A Multiple Comparison Procedure for Populations with Unequal Variances

This article investigates an exact method that extends Dunnett’s method on the multiple comparisons with a control (MCC) to the case of unequal error variances when the ratios of population variances of k new treatments to that of the control group are known from previous experience. The advantages of the proposed method is illustrated through an example. The simulation results show that the typical methods assuming the equal variance will have inflated error rate and may lead to erroneous inference. In addition, two approximate approaches are proposed to provide the simultaneous confidence intervals for the differences between each new treatment and the control mean with unknown ratios and unequal variances. The Monte Carlo study shows that the proposed approach always controls the family-wise error rate at a specified nominal level α, while some established method has inflated error rate in some instances.