Open Access
2014 The cost of using exact confidence intervals for a binomial proportion
Måns Thulin
Electron. J. Statist. 8(1): 817-840 (2014). DOI: 10.1214/14-EJS909


When computing a confidence interval for a binomial proportion $p$ one must choose between using an exact interval, which has a coverage probability of at least $1-\alpha$ for all values of $p$, and a shorter approximate interval, which may have lower coverage for some $p$ but that on average has coverage equal to $1-\alpha$. We investigate the cost of using the exact one and two-sided Clopper–Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then in terms of the increase in sample size required to obtain a desired expected length. Using asymptotic expansions, we also give a closed-form formula for determining the sample size for the exact Clopper–Pearson methods. For two-sided intervals, our investigation reveals an interesting connection between the frequentist Clopper–Pearson interval and Bayesian intervals based on noninformative priors.


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Måns Thulin. "The cost of using exact confidence intervals for a binomial proportion." Electron. J. Statist. 8 (1) 817 - 840, 2014.


Published: 2014
First available in Project Euclid: 16 June 2014

zbMATH: 1348.62092
MathSciNet: MR3217790
Digital Object Identifier: 10.1214/14-EJS909

Primary: 62F25
Secondary: 62F12

Keywords: asymptotic expansion , Binomial distribution , Confidence interval , expected length , proportion , sample size determination

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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