Adrian E. Raftery

It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented. Implementing this is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P-values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis of interest, such as a convergence theory or a hypothesis about societal norms.