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I'm comparing 12 Metagenomes. I'm using HMM counts of a number of proteins known to exists as groups within certain operons. I have grouped the HMM counts for each type of operon and calculated the Shannon-Weaver index for each Metagenome.

My question is: Can I compare these Indices? Is there a better test to use than Mann Whitney U test? I would like to do this on the ungrouped data, but I have many zeroes for some fields?

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I'm not an expert on Shannon-Weaver Index, but according to wikipedia it is the same as exponentially transformed Renyi entropy. If it is the case, you can compare them since they are scale invariant summary statistics. If you want error bars, you can always try resampling methods such as bootstrapping. Hypothesis testing can also be done with bootstrapping, although the power of the statistical test may not be very strong and fail to reject the null.

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It is fairly simple to normalize this measure by the number of observations, so you can have values in the 0-1 range at the end, which are way easier to compare.

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