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The cost of using exact confidence intervals for a binomial proportion
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2014 (English)In: Electronic Journal of Statistics, ISSN 1935-7524, E-ISSN 1935-7524, Vol. 8, 817-840 p.Article in journal (Refereed) Published
Abstract [en]

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 a 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 a. We investigate the cost of using the exact one and two-sided Clopper-Pearson confidence intervals rat her 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.

Place, publisher, year, edition, pages
2014. Vol. 8, 817-840 p.
Keyword [en]
Asymptotic expansion, binomial distribution, confidence interval, expected length, sample size determination, proportion
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-226501DOI: 10.1214/14-EJS909ISI: 000338327100001OAI: oai:DiVA.org:uu-226501DiVA: diva2:726002
Available from: 2014-06-17 Created: 2014-06-17 Last updated: 2017-12-05Bibliographically approved

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Thulin, Måns

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