Statistical difference for multivariate data

Suppose I have sets of compounds in some arbitrary multivariate space.  The components of the space may or may not

be orthogonal or normalized.  How might I calculate statistical differences for these sets of compounds analogous

to a T test (or similar) in one continuous dimension, but for the multi-dimensional case?

Ideas?  Does anyone have a Pipeline Pilot protocol, or perhaps a protocol that calls R stats functions for performing

this analysis that they can share?

Apologies in advance for my statistical ignorance if this is a "solved" problem!

Thank you.

Regards,

Jim Metz

James.Metz@Abbvie.com

Abbvie