The development of power estimates and sample size requirements for seven multiple comparisons procedures

Abstract

Multiple comparisons procedures are important because many nurse researchers use them to interpret their research findings. The goal of clinical research is to compare the relative effectiveness between treatments. However, power analysis procedures for omnibus tests were not specifically developed to estimate sample sizes required for such comparisons. Thus, this dissertation was designed to develop power and sample size tables for seven multiple comparisons procedures--Fisher LSD, Duncan multiple range test, Tukey HSD, Newman-Keuls range test, REGWQ, Bonferroni t, and Sidak multiplicative inequality. In order to both facilitate the design of multiple group studies and to provide more precise estimates of the relative power of these multiple comparisons procedures, based upon Bausell's (1996) rationale of statistical power for multiple comparisons, a total of 270 power and sample size tables were generated across a wide range of experimental conditions. Among the seven procedures examined in this dissertation, Fisher LSD and Duncan multiple range test were among those with the greatest statistical power, while Bonferroni t and Sidak multiplicative inequality were the ones with the least statistical power. To demonstrate how the seven procedures vary in terms of their sample size requirements, the relative and exact differences of sample size requirements are presented and discussed.