Testing powers of the ratio of variances of two normal populations with a common mean

Abstract

This article addresses the problem of hypothesis testing about the powers of the ratio of variances of two normal populations with a common mean. Different test procedures are proposed, such as the likelihood ratio test, the standardized likelihood ratio test, the parametric bootstrap likelihood ratio test, the computational approach test and its modification. Further, several generalized p-value approach test procedures are derived using some of the existing common mean estimators. The performances of all the suggested test methods are compared numerically in terms of their size values and power functions. In light of our simulation findings, we provide a few suggestions for utilizing the proposed test methods. Finally, we analyse real-life data to show the potential application of the proposed model.

Keywords:

• Bootstrap samples
• common mean
• generalized p-value
• plug-in estimators
• ratio of variances
• power function
• simulation study
• size value

2010 AMS Subject Classifications:

• 62F03
• 62F05
• 62F10
• 65C05

Acknowledgments

The authors would like to sincerely thank the two anonymous reviewers, whose constructive and thoughtful comments on the earlier version of the manuscript led to greater improvements in the manuscript's content.

Disclosure statement

The authors declare that there are no relevant financial or non-financial competing interests to report for this work.