Permutation test of multivariate homogeneity of groups dispersions (variances)

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.

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.

Author

Gavin L. Simpson

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
#> 
#> 	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:
#> (Showing 8 of 23 eigenvalues)
#>  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
#> 1.7552 1.1334 0.4429 0.3698 0.2454 0.1961 0.1751 0.1284 

## Perform test
anova(mod)
#> 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

## Permutation test for F
pmod <- permutest(mod, permutations = 99, pairwise = TRUE)

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


## Has permustats() method
pstat <- permustats(pmod)
densityplot(pstat, scales = list(x = list(relation = "free")))

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