The feasibility and effectiveness of a Bayesian method for estimating regressions in m groups is studied by application of the method to data from the Basic Research Service of The American College Testing Program. Evidence supports the belief that in many testing applications the collateral information obtained from each subset of m-1 colleges…

Analysis of a two-way sample of means is considered when corresponding population means are believed a priori to satisfy a partial order restriction. Simulation and the Gibbs sampler are used to summarize posterior distributions, and the posterior distribution is used to predict GPAs of first-year students at University of Iowa. (SLD)