Abstract:
Given α ∈ (0,1), the coverage probability of the 100(1 − α)% Clopper-Pearson Confidence Interval (CPCI) for estimating a binomial parameter p is proved to be larger than or equal to 1−α/2 for sample sizes less than a bound that depends on p. This is a mathematical evidence that, as noticed in recent papers on the basis of numerical results, the CPCI coverage probability can be much higher than the desired confidence level and thence, that the Clopper-Pearson approach is mostly inappropriate for forming confidence intervals with coverage probabilities close to the desired confidence level.
