Modified Sequentially Rejective Multiple Test Procedures

An Improved Sequentially Rejective Bonferroni Test Procedure

“…For situations where there are logical implications among the k hypotheses (e.g., the truth of some of the hypotheses necessarily implies the truth of some others), Shaffer ( 1986) shows that it is possible to modify Holm's procedure to provide a further increase in power at the cost of greater complexity.…”

Pairwise Multiple Comparison Tests when Data are Nonnormal

“…The results tabled by indicate that when trimmed means and Winsorized variances are substituted into Welch's (1938) heteroscedastic statistic, rates of Type I error can indeed be controlled under these same conditions with many stepwise MCPs (e.g., Shaffer's, 1986, sequentially rejective Bonferroni procedure, Hayter's, 1986, two-stage 432 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT modified LSD procedure, range-type procedures, and Hochberg's, 1988, step-up sequentially acceptive Bonferroni procedure). Accordingly, we recommend that for pairwise comparisons of treatment group means, researchers adopt one of the MCPs enumerated by Keselman, Huberty, et al (1998) when data are nonnormal, variances are unequal, and the design is unbalanced-conditions that, according to various authors, characterize behavioral science investigations.…”

The Composite Hypothesis Contrast Procedure: A Novel Sequential Multiple-Comparison Approach

“…There it is found that with a three-mean effect size defined as f 2 = ω 2 /(1 -ω 2 ), both where f is held constant at 0.471 in Parts A and B of Table 1 and as a general rule: (1) when the two averaged experimental means are equal and different from the control mean (Panel A), Stage 1 of the present composite hypothesis contrast (CHC) approach overpowers at least three of its would-be competitors, namely, Fisher's Holm's (1979) sequential Bonferroni procedure and Dunnett's (1955) "each vs. one" multiple-comparison procedure applied to the larger of the two second-stage experimental vs. control comparisons; and (2) when the three means are more equally separated within the three-mean interval (Panel B), the one-and two-tailed test powers of the CHC approach are only slightly lower than those of the corresponding Holm and Dunnett powers, with the CHC approach's one-tailed powers still remaining higher than those of Fisher's LSD test. In a previous study, Serlin and Mailloux (1999) investigated the analysis of designs with two conditions and two outcome measures, analogous to Design 3 above. They added together the two standardized outcome measures to form a composite that is similar to the composite that was described earlier here.…”

“…The assertion follows, chronologically, from Fisher's (1935) least significant difference (LSD) protected multiple-comparison procedure when applied in a three-mean context; Fletcher's (personal communication, October 3, 1981) perceptive insights about that particular application of the procedure; Shaffer's (1986) introduction to, and cogent discussion of, the notion of logical implications of subsumed hypotheses; and the Monte Carlo simulation demonstrations of Seaman, Levin, and Serlin (1991), Zhou and Levin (2004), and others.…”