I'm trying to reduce noise (improve separability) among groups in a data set with 26 numerical variables and 10.000 samples. Each sample is a chemical profile, with each variable indicating the quantity of some chemical constituent. Most of the variables are far from normal.
My question is: how can I test whether samples are from separate multivariate distributions?
My intuition is to bootstrap the means for each variable within groups and then perform a permuted MANOVA test (or Hotelling's T-square) to simulate a null distribution. I know this works in the univariate case, as I've done so on microarray data, but I'm rather confused about whether or not I'm still violating assumptions.
The idea is to select samples I'm confident (at some alpha) are from different distributions, then use them as the basis of a clustering function. My data is highly collinear, which may indicate that certain samples have a common origin, and therefore the assigning of novel samples to known clusters would be informative.
Thanks a lot.