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Zbl 1079.62517
Fouladi, Rachel T.; Yockey, Ronald D.
Type I error control of two-group multivariate tests on means under conditions of heterogeneous correlation structure and varied multivariate distributions. (English)
[J] Commun. Stat., Simulation Comput. 31, No. 3, 375-400 (2002). ISSN 0361-0918; ISSN 1532-4141/e

Summary: A Monte Carlo study was conducted to evaluate the performance of two-group multivariate tests on means under conditions of homogeneous and heterogeneous correlation structure and multivariate normality and nonnormality. The test statistics under study included those based on the work of Hotelling and alternative procedures proposed by James, Yao, Johansen, Nel and van der Merwe, and Kim. Results indicated that the F statistic based on Hotelling's $T^2$ was outperformed by the alternative procedures which showed good Type I error control under moderate to large sample sizes. Under small sample sizes, the alternative procedures tended to have unacceptable Type I error control. The F statistic based on Hotelling's $T^2$ is recommended for use when the sample size in each group is small (e.g., $n = p + 1$) and correlation heterogeneity is mild $(<.3)$, or when groups are approximately equal in size. Though simulated conditions of multivariate nonnormality had some impact on the Type I error rates on some of the procedures, the impact was in general small and apparent only under the smaller sample size conditions.

MSC 2000:: *62H15 Multivariate hypothesis testing
65C05 Monte Carlo methods

Keywords: Hotelling's $T^2$; MANOVA; Heterogeneity of covariance matrices; Heterogeneity of correlation matrices; Multivariate normality; Multivariate nonnormality; Behrens-Fisher problem

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