Adaptive Tests for Ordered Categorical Data

Consider testing for independence against stochastic order in an ordered 2xJ contingency table, under product multinomial sampling. In applications one may wish to exploit prior information concerning the direction of the treatment effect, yet ultimately end up with a testing procedure with good frequentist properties. As such, a reasonable objective may be to simultaneously maximize power at a specified alternative and ensure reasonable power for all other alternatives of interest. For this objective, none of the available testing approaches are completely satisfactory. A new class of admissible adaptive tests is derived. Each test in this class strictly preserves the Type I error rate and strikes a balance between good global power and nearly optimal (envelope) power to detect a specific alternative of most interest. Prior knowledge of the direction of the treatment effect, the level of confidence in this prior information, and possibly the marginal totals might be used to select a specific test from this class