Convex hull test for ordered categorical data

When testing for stochastic order in ordered 2 x J contingency tables, it i s common to select the cutoff required to declare significance so as to ens ure that the size of the test is exactly ct conditionally on the margins. I t is valid, however, to use the margins to select not only the cutoff but a lso the form of the test. Linear rank tests, which are locally most powerfu l and frequently used in practice, suffer from the drawback that they may h ave power as low as zero to detect some alternatives of interest when the m argins satisfy certain conditions. The Smirnov and convex hull tests are sh own, through exact conditional power calculations and simulations, to avoid this drawback. The convex hull test is also admissible and palindromic inv ariant and minimizes the required significance level to have limiting power of one as the alternative moves away from the null in any direction.