Revisiting Beal's Confidence Intervals for the Difference of Two Binomial Proportions

Abstract

Confidence interval construction for the difference of two independent binomial proportions is a well-known problem with a full panoply of proposed solutions. In this paper, we focus largely on the family of intervals proposed by Beal (1987). This family, which includes the Haldane and Jeffreys–Perks intervals as special cases, assumes a symmetric prior distribution for the population proportions p ₁ and p ₂. We propose new methods that allow the currently observed data to set the prior distribution by taking a parametric empirical-Bayes approach; in addition, we also provide an investigation of the new interval' behaviors in small-sample situations. Unlike other solutions, our intervals can be used adaptively for experiments conducted in multiple stages over time. We illustrate this notion using data from an Argentinean study involving the Mal Rio Cuarto virus and its transmission to susceptible maize crops.

Keywords:

• Adaptive estimation
• Agresti–Caffo intervals
• Empirical Bayes methods
• Maximum likelihood
• Plant disease

Mathematics Subject Classification:

• Primary 62F25
• Secondary 62L12

Acknowledgments

Part of this work stems from the first author's Master's Report, which was completed while both authors were members of the Department of Statistics at Kansas State University. We thank Shie-Shien Yang, Jim Neill, and Christopher Bilder for their helpful comments and criticisms.

Notes

Source: Ornaghi et al. (1999).

Source: Ornaghi et al. (1999).