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Testing of hypotheses in multivariate split-plot designs with arbitrary dispersion matrices. (Spanish. English summary) Zbl 1011.62061

Summary: The aim of this paper is to evaluate several multivariate procedures for testing omnibus null hypotheses for data gathered from multivariate split plot designs when the assumption of homogeneity of dispersion matrices is violated. An examination of these procedures for a wide number of variables confirms, on the one hand, the robustness of the Welch-James multivariate solution given by S. Johansen [Biometrika 67, 85-92 (1980; Zbl 0422.62066)] for testing the trials main effect hypothesis and, on the other hand, the robustness of the multivariate generalization of the Brown-Forsythe procedure [M.B. Brown and A.B. Forsythe, Technometrics 16, 129-132 (1994; Zbl 0275.62047)] for testing the groups \(x\) trial interactions. Our results also show that the power advantage was small in conditions in which the Welch-James and Brown-Forsythe tests control the Type I error rates.

MSC:

62H15 Hypothesis testing in multivariate analysis
62K99 Design of statistical experiments
62K10 Statistical block designs
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