For Post Hoc’s Sake: Determining Sample Size for Tukey Multiple Comparisons in 4-Group ANOVA

Abstract

The determination of an appropriate sample size is a difficult, yet critically important, element in the research design process. Sample sizes in ANOVA are most often based on an overall standardized difference in the means, but these recommended sample sizes provide statistical power only for the omnibus F test. Adequate sample size for the omnibus test does not necessarily provide sufficient statistical power for the post hoc multiple comparisons typically performed following a statistically significant omnibus F test. The purpose of this paper is to use Monte Carlo techniques to determine sample sizes that will provide adequate statistical power for Tukey post hoc multiple comparison procedure (MCP) in 4-group ANOVA. Sample size tables are included.