Monte Carlo simulation reveals superior robustness for the Pillai-Bartlett trace test against assumption violations in MANOVA models, suggesting it as the optimal choice over the largest-root test.
Monte Carlo methods were used to study the performance of the largest-root test, two trace-type tests and three determinantal tests in the fixed-effects MANOVA model when certain assumptions are violated. Results indicated that for protection against nonnormality and heterogeneity of covariance matrices, the largest-root test should be avoided, while the Pillai-Bartlett trace test may be recommended as the most robust of the MANOVA tests, with adequate power to detect true differences in a variety of situations.
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Chester L. Olson (1974) studied this question.
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