title: A comment on sample size calculations for binomial confidence intervals.
abstract: In this article we examine sample size calculations for a binomial proportion based on the confidence interval width of the Agresti-Coull, Wald and Wilson Score intervals. We pointed out that the commonly used methods based on known and fixed standard errors cannot guarantee the desired confidence interval width given a hypothesized proportion. Therefore, a new adjusted sample size calculation method was introduced, which is based on the conditional expectation of the width of the confidence interval given the hypothesized proportion. With the reduced sample size, the coverage probability can still maintain at the nominal level and is very competitive to the converge probability for the original sample size.
authors.affiliation: Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA.
authors.forename: Lai
authors.initials: L
authors.lastname: Wei
authors.affiliation: Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Hutson
keywords: Agresti—Coull interval; Wald interval; Wilson Score interval; binomial proportion; expected width; sample size calculation