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Inference

Confidence Interval of the Difference of Two Independent Binomial Proportions Using Weighted Profile Likelihood

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Pages 645-659 | Received 27 Aug 2007, Accepted 24 Oct 2007, Published online: 17 Mar 2008
 

Abstract

Interval estimation of the difference of two independent binomial proportions is an important problem in many applied settings. Newcombe (Citation1998) compared the performance of several existing asymptotic methods, and based on the results obtained, recommended a method known as Wilson's method, a modified version of a method originally proposed for single binomial proportion. In this article, we propose a method based on profile likelihood, where the likelihood is weighted by noninformative Jeffrey' prior. By doing extensive simulations, we find that the proposed method performs well compared to Wilson's method. A SAS/IML program implementing this method is also given with this article.

Mathematics Subject Classification:

Acknowledgment

The authors would like to thank Professor Newcombe for providing us with his FORTRAN program by which all results of M7 in this article are computed. We are also grateful for many helpful comments he gave us to improve the manuscript.

Notes

M7 = Method 7 (True Profile Likelihood) of Newcombe (1998), NW = Modified Wilson's Method, PF = Weighted Profile Likelihood Method, AM = Agresti and Min (2001), CZ = Chan and Zhang (1999).

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