I have been encountering a puzzling phenomenon when performing PERMANOVA tests with beta-group-significance in Qiime2 (v2018.2). The p-value for tests performed in Qiime2 are consistently lower than the results from the adonis function in the R package vegan. This is true for several data sets, but I have documented the analysis for one dataset at: https://github.com/maggimars/MicrobiomeSelection.
For this particular example, the adonis p-value for between group differences is 0.023, the R-squared is 0.506 and the F.Model is 2.0557. When the same analysis is repeated with Qiime2 beta-group-significance, the p-value is 0.003 and the psuedo-F is 3.0469.
I was under the impression that adonis and PERMANOVA in Qiime2 should yield the same results. Is there a simple reason why I may be seeing different results with the two methods?
The explanation you cited, together with this post, suggest that the F-values of the two tests should be identical, but they don't seem to be (if F.Model and psuedo-F are the same thing). Are they? If so, why aren't they the same?
I'm not fully aware of the details of R vegan package, but a similar discussion already came up a couple of years ago on QIIME1 forum. See: https://groups.google.com/d/msg/qiime-forum/qyDJAdECBnc/y3Mu-7iuvCUJ
In principle, your results should be the same provided that you use the same set of parameters, but it's likely that vegan treats your samples differently to QIIME2. In that case, you would compare 2 different sets of samples and get slightly different results.