A Comparison of Binomial Proportion Interval Estimation Methods

Some recent research has confirmed that the standard Wald (normal) confidence interval approximation for the binomial proportion is inadequate in key respects, especially for extreme values of p . Even for moderately large values of n the coverage probabilities can prove to be erratic for various specific values of p . This fact makes general rules for the use of the Wald method problematic. Alternative methods have been proposed, and this paper compares some of those alternatives with new capabilities built in to SAS Version 8.2 to calculate exact intervals. A decision rule is proposed for the selection of an appropriate technique. Also, a few extensions to other discrete distributions will be considered. This topic is relevant to both statisticians and programmers because of the fact that binomial proportion estimation is so commonly needed in a wide variety of situations, and the Wald (normal approximation) technique is taught in even the most basic statistics courses. Non-statisticians therefore often handle the task of interval estimation of this type.