Generalized confidence intervals for the ratio of means of two normal populations

✍ Scribed by Jack C Lee; Shu-Hui Lin

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 244 KB
• Volume: 123
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(03)00141-1

✦ Synopsis

Based on the generalized p-values and generalized conÿdence interval developed by Tsui and Weerahandi (J. Amer. Statist. Assoc. 84 (1989) 602), Weerahandi (J. Amer. Statist. Assoc. 88 (1993) 899), respectively, hypothesis testing and conÿdence intervals for the ratio of means of two normal populations are developed to solve Fieller's problems. We use two di erent procedures to ÿnd two potential generalized pivotal quantities. One procedure is to ÿnd the generalized pivotal quantity based directly 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 Â, and then to construct the 1 -generalized conÿdence 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 conÿdence intervals based on generalized p-values without the assumption of identical variance are more e cient than two other methods, especially in the situation in which the heteroscedasticity of the two populations is serious.