Add the modified pseudo F statistic from Anderson et al 2017 to account for heterogeneity in adonis/adonis2

[gavinsimpson]

Anderson et al (2017: doi: 10.1111/anzs.12176) have proposed a modification to the pseudo F statistic in PERMANOVA that accounts for group heterogeneity.

The modified F is:

and provide an efficient way to get the group dispersions from the projection matrix that forms part of the calculation of F. This should fit nicely with our permutation-based testing.

Anderseon et al (2017) also provide two bootstrap-based testing options which we might explore, but these are of lesser priority.

Thoughts? (I can pass on the paper if you don't have access to it)

[MoREpro]

I would really need this modified F as my data have a very unbalanced design and the dispersion is heavily inhomogeneous in different groups. H would be really happy to see this implemented but unfortunately I’m not able to do it.

[caonetto]

Same here.