A Study of the Powers of Several Methods of Multiple Comparisons

Abstract

Abstract Powers of multiple comparisons procedures are studied for fixed maximal experimentwise levels. Analytical considerations show Tukey-Scheffé methods to have least power, Duncan's to be intermediate, Ryan's most powerful. (Newman-Keuls tests could preserve experimentwise levels only if modified radically and impractically.) Extensive Monte-Carlo trials show these power differences to be small, especially for range statistics. We therefore generally recommend the Tukey technique for its elegant simplicity and existent confidence bounds—its power is little below that of any other method. Simulation was for 3, 4 and 5 treatments: the conclusions might need modification for more treatments.