Statistically Proper Multiple Range Tests for a Within Subject Factor in a Repeated Measures Design

It is a common practice in many research areas that multiple range tests for a between subject factor such as Tukey are applied to a within subject factor in a repeated measures design. Tukey procedure, however, sometimes detects no pairs with different means even when the hypothesis of all equal level means is rejected. This study attempts to provide a rationale for the proposition that Tukey is inappropriate post hoc procedure for a within subject factor in which the observations are correlated. We introduce two multiple range tests, Bonferroni and Scheffe, for a within subject factor and show that Bonferroni is more appropriate than Scheffe for pairwise multiple comparisons. Subsequent simulation study indicates that Tukey has significantly less power than Bonferroni in detecting actual difference between means of some pairs when the observations of a within subject factor are highly correlated.