Exact Approaches for the Ratio of Means of Two Normal Populations

• Activity Number: 357
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Shu-Hui Lin*+ and Lee Jack C.
• Affiliation(s): Chiao-Tung University and National Chiao-Tung University
• Keywords: Fieller’s theorem ; Generalized p-values ; Generalized test variables ; Heteroscedasticity ; Pseudo Behrens-Fisher problem ; Ratio estimation

Abstract

Based on the generalized p-values developed by Tsui and Weerahandi (1989), hypothesis testing and confidence intervals for the ratio of means of two normal populations are constructed in order to solve Fieller's problems. We use two different procedures for finding two potential generalized test variables. One procedure is to find the generalized test variables directly based on the ratio of means. The other is to treat the problem as a pseudo Behrens-Fisher problem through testing the two-sided hypothesis on the ratio of means and then constructing the confidence interval as a counterpart of generalized p-values. Illustrative examples show that the two proposed methods are numerically equivalent for large-sample sizes. Furthermore, our simulation study shows that confidence intervals based on generalized p-values, without the assumption of identical variance, are more efficient than the other methods restricted to the assumption of equal variance, especially in the situation in which the heteroscedasticity of the two populations is serious.