A Note on Inferences About the Probability of Success

There is an extensive literature dealing with inferences about the probability of success. A minor goal in this note is to point out when certain recommended methods can be unsatisfactory when the sample size is small. The main goal is to report results on the two-sample case. Extant results suggest using one of four methods. The results indicate when computing a 0.95 confidence interval, two of these methods can be more satisfactory when dealing with small sample sizes