Inference Based on General Linear Models for Order Restricted Randomization

This article develops statistical inference for the general linear models in order restricted randomized (ORR) designs. The ORR designs use the heterogeneity among experimental units to induce a negative correlation structure among responses obtained from different treatment regimes. This negative correlation structure acts as a variance reduction technique for treatment contrast. The parameters of the general linear models are estimated and a generalized F-test is constructed for its components. It is shown that the null distribution of the test statistic can be approximated reasonably well with an F-distribution for moderate sample sizes. It is also shown that the empirical power of the proposed test is substantially higher than the powers of its competitors in the literature. The proposed test and estimator are applied to a data set from a clinical trial to illustrate how one can improve such an experiment.