The cost of using exact confidence intervals for a binomial proportion
Abstract
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.
Keywords
Cite
@article{arxiv.1303.1288,
title = {The cost of using exact confidence intervals for a binomial proportion},
author = {Måns Thulin},
journal= {arXiv preprint arXiv:1303.1288},
year = {2015}
}