Performance of Four Multivariate Tests Under Variance-Covariance Heteroscedasticity

Abstract

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.

Restaurant servers’ perceptions of customer tipping intentions

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Consequences of Assumption Violations Revisited: A Quantitative Review of Alternatives to the One-Way Analysis of Variance F Test

“…Consequently, their willingness to adopt an ANOVA alternative may increase if they are able to recognize its applicability to a diverse range of design types. For example, have shown how to extend Welch's (1951) test to a variety of univariate and multivariate designs; James's (1951) procedure has been considered within the context of factorial univariate designs (Algina & Olejnik, 1984;Hsiung, Olejnik, & Oshima, 1994;Wilcox, 1989) and multivariate one-way independent groups designs (Algina, Oshima, & Tang, 1991;Tang & Algina, 1993); and the Brown-Forsythe test (Brown & Forsythe, 1974) has been studied for use in testing interaction hypotheses in repeated measures designs (Algina, 1994).…”

Testing Multivariate Effect Sizes in Multiple-Endpoint Studies

“…Tang and Algina (1993) show that the second-order test is superior to the first-order test, although computationally more intense. where Tr٪ represents the trace of a matrix.…”