A STUDY OF MULTIVARIATE PERMUTATION TESTS WHICH MAY REPLACE HOTELLINGT(2) TEST IN PRESCRIBED CIRCUMSTANCES

Multivariate permutation tests are described and studied which may be profitably substituted for Hotelling's on example T2 test in situation s commonly arising in behavioral science research. These tests (a) may be computed even when the number of variables exceeds the number of s ubjects, (b) are distribution-free, (c) may be tailored for sensitivit y to specific treatment alternatives, and (d) provide one-sided as wel l as two-sided tests of hypotheses. Power comparisons were made betwee n the permutation tests and Hotellings T2 test under a variety of trea tment effect model, correlation structure and number of variables comb inations. Results show that the permutation tests have significant pow er advantages over the T2 in a variety of circumstances, but may have considerably less power in others.