THE EFFECTS OF VARIANCE HETEROGENEITY ON SIMULTANEOUS MULTIPLE‐COMPARISON PROCEDURES WITH EQUAL SAMPLE SIZE

The robustness of three multiple-comparison procedures (multiple t test, Tukey WSD and Scheffe S test) to the violation of the homogeneous population variance assumption was investigated using three different standard error estimates. These estimates were (1) the square root of two mean square within/n, (2) the standard error of the traditional t test and (3) the standard error of the Behrens-Fisher t′ statistic. The procedures were highly robust to variance heterogeneity using the Behrens-Fisher standard error estimate. The procedures were considerably less robust using MSW. The universal use of the Behrens-Fisher statistic with the Welch solution for critical values is recommended.