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Cited by 3,538

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Interval Estimation for a Binomial Proportion

Brown, Lawrence D., Cai, T. Tony, DasGupta, Anirban·2001·Statistical Science
DOI 10.1214/ss/1009213286
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Abstract

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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Citations

Cites

Research works printed but not linked: 40

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Metadata

Authors
Brown, L. D., Cai, T. T., & DasGupta, A.
Venue
Statistical Science
Publisher
Institute of Mathematical Statistics
Published
2001-05-01
Volume
16
Issue
2
Pages
101-133
ISSN
0883-4237 (ISSN-L)
DOI
10.1214/ss/1009213286
OpenAlex
W2106578604
Cited by
3,538
References
2
FWCI
23.75
Type
journal article
Language
ca
Open access
closed

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