Analysis of similarities (ANOSIM) provides a way to test statistically whether there is a significant difference between two or more groups of sampling units.
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dat 
Data matrix or data frame in which rows are samples and columns are response variable(s), or a dissimilarity object or a symmetric square matrix of dissimilarities. 
grouping 
Factor for grouping observations. 
permutations 
a list of control values for the permutations
as returned by the function 
distance 
Choice of distance metric that measures the
dissimilarity between two observations. See 
strata 
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. 
parallel 
Number of parallel processes or a predefined socket
cluster. With 
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 (N1) / 4)
The divisor is chosen so that R will be in the interval 1 … +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 nullmodel. 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
.
The function returns a list of class "anosim"
with following
items:
call 
Function call. 
statistic 
The value of ANOSIM statistic R 
signif 
Significance from permutation. 
perm 
Permutation values of R. The distribution of
permutation values can be inspected with function 
class.vec 
Factor with value 
dis.rank 
Rank of dissimilarity entry. 
dissimilarity 
The name of the dissimilarity index: the

control 
A list of control values for the permutations
as returned by the function 
The anosim
function can confound the differences between groups
and dispersion within groups and the results can be difficult to
interpret (cf. Warton et al. 2012). The function returns a lot of
information to ease studying its performance. Most anosim
models could be analysed with adonis
which seems to be a
more robust alternative.
Jari Oksanen, with a help from Peter R. Minchin.
Clarke, K. R. (1993). Nonparametric multivariate analysis of changes in community structure. Australian Journal of Ecology 18, 117–143.
Warton, D.I., Wright, T.W., Wang, Y. 2012. Distancebased 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 adonis
is a more robust
alternative that should preferred.
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