EXACT PROBABILITIES ASSOCIATED WITH TUKEY'S AND DUNNETT'S MULTIPLE COMPARISONS PROCEDURES IN IMBALANCED ONE-WAY ANOVA

A FORTRAN program using Simpson's rule is reported for computing exact p-values associated with Tukey's and Dunnett's multiple comparisons procedures in an imbalanced one-way ANOVA model. A FORTRAN program for Dunnett's test is provided by Dunlap, Marx and Agamy (1981) in the case of all the sample sizes of treatment groups, except for a control group, being homogeneous. We modify their program to keep better computational accuracy and extend it to imbalanced Tukey's and Dunnett's tests. We investigate the computational accuracy and CPU times by applying it to many actual critical values in some published tables. Exact p-values of Tukey's test for some critical values of Hunter method, which are given by Stoline (1981) as the examples that Tukey-Kramer method is slightly more conservative than Hunter method for certain imbalanced cases, are illustrated with the corresponding approximate p-values of Tukey-Kramer's test.