On the Confidence Interval for the Binomial Parameter

The use of confidence intervals (CIs) is strongly recommended in the 5th edition of the Publication Manual of the American Psychological Association. The CI for the binomial parameter π is customarily obtained using Wald method, which uses the normal approximation to the binomial distribution and the estimated standard error. Wald CI has been shown to be unsatisfactory and alternative CIs have been proposed, but this literature appears to have gone unnoticed to psychologists. Only one of these alternatives is dual with the conventional Score test for π, thus meeting the requirements stated in the Publication Manual. Three examples illustrate the appropriate choice of a CI for π in the context of growing concern with good statistical practices.