Approximating the Level Probabilities for a Unimodal Ordering
Larry A. Lucas, Tim Robertson, Farroll T. Wright · Communications in Statistics - Simulation and Computation · 1989
Bartholomew's and tests are used for testing the homogeneity of normal means with the alternative restricted by a partial ordering on the means. The null distributions of these test statistics are mixtures of chi-square and beta distributions and depend on the partial order only through the mixing coefficients, which are called level probabilities. We study the level probabilities corresponding to the unimodal orderings, μ l ≤ ··· ≤ μ h ≥ μ h+1 ≥ ··· ≥ μ k with 1 < h < k. Employing techniques similar to those used for simple orders and simple tree orderings, we develop approximations to the level probabilities for a unimodai ordering. This approximation is found to be adequate for most practical purposes.