A Study of Multivariate Permutation Tests Which May Replace Hotelling's T2 Test in Prescribed Circumstances

Multivariate permutation tests are described and studied which may be profitably substituted for Hotelling's one-sample P test in situations commonly arising in behavioral science research. These tests (a) may be computed even when the number of variables exceeds the number of subjects, (b) are distribution-free, (c) may be tailored for sensitivity to specific treatment alternatives, and (d) provide one-sided as well as two-sided tests of hypotheses. Power comparisons were made between the permutation tests and Hotelling's T(2) test under a variety of treatment effect model, correlation structure and number of variables combinations. Results show that the permutation tests have significant power advantages over the T(2) in a variety of circumstances, but may have considerably less power in others.