The cost of using exact confidence intervals for a binomial proportion

By M. Thulin. 2013

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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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/77a97ff7a98cb7a3b9e362e192e1cbbbee1f2ec9