Multiple comparisons with a control under heteroscedasticity

Abstract

This article investigates three procedures on the multiple comparisons with a control in the presence of unequal error variances. The advantages of the proposed methods are illustrated through two examples. The performance of the proposed methods and other alternative methods is compared by simulation studies. The results show that the typical methods assuming equal variance will have inflated error rate and may lead to erroneous inference when the equal variance assumption fails. In addition, the simulation study shows that the proposed approaches always control the family-wise error rate at a specified nominal level α, while some established methods are liberal and have inflated error rate in some scenarios.

Keywords:

• multiple comparisons with a control
• family-wise error rate
• simultaneous confidence intervals
• heteroscedasticity
• Levene test

Acknowledgements

The authors would like to thank the referees for their patience and constructive comments that helped to make this article more precise.