Inequality constrained hypotheses for ANOVA

Abstract

In this paper a novel approach for the evaluation of inequality constrained hypotheses is described. An inequality constrained hypothesis (Hi) is an hypothesis with order restrictions between the parameters of interest. The Bayes factor is used to compare Hi with its complement Hc, that is all situations in which Hi is not true. This approach is applied to ANOVA models and the performance is evaluated by looking at the error probabilities, which are the counterparts of Type 1 and Type 2 errors in the traditional null hypothesis testing framework. Furthermore, the robustness of the approach proposed with respect to violations of the assumption of homogeneity of variances is evaluated. Two examples are also analyzed using this new approach. The overall result is that the approach works well, with low error probabilities for Hi for relatively small sample sizes. Furthermore, the approach is robust to violations to the assumptions of homogeneity of variances.