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Sample Size Determination for Binomial Proportion Confidence Intervals

This article revisits the problem of determining sample size for interval estimation of a binomial proportion. It is motivated by the author's experience as an expert witness in a legal case. The legal case involves a class action suit against a large service provider for alleged over-collection of special service fees. We discuss how: (1) focusing on relative error of the binomial outcome instead of absolute error of the Bernoulli probability p can have a dramatic effect on sample size recommendations, and (2) a year-by-year analysis may differ from a single-year analysis. We also discuss the challenges in presenting such statistical results to nonstatisticians, and propose simplifications to enhance communicability.