I'm analyzing chemical profiles of amphetamine samples, and each sample has 26 numerical variables describing the relative quantity of some chemical constituent. Only a few of the 26 variables have pretty Gaussian distributions, the rest are amorphous (e.g. one very large "0" bin and a small Gaussian-like hill to the right).
I'd like to test whether populations differ by geographical origin (or some other ordinal variable), but I'm not sure how to test against this null hypothesis because the underlying assumption of multivariate normality is violated. Can I perform a Hotelling's T-square test via permutation, or am I looking for something like the Kullback-Leibler divergence?
My training is in biology and most certainly did not prepare me for this, so I apologize in advance for having missed obvious things. Thanks a lot.