Abstract:

Estimation of the probability of the binomial distribution is a basic problem, which appears in almost all introductory statistics course, and is preformed frequently in various studies. In some cases, the parameter of interest is a difference between two probabilities, and the current work studies the construction of confidence intervals for this parameter when the sample size is small. Our goal is to find the shortest confidence intervals under the constraint of coverage probability being large than a predetermined level. For the two-sample case there is no known algorithm that achieves this goal, but rather different heuristics procedures were suggested.

This work fills this gap, namely, we construct an algorithm that computes for small sample-sizes the optimal confidence intervals. These are compared to the sub-optimal procedures that were suggested previously, and we find that the improvement is generally not very large.