Comment: Randomized Confidence Intervals and the Mid-P Approach

Abstract

We enjoyed reading the interesting, thought-provok ing article by Geyer and Meeden. In our comments we will try to place their work in perspective rela tive to the original proposals for exact and random ized confidence intervals for the binomial parameter. We propose a fuzzy version of the original binomial randomized confidence interval, due to Stevens (1950). Our approach motivates an existing nonrandomized confidence interval based on inverting a test using the mid-P value. The mid-P confidence interval provides a sensible compromise that mitigates the effects of con servatism of exact methods, yet provides results that are more easily understandable to the scientist.