Optimal Method for Realizing Two-Sided Inferences About a Linear Combination of Two Proportions

• Published in: Communications in statistics. Simulation and computation Vol. 42; no. 2; pp. 327 - 343
• Main Authors: Andrés, A. Martín, Hernández, M. Álvarez
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.02.2013; Taylor & Francis Ltd
• Subjects: Confidence interval; Confidence intervals; Linear combination of two proportions; Methods; Newcombe-Zou method; Peskun method; Score exact and approximate methods; Studies; Wald and adjusted Wald methods
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2011.650263

In order to reach the inference about a linear combination of two independent binomial proportions, various procedures exist (Wald's classic method, the exact, approximate, or maximized score methods, and the Newcombe-Zou method). This article defines and evaluates 25 different methods of inference, and selects the ones with the best behavior. In general terms, the optimal method is the classic Wald method applied to the data to which z 2 α/2 /4 successes and z 2 α/2 /4 failures are added (≈1 if α = 5%) if no sample proportion has a value of 0 or 1 (otherwise the added increase may be different). Supplemental materials are available for this article. Go to the publisher's online edition of Communications in Statistics - Simulation and Computation to view the free supplemental file.