Measuring Predictive Efficiency of Implication Hypotheses Between Binary Attributes

Bayesian inference Procedures for prediction analysis in 2 x 2 contingency tables are illustrated by the analysis of successes to six types of problems associated with the acquisi-tion of fractions. According to Hildebrand, Laing, and Rosenthal (1977), hy-potheses such as "success to problem type A implies in most ca es success to problem type B " can be evaluated from a numerical index. This index has been considered in various other frameworks and can be interpreted in terms of a measure of predictive efficiency of implication hypotheses. Confidence interval procedures previously proposed for this index are reviewed an extended. Then, under a multinomial model with a conjugate Dirichlet pr or distribution, the Bayesian posterior distribution of this index is characterized, leading to straightforward numerical methods. ~ The choices of "noninformative " priors for discrete data are shown to be no more arbitrary o subjective than the choices involved in the frequentist approach. Moreover, a simulation study of frequentist coverage probabilities favorably compares Bayesian credibility in-tervals with conditional confidence intervals