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Several metanalytic studies of group variability use variance ratios as measures of effect size. Problems with this approach are discussed, including limitations of using means and medians of ratios. Mean logarithms and the geometric mean are not adversely affected by the arbitrary choice of numerator. (SLD)

KEY WORDS: multiple comparisons, simultaneous testing, p-values, closed test procedures, pairwise comparisons CONTENTS INTRODUCTION ORGANIZING CONCEPTS Primary Hypotheses, Closure, Hierarchical Sets, and Minimal Hypotheses Families Type I Error Control Power [...]

Four pairwise multiple comparison procedures for achieving approximate familywise Type I error control were investigated when multisample sphericity was violated. The test statistic in all cases was the ratio of the corresponding sample mean difference divided by an estimate of its variance. Bonferroni, Studentized range, and Studentized maximum modulus critical values, each with Satterthwaite degrees of freedom, and an analog of the Cochran critical value were used with the test statistic. Results indicated that all procedures, except for the Cochran procedure, provided reasonable Type error control in most cases. The Cochran procedure generally was very conservative.

Two alternative procedures are described for testing the significance of differences of group means. The first consists of a reduction in the critical value when comparing the largest and smallest means. The other alternative uses the unmodified range test without a preliminary F test. An example is provided. (Author/CTM)

A presumed benefit of factorial design, noted in much of the literature on the subject, is efficiency of estimation. It is often stated that contrasts among the means of the [...]