Generalized F test and generalized deviance test in two-way ANOVA models for randomized trials

We consider the problem of detecting treatment effects in a randomized trial in the presence of an additional covariate. By reexpressing a two-way analysis of variance (ANOVA) model in a logistic regression framework, we derive generalized F tests and generalized deviance tests, which provide better power in detecting common location-scale changes of treatment outcomes than the classical F test. The null distributions of the test statistics are independent of the nuisance parameters in the models, so the critical values can be easily determined by Monte Carlo methods. We use simulation studies to demonstrate how the proposed tests perform compared with the classical F test. We also use data from a clinical study to illustrate possible savings in sample sizes.