The cost of using exact confidence intervals for a binomial proportion
2014 (English)In: Electronic Journal of Statistics, ISSN 1935-7524, Vol. 8, 817-840 p.Article in journal (Refereed) Published
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.
Asymptotic expansion, binomial distribution, confidence interval, expected length, sample size determination, proportion
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-226501DOI: 10.1214/14-EJS909ISI: 000338327100001OAI: oai:DiVA.org:uu-226501DiVA: diva2:726002