The evaluation of confidence sets with application to binomial intervals

An expected volume coefficient (EV) is defined and proposed to displace volume and selectivity as criteria for the evaluation of confidence sets, and a proposal for evaluation is given. This proposal addresses anomolies that occur with sets based on discrete probability distributions; for example, that classical exact confidence intervals are wider than approximate ones. Options for the other key criterion, coverage, range from attaining average coverage, a liberal (i.e., leading to smaller sets) criterion, to attaining coverage for all values of the unknown parameter and all sample sizes, a very conservative criterion for sets based on discrete distributions. Use of EV is demonstrated with two-sided confidence intervals for the binomial probability parameter? leading to new recommendations; in particular, a Wald logit interval with negative continuity correction.