Stepwise multiple testing procedures for the successive comparison of variances

Abstract

In this paper, stepwise multiple testing procedures are proposed for comparing successive populations in a sequence of several independent normal populations using index parameter variance. The proposed procedures have advantages over the single-step procedures and closed testing procedures available in the existing literature. The proposed stepwise testing procedures, control the family-wise error rate (FWER) strongly, and dramatically improve in power over the relevant single-step procedures. The closed testing procedure, which is step-down in nature and is developed for a testing problem, is very complex in its implementation, and this complexity increases further as the number of successive comparisons increases. The relevant critical constants have been tabulated to facilitate the implementation of the proposed procedures. We also proposed testing procedures for comparing the successive populations in a sequence of two-parametric exponential populations with regards to their scale parameters. In an effort to discern the efficiency of proposed procedures, simulated power comparisons with relevant existing procedures are presented, and the working of the proposed procedures is exemplified by means of two real-life data sets.

KEYWORDS:

• Single-step procedure
• closed testing procedure
• family-wise error rate (FWER)
• simulated power comparisons
• critical constants

Acknowledgments

The authors are enormously grateful to the reviewers and the editor for their insightful comments and suggestions, which helped us in improving the quality of the manuscript.