Bootstrap tests for simultaneous monotone ordering of effects in a two-way ANOVA

In a two-way additive analysis of variance (ANOVA) model, we consider the problem of testing for homogeneity of both row and column effects against their simultaneous ordering. The error variances are assumed to be heterogeneous with unbalanced samples in each cell. Two simultaneous test procedures are developed-the first one using the likelihood ratio test (LRT) statistics of two independent hypotheses and another based on the consecutive pairwise differences of estimators of effects. The parametric bootstrap (PB) approach is used to find critical points of both the tests and the asymptotic accuracy of the bootstrap is established. An extensive simulation study shows that the proposed tests achieve the nominal size and have very good power performance. The robustness of the tests is also analyzed under deviation from normality. An "R" package is developed and shared on "GitHub" for ease of implementation of users. The proposed tests are illustrated using a real data set on the mortality due to alcoholic liver disease and it is shown that age and gender have a significant impact on the increasing incidence of mortality.