Permutation test of multivariate homogeneity of groups dispersions (variances)
Description
Implements a permutationbased test of multivariate homogeneity of
group dispersions (variances) for the results of a call to
betadisper
.
Usage
1 2 3 4 5 
Arguments
x 
an object of class 
pairwise 
logical; perform pairwise comparisons of group means? 
permutations 
a list of control values for the permutations
as returned by the function 
parallel 
Number of parallel processes or a predefined socket
cluster. With 
... 
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

pairwise 
a list with components 
groups 
character; the levels of the grouping factor. 
control 
a list, the result of a call to

Author(s)
Gavin L. Simpson
References
Anderson, M.J. (2006) Distancebased 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  data(varespec)
## BrayCurtis 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)

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