Open Access
May 2001 Interval Estimation for a Binomial Proportion
Lawrence D. Brown, T. Tony Cai, Anirban DasGupta
Statist. Sci. 16(2): 101-133 (May 2001). DOI: 10.1214/ss/1009213286


We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standard Wald confidence interval has previously been remarked on in the literature (Blyth and Still, Agresti and Coull, Santner and others). We begin by showing that the chaotic coverage properties of the Wald interval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects and cannot be trusted.

This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examined for its coverage probability and its length. Based on this analysis, we recommend the Wilson interval or the equal-tailed Jeffreys prior interval for small n and the interval suggested in Agresti and Coull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.


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Lawrence D. Brown. T. Tony Cai. Anirban DasGupta. "Interval Estimation for a Binomial Proportion." Statist. Sci. 16 (2) 101 - 133, May 2001.


Published: May 2001
First available in Project Euclid: 24 December 2001

zbMATH: 1059.62533
MathSciNet: MR1861069
Digital Object Identifier: 10.1214/ss/1009213286

Keywords: Bayes , Binomial distribution , confidence intervals , coverage probability , Edgeworth expansion , expected length , Jeffreys prior , Normal approximation , Posterior

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.16 • No. 2 • May 2001
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