Exact sample size determination for binomial experiments

In experiments designed to estimate a binomial parameter, sample sizes are often calculated to ensure that the point estimate will be within a desired distance from the true value with sufficiently high probability. Since exact calculations resulting from the standard formulation of this problem can be difficult, “conservative” and/or normal approximations are frequently used. In this paper, some problems with the current formulation are given, and a modified criterion that leads to some improvement is provided. A simple algorithm that calculates the exact sample sizes under the modified criterion is provided, and these sample sizes are compared to those given by the standard approximate criterion, as well as to an exact conservative Bayesian criterion.