So, if I have two groups of samples, one from s and one from , and I do a test on them, I hope that permanova is testing the hypothesis that d vs and d vs is smaller than d vs . (Because then I can say that the difference in the microbiome between and is larger than the differences in the microbiome within each group.)
…This works pretty well if variation/dispersion within each group is close to the same size, because then it becomes a pretty easy comparison. But, if d vs >>> d : vs , then when you test the distance, d vs > d : vs , because the larger dispersion in the group shifts that dispersion.
…Here’s the good news! You can apply the permdisp test (it’s an option under
qiime diversity beta-group-significance) and that will test that assumption around dispersion within your groups. It also gives you a handy little boxplot that can let you look at the within and between group distances and get a sense for yourself.