Testing for one-sided group effects in repeated measures study

Abstract

In repeated measures experiments, one-sided tests for group effects are developed using the likelihood ratio principle. The constrained maximum likelihood estimators under hypotheses of one-sided group effects are approximated by projecting unconstrained maximum likelihood estimators onto the first-quadrant. From these constrained maximum likelihood estimators, likelihood ratio tests are constructed. The limiting null distributions of the proposed test statistics are shown to be chi-bar square distributions. A simulation study shows that the proposed tests have improved power over the usual chi-square statistics for testing group effects. Two real data sets are analyzed to illustrate the proposed statistics.