Analysis of similarities (ANOSIM) provides a way to test statistically whether there is a significant difference between two or more groups of sampling units.
anosim(x, grouping, permutations = 999, distance = "bray", strata = NULL,
parallel = getOption("mc.cores"))The function returns a list of class "anosim" with following
items:
Function call.
The value of ANOSIM statistic \(R\)
Significance from permutation.
Permutation values of \(R\). The distribution of
permutation values can be inspected with function permustats.
Factor with value Between for dissimilarities
between classes and class name for corresponding dissimilarity
within class.
Rank of dissimilarity entry.
The name of the dissimilarity index: the
"method" entry of the dist object.
A list of control values for the permutations
as returned by the function how.
Analysis of similarities (ANOSIM) provides a way to test statistically
whether there is a significant difference between two or more groups
of sampling units. Function anosim operates directly on a
dissimilarity matrix. A suitable dissimilarity matrix is produced by
functions dist or vegdist. The
method is philosophically allied with NMDS ordination
(monoMDS), in that it uses only the rank order of
dissimilarity values.
If two groups of sampling units are really different in their species
composition, then compositional dissimilarities between the groups
ought to be greater than those within the groups. The anosim
statistic \(R\) is based on the difference of mean ranks between
groups (\(r_B\)) and within groups (\(r_W\)):
$$R = (r_B - r_W)/(N (N-1) / 4)$$
The divisor is chosen so that \(R\) will be in the interval \(-1 \dots +1\), value \(0\) indicating completely random grouping.
The statistical significance of observed \(R\) is assessed by
permuting the grouping vector to obtain the empirical distribution
of \(R\) under null-model. See permutations for
additional details on permutation tests in Vegan. The distribution
of simulated values can be inspected with the permustats
function.
The function has summary and plot methods. These both
show valuable information to assess the validity of the method: The
function assumes that all ranked dissimilarities within groups
have about equal median and range. The plot method uses
boxplot with options notch=TRUE and
varwidth=TRUE.
Clarke, K. R. (1993). Non-parametric multivariate analysis of changes in community structure. Australian Journal of Ecology 18, 117--143.
Warton, D.I., Wright, T.W., Wang, Y. 2012. Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89--101
mrpp for a similar function using original
dissimilarities instead of their ranks.
dist and vegdist for obtaining
dissimilarities, and rank for ranking real values. For
comparing dissimilarities against continuous variables, see
mantel. Function adonis2 is a more robust
alternative that should preferred.
data(dune)
data(dune.env)
dune.dist <- vegdist(dune)
dune.ano <- with(dune.env, anosim(dune.dist, Management))
summary(dune.ano)
plot(dune.ano)
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