During stats courses on Uni I learnt (if I remember correctly and hopefully don't put my teachers to shame) that if you want to compare multiple groups with each other you look at the residuals of an ANOVA test. If the residuals are normally distributed, it is the right test to use and you can do a post-hoc on it (Tukey for instance). If not, you go to Kruskal-Wallis and can do a Scheffe post hoc.
I am doing data analysis in R and find much more complicated answers to this problem when googling, among which is https://www.researchgate.net/post/Which_post_hoc_test_is_best_to_use_after_Kruskal_Wallis_test
I have count data on species on 9 different sites (6 samples per site). Most species only occur there very rarely and in very low numbers. So the frequency of count 0 is very high. In R I can run an anova, both assuming a Gaussian distribution, but also assuming Poisson, quasi-Poisson and negative binomial distributions. I managed to make a plot with the observed frequencies of my counts and the expected frequencies based on these distributions, and none of the distributions seem to match nicely. This is a graph for one of those species:
So if I am correct, the only thing that is left to me is using a non-parametric test like Kruskal-Wallis to compare the mean counts between the 9 different sites. Is this correct? And if so, what post hoc test could I use to test the pairwise between-site differences?