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Power comparisons are provided for three permutation tests and the Bartlett-Nanda-Pillai trace test in completely randomized experimental designs with correlated multivariate dependent variables. Five bivariate distributions, five levels of correlation, equal and unequal sample sizes, two variations of location shifts, and two types of commensuration are considered in the power analyses. With very few exceptions, the power of the Bartlett-Nanda-Pillai trace test is found to be less than the corresponding power for at least one of the permutation tests.
Mielke et al. (Tue,) studied this question.