Improved Confidence Statements for the Binomial Parameter

In the computation of two-sided confidence intervals for the binomial parameter p (using the binomial mass function), it is known that such intervals achieve a confidence coefficient that in general is not equal to the confidence level 1 – α, say. In this article we present some general results on the confidence coefficient and tabulate them for selected pairs (α, n = number of trials). We treat only the nominal equal tail probability case because it is the most commonly taught and used.