permutest.betadisper: 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 betadisper
permutest(x, pairwise = FALSE,
          permutations = 999,
          parallel = getOption("mc.cores"),
          ...)

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 how.

Arguments

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.

Author

Gavin L. Simpson

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.

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.

Examples

Run this code

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)

## lattice graphics with permustats
pstat <- permustats(pmod)
permulattice(pstat, "densityplot", scale = list(x=list(relation="free")))
permulattice(pstat, "qqmath", scales = list(relation = "free"))

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