I am currently working with Qiime 2 to analyze alpha & beta diversity with microbiome data of 48 sample.
(Animal stool samples)

I finished working of Beta diversity and got the data of significance. (Weighted UniFrac, Bray-curtis)

However, I received this message and need some help from you.

The message is as below*
" PERMANOVA can be sensitive to variation in dispersion - please examine whether the treatments differed in dispersion"

/ My question is, what type of variation test would be proper to compare the distance squares of microbial data and how can I do with python or R ? ( I am seriously considering Scheffe's test)

As far as I know, the input data of dispersion comparison is the distance square of each object

If I choose the right type of test, then Can I get the distance square data of each group from Qiime2 ?

And also, I want to hear any kind of recommendation to solve the question above from anyone who are familiar with the PERMANOVA statistics.
: the exact reason and meaning of the question or what kind of tools to solve the question are very welcomed because I can't understand that the reason to do another check for dispersion difference because dispersion test is already considered to examine the PERMANOVA results (F-test).

Just explanation about calculating the PERMANOVA is also welcomed !

I would recommend using the permdisp test (it's called betadispr in R). It's implemented in the beta-group-significance function; check the documentation to see which flag you need to use. The one caveat to this test is that it requires categorical data.

Best,
Justine

Here's some more discussion of the test, and idea: