Community Analysis Package
Analysis of Similarity (ANOSIM)
To undertake this test you must first have defined the group membership of the
individual samples (see 
Edit Groups
This test was developed by 
Clark (1988, 1993)
 as a test of the significance of
the groups that had been defined 
a priori
The idea is simple, if the assigned groups are meaningful, samples within groups
should be more similar in composition than samples from different groups.
The null hypothesis is therefore that there are no differences between the
members of the various groups.
Clark (1988, 1993)
  proposed the following statistic to measure the differences
between the groups:
   are the mean of the ranked similarity BETWEEN groups and WITHIN
groups respectively and
 n is the total number of samples (objects).
R scales from +1 to  1. +1 indicates that all the most similar samples are within
the same groups. R = 0 occurs if the high and low similarities are perfectly mixed
and bear no relationship to the group. A value of  1 indicates that the most similar
samples are all outside of the groups. While negative values might seem to be a
most unlikely eventuality it has been found to occur with surprising frequency.
To test for  significance the ranked similarity within and between groups is
compared with the similarity that would be generated by random chance.
Essentially the samples are randomly assigned to groups 1000 times and R
calculated for each permutation. The observed value of R is then compared
against the random distribution to determine if it is significantly different from that
which could occur at random.
If the value of R is significant you can conclude that there is evidence that the
samples within groups are more similar than would be expected by random
ANOSIM Results

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