data.frame"`. `pairwise` a list with components `observed` and `permuted` containing the observed and permuted p-values for pairwise comparisons of group mean distances (dispersions or variances). `groups` character; the levels of the grouping factor. `control` a list, the result of a call to `permControl`.

Gavin L. Simpson

### References

Anderson, M.J. (2006) Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62(1), 245–253.

Anderson, M.J., Ellingsen, K.E. & McArdle, B.H. (2006) Multivariate dispersion as a measure of beta diversity. Ecology Letters 9(6), 683–693.

For the main fitting function see `betadisper`. For an alternative approach to determining which groups are more variable, see `TukeyHSD.betadisper`.

### Examples

```data(varespec)

## Bray-Curtis distances between samples
dis <- vegdist(varespec)

## First 16 sites grazed, remaining 8 sites ungrazed
groups <- factor(c(rep(1,16), rep(2,8)), labels = c("grazed","ungrazed"))

## Calculate multivariate dispersions
mod <- betadisper(dis, groups)
mod

## Perform test
anova(mod)

## Permutation test for F
permutest(mod, pairwise = TRUE)

## Tukey's Honest Significant Differences
(mod.HSD <- TukeyHSD(mod))
plot(mod.HSD)
```

[Package vegan version 1.16-32 Index]