Likelihood ratio and multiple comparison-based tests in a two-way additive ANOVA under tree order constraints

This paper deals with the problem of testing the homogeneity of treatment effects against a simple tree order alternative in a two-way additive heteroscedastic ANOVA model. We propose the likelihood ratio test (LRT) along with two multiple comparison tests based on pairwise differences between control and treatment means. The critical values are estimated using the bootstrap method. The asymptotic validity of the bootstrap is established. Simultaneous confidence intervals for the pairwise differences between control and treatment mean effects are also derived. Furthermore, a robustness study is conducted under non-normal distributions, including Laplace, t, Weibull, and three types of mixture normal distributions. To facilitate the implementation of our proposed methods, we have developed an ‘R’ package and shared it publicly on ‘GitHub’. The performance of the proposed test procedures is demonstrated through applications to a memory-recall dataset from a psychological study and a weight gain dataset from a biomedical experiment.