The cost of using exact confidence intervals for a binomial proportion

作者：Thulin Mans^*

来源：Electronic Journal of Statistics, 2014, 8(1): 817-840.

DOI：10.1214/14-E4S909

• Asymptotic expansion
• binomial distribution
• confidence interval
• expected length
• sample size determination
• proportion

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.

• 出版日期2014