Protecting the overall rate of Type I errors for pairwise comparisons with an omnibus test statistic

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Abstract

Compares 2 procedures for protecting the number of false rejections for a set of all possible pairwise comparisons. The 2-stage strategy of computing pairwise comparisons, conditional on a significant omnibus test, is compared with the multiple comparison strategy that sets a “familywise” critical value directly. The ANOVA test, the Brown and Forsythe test, and the Welch omnibus test, as well as 3 procedures for assessing the significance of pairwise comparisons, are combined into 9 2-stage testing strategies. The data from this study establish that the common strategy of following a significant ANOVA F with Student's t tests on pairs of means results in a substantially inflated rate of Type I error when variances are heterogeneous. Type I error control, however, can be obtained with other 2-stage procedures, and the authors tentatively consider the Welch F″elch t″ combination desirable. In addition, the 2 techniques for controlling Type I error do not substantially differ as much as might be expected; some 2-stage procedures are comparable to simultaneous techniques. (18 ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved)

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