Measures of Location for Confidence Intervals for Proportions

Numerous methods have been developed to calculate confidence intervals for the binomial proportion . Boundedness and discreteness of the sample space imply that none achieves exactly the nominal /2 left and right non coverage. We consider whether intervals calculated by a particular method tend to be located too close to, or too far out from, the center of symmetry of the support scale, 1/2. Interval location may be characterized by the balance of mesial and distal non coverage in a study evaluating coverage. A complementary approach, applicable to a calculated interval, is derived from the Box-Cox family of scale transformations.