Author:

Keywords:

statistical evidence, model selection, bayes factor, hierarchical modeling, random effects, order-restrictions, weighted likelihood ratio, null hypothesis, markov-chain, marginal likelihood, model uncertainty, signal-detection, linear-models, p-values, t-test, parameters, Social Sciences, Psychology, Psychology, Experimental, Statistical evidence, Model selection, Bayes factor, Hierarchical modeling, Random effects, Order-restrictions, WEIGHTED LIKELIHOOD RATIO, MARGINAL LIKELIHOOD, MODEL SELECTION, NULL HYPOTHESIS, SIMULATION, PARAMETERS, INFERENCE, WINBUGS, CHOICE, Bayes Theorem, Behavioral Research, Cognitive Science, Data Interpretation, Statistical, Humans, Likelihood Functions, Models, Statistical, 0801 Artificial Intelligence and Image Processing, 1701 Psychology, 1702 Cognitive Sciences, Experimental Psychology, 5201 Applied and developmental psychology, 5202 Biological psychology, 5204 Cognitive and computational psychology

Abstract:

In the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method's validity, generality, and flexibility. (C) 2009 Elsevier Inc. All rights reserved.