“Everything Old Is New Again”: Human-friendly Scheffé contrasts and “All That Jazz”

• In Event: Advancement of Statistical Methodology

Abstract

Most applied researchers are familiar with multiple comparison procedures (MCPs), like Scheffé (1953), used to explore pairwise group mean comparisons following a statistically significant one-way analysis of variance (ANOVA). Most researchers have learned that Scheffé lacks power because it adjusts for all possible pairwise and complex comparisons—consequently, few use it. We believe they are missing potentially useful information: only Scheffé is congruent with ANOVA (i.e., guarantees a significant comparison—pairwise or non-pairwise—following a significant ANOVA) and there is a Scheffé contrast can be calculated that provides the set of contrast coefficients that maximally differentiates some combination of the groups (Keppel & Wickens, 2004; Williams, 1978). Our purposes were to: (1) implement code that finds Scheffé maximum contrasts—and a “human-friendly” version of Scheffé, (2) test them statistically with Scheffé’s MCP and Brown-Forsythe’s adjustment for unequal variances, and (3) run Monte Carlo simulations to extend previous research.

Authors

• Frank Agyemang Oppong, Ohio University

• Yuqing Liu, Ohio University

• Nina Adanin, Northwest Missouri State University

• Gordon Brooks, Ohio University