Measures of Location for Confidence Intervals for Proportions

Numerous methods have been developed to calculate confidence intervals for the binomial proportion π. Boundedness and discreteness of the sample space imply that none achieves exactly the nominal α/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.