THE EVALUATION OF CONFIDENCE SETS WITH APPLICATION TO BINOMIAL INTERVALS

An expected volume coefficient (EV) is defined and proposed to displac e 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 distribut ions; 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 sm aller sets) criterion, to attaining coverage for all values of the unk nown 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 legit interval with negative continuity correction.