Researchers often have expectations about the research outcomes in regard to inequality constraints between, e.g., group means. Consider the example of researchers who investigated the effects of inducing a negative emotional state in aggressive boys. It was expected that highly aggressive boys would, on average, score higher on aggressive responses toward other peers than moderately aggressive boys, who would in turn score higher than nonaggressive boys. In most cases, null hypothesis testing is used to evaluate such hypotheses. We show, however, that hypotheses formulated using inequality constraints between the group means are generally not evaluated properly. The wrong hypotheses are tested, i.e. the null hypothesis that group means are equal. In this article, we propose an innovative solution to these above-mentioned issues using Bayesian model selection, which we illustrate using a case study.

Van de Schoot, R., Hoijtink, H., Mulder, J., Van Aken, M. A. G., Orobio de Castro, B., Meeus, W., & Romeijn, J.-W. (2011). Evaluating expectations about negative emotional states of aggressive boys using Bayesian model selection. Developmental Psychology, 47(1), 203-212.

As correctly noted by Anouk van Dijk, there is a mistake in Equation 3 (p.719).

The value of the marginal likelihood for Model A should be 2.83e-67 instead of 5.71e-67. The resulting Bayes Factor is 0.064 instead of 0.031. In Equation 3, 0.064 should be used for BFba resulting in a Bayes Factor of 31.25 instead of 64.51. We regret that this mistake was made, but the overall conclusion has not been affected.

Herbert Hoijtink
Professor Applied Bayesian Statistics
Herbert's main research interest is the evaluation of Informative Hypotheses. These are hypotheses constructed using (in)equality constraints among the parameters of interest.
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Wim Meeus
Professor Adolescent Psychology
Wim specializes in longitudinal adolescent studies, particularly regarding the development of personality and identity, personal relations and problematic behavior.
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