Luca La Rocca writes:
You may like to know that the approach suggested in your post, Don’t do the Wilcoxon, is qualified as “common practice in Genome-Wide Association Studies”,
according to this forthcoming paper in Biometrics to which I have no connection (and which I didn’t inspect beyond the Introduction).
The idea is that, instead of doing Wilcoxon or some other rank-based test, you first rank the data, then convert them to z-scores using an inverse-normal transformation, then just analyze these transformed data using regression or Anova or whatever.
It’s a natural idea, not one that I take any particular credit for. We put it in BDA just to explain how a Bayesian might want to attack a problem for which someone might have otherwise applied a nonparametric test. I’m pretty sure the idea has been reinvented a zillion other times before and after I did it. So I’m glad that, at least in some fields, it’s a standard approach.