Stepwise Multiple Comparison Procedures

Abstract This article proposes two new stepwise multiple comparison significance tests which control the experimentwise type I error rate and compares these tests with some existing procedures. The new (step-up) tests begin by examining the gaps between adjacent ordered sample means, then the three stretches, etc., until the range is reached. This reverses a procedure (step-down) proposed by Ryan (1960). Tables for the new tests were constructed using improved Monte Carlo techniques. A simulation study showed that one of the new step-up tests and a modification of the Ryan procedure provided significantly greater power than the commonly used Tukey honestly significant difference test.