Microbiome & multi-omics / ANOSIM
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ANOSIM ranks all pairwise distances and compares the mean rank of between-group distances with that of within-group distances: R = (r̄between − r̄within) / (n(n − 1)/4). R near 1 means groups are much more different from each other than within themselves, near 0 means no separation, and negative values mean within-group differences are larger.
P comes from permuting group labels; a fixed seed makes it reproducible. With three or more groups, pairwise ANOSIM with multiple-testing correction is available.
The plot shows distance ranks: the first box is between-group distances, the others within-group distances per group. R is large when the between box sits clearly above the within boxes.
ANOSIM is also affected by unequal within-group dispersion; use PERMANOVA as well when you need an effect size (variance explained).
Clarke K. R. (1993) Australian Journal of Ecology 18:117–143. The R statistic matches scikit-bio anosim (R vegan anosim); distances match scipy.spatial.distance.
Permutation tests are slow with more than 1,000 samples.
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