A note on decision theoretic coefficients for tests

Abstract

Recently it was suggested that the Bayes risk might be used to characterize tests. To conform to common practices about indexes, a rescaling of the Bayes risk was proposed. The motivation for this new coefficient, d, was to provide an index that has a large value when the Bayes risk is small and that has a value in the closed interval [0, 1]. However, since d might have a value outside this range, a modification of d is described which yields an index that always has a value between zero and one.