I have a multivariate dataset with data from several groups. I'm interested in determining at what point are two groups similar enough such that they can be treated as a single group for sampling purposes? At the moment I'm treating each group as a separate population. Logically it seems like the groups could all be treated as one, but when looking at the data they aren't completely homogenous. I'd like to know if the groups are similar enough such that I can sample from only one of them and get the same information from the population. Some of the things that I've been looking at are the multivariate variance using the betadisper() function in vegan as well as adonis() and anosim() to look at the homogeneity of composition. I've also done a univariate analyses (anova, kruskal wallis) to see how they differ by element. However, I don't know at what point I could say they are similar enough to be treated as one as it seems very subjective or which ones are more different than others really.

Are there any rules of thumb that could be applied to this situation? Are there any alternate tests that could be used to provide a more concrete answer?

A little more about the data:

  • I'm using it to build a training set for a classification problem.
  • The data is compositional data which might impact the methods that could be applied.
  • The groups have unequal sizes.

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