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Community Analysis Package

9.2

Analysis of Similarity (ANOSIM)

To undertake this test you must first have defined the group membership of the

individual samples (see 

Edit Groups

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).

This test was developed by 

Clark (1988, 1993)

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 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)

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  proposed the following statistic to measure the differences

between the groups:

 where

   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

chance.

ANOSIM Results

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