Half in jest we use a story about a black bear to illustrate that there are some discrepancies between the formal use of the p-value and the way it is often used in practice. We argue that more can be learned from data by evaluating informative hypotheses, than by testing the traditional null hypothesis. All criticisms of classical null hypothesis testing aside, the best argument for evaluating informative hypotheses is that many researchers want to evaluate their expectations directly, but have been unable to do so because the statistical tools were not yet available. It will be shown that a Bayesian model selection procedure can be used to evaluate informative hypotheses in structural equation models using the software Mplus. In the current paper we introduce the methodology using a real-life example taken from the field of developmental psychology about depressive symptoms in adolescence and provide a step-by-step description so that the procedure becomes more comprehensible for applied researchers. As this paper illustrates, this methodology is ready to be used by any researcher within the social sciences.

Van de Schoot, R., Verhoeven, M., & Hoijtink, H. (2013). Bayesian evaluation of informative hypotheses in SEM using Mplus: A black bear story. European Journal of Developmental Psychology, 10(1), 81-98. http://dx.doi.org/10.1080/17405629.2012.732719

The Mplus output file

Access to the data can be requested.

As was correctly noted by Arun Arunachalam and Joop Hox, independently, there is an error in the formula on page 93 of this paper. The denominator in formula 1b of Step 5 should have been .0833 instead of .0416 which influences the reported Bayes Factors on page 93: BFHi2 VS Hu = 6.18, BFHi2 VS Hnot = 23.36, and BFHi2 VS Hi1 = 2.04. The main conclusions do not change because of the new results.

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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