<p>In many experimental designs, it is known a priori that the mean effects of the factors follow a monotone ordering. In this article, the problem of testing the homogeneity of the effects of both the factors against the alternative of their simultaneous monotone ordering is studied for a two-way crossed heteroscedastic ANOVA model. An intersection type test based on likelihood ratios of two sub-hypotheses and two multiple comparison tests are developed. Algorithms are proposed for the implementation of these tests using a parametric bootstrap approach and the asymptotic accuracy of this approach is also established. Extensive simulations are carried out to study the efficacy of these tests in controlling the type-I error rates and achieving a good power performance. It is shown that the proposed tests achieve the nominal size values regardless of the dimension of the design, number of replications in each cell and level of heterogeneity of error variances. Further, they are seen to have very good powers indicating consistency of tests. The proposed tests are further examined for their robustness under deviation from normality. An ‘<Emphasis FontCategory="NonProportional">R</Emphasis>’ package is developed and shared on the open platform ‘GitHub’ for easy usage by practitioners. Finally, the applicability of our proposed test procedures is illustrated using two real data sets on mortality rates.</p>