Performance of Four Multivariate Tests Under Variance-Covariance Heteroscedasticity.

Type I error rates (τ) of four multivariate tests - Pillai-Bartlett trace, Johansen's test, James' first order test and James' second order test - were compared for heterogeneous covariance matrices. A total of 360 simulated experiments were conducted. Johansen's test and James' second order test performed better than the other two tests. The τ of Johansen's test should be very close to a when the ratio of total sample size to number of variables (N/p) is large, and the smaller samples are associated with covariance matrices with smaller elements. James' second order test outperformed the other tests under extreme conditions; that is, when Nip is small, the heterogeneity of covariance matrices is large, the sample size ratio is large, or the smaller samples are associated with covariance matrices with larger elements.

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