R: Permutation test of multivariate homogeneity of groups...

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,
              permutations = 999,
              parallel = getOption("mc.cores"),
              ...)

### 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.

### 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 `how`.

### Author(s)

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.

### See Also

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
    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, scales = list(x = list(relation = "free")))
    qqmath(pstat, scales = list(relation = "free"))

[Package vegan version 2.4-3 Index]