I might as well ask this here, since I hope that others will ask therir questions here (and hopefully get answers!):

This relates to elliptical Fourier analysis, but the EFA isn't the problem.  EFA spits out 22 variables (Fourier coefficients) for each specimen.  I am attempting to compare different samples (each containing a number of specimens) using methods other than principal component analysis.  That is, I am looking for a statistical test that will compare the samples and tell me if they came from the same population or not. 

This sounds easy, in theory, because the multivariate version of the Student's t-test is Hotelling's T².  Unfortunately, to run discriminant analysis, I need multivariate normality, and to run Hotelling's T², I need equal variance-covariance matrices.  According to skewness and kurtosis tests, I do not have multivariate normality, and according to Box's M test (which has the tendancy to be too sensitive to inequality), I do not have equal variance-covariance matrices.

I am basing my statistical methods on a number of papers (which I am going back through now), and I don't think anyone has worried about this before running discriminant analysis on the elliptical Fourier coefficients.  This bothers me, so I am hoping for some input on what I should be able to do or not do in this case.