`Is the Hypothesis Correct’ or `Is it not’? Bayesian Evaluation of One Informative Hypthesis in ANOVA.

Abstract

Researchers in the behavioral and social sciences often have one informative hypothesis with respect to the state of affairs in the population from which they sampled their data. The question they would like an answer to is ‘‘Is the Hypothesis Correct’’ or ‘‘Is it Not.’’ Classical statistics has not yet provided an approach with which this question can be answered. In this paper it will be shown that there is a Bayesian approach that does provide an answer to this question. Using two ANOVA examples the context of this paper will be sketched. Subsequently it will be shown how the Bayes factor can be used to quantify the support in the data for an informative hypothesis (‘‘It is’’) and its complement (‘‘It is not’’). Subsequently, the performance of the method proposed will be evaluated by means of error probabilities and evaluation of the robustness with respect to violations of the assumption of homogeneous within group variances. Finally, the methodology will be elaborated and it will be illustrated how the approach proposed can be implemented using WinBUGS.