permutest.betadisper: Permutation test of multivariate homogeneity of groups...
In vegan: Community Ecology Package

Description Usage Arguments Details Value Author(s) References See Also Examples

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

## S3 method for class 'betadisper'
permutest(x, pairwise = FALSE,
          permutations = 999,
          parallel = getOption("mc.cores"),
          ...)

`x`	an object of class `"betadisper"`, the result of a call to `betadisper`.
`pairwise`	logical; perform pairwise comparisons of group means?
`permutations`	a list of control values for the permutations as returned by the function `how`, or the number of permutations required, or a permutation matrix where each row gives the permuted indices.
`parallel`	Number of parallel processes or a predefined socket cluster. With `parallel = 1` uses ordinary, non-parallel processing.
`...`	Arguments passed to other methods.

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.

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 `how`.

Gavin L. Simpson

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.

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
pmod <- permutest(mod, permutations = 99, pairwise = TRUE)

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

## Has permustats() method
pstat <- permustats(pmod)
densityplot(pstat)
qqmath(pstat)

Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3

	Homogeneity of multivariate dispersions

Call: betadisper(d = dis, group = groups)

No. of Positive Eigenvalues: 15
No. of Negative Eigenvalues: 8

Average distance to median:
  grazed ungrazed 
  0.3926   0.2706 

Eigenvalues for PCoA axes:
 PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
1.7552 1.1334 0.4429 0.3698 0.2454 0.1961 0.1751 0.1284 
Analysis of Variance Table

Response: Distances
          Df  Sum Sq  Mean Sq F value  Pr(>F)  
Groups     1 0.07931 0.079306  4.6156 0.04295 *
Residuals 22 0.37801 0.017182                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = distances ~ group, data = df)

$group
                      diff        lwr          upr     p adj
ungrazed-grazed -0.1219422 -0.2396552 -0.004229243 0.0429502