Comment: Randomized Confidence Intervals and the Mid-P Approach

We enjoyed reading the interesting, thought-provoking article by Geyer and Meeden. In our comments we will try to place their work in perspective relative to the original proposals for exact and randomized 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 conservatism of exact methods, yet provides results that are more easily understandable to the scientist.