Bayesian Evaluation of Informative Hypotheses

doi:10.1007/978-0-387-09612-4

Cited by 75 publications

(11 citation statements)

References 39 publications

(93 reference statements)

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“…Bayes is a general all-purpose method that can be applied to any specified distribution or to a bootstrapped distribution (e.g., Jackman, 2009; Kruschke, 2010a; Lee and Wagenmakers, 2014; see Kruschke, 2013b, for a Bayesian analysis that allows heavy-tailed distributions). Bayes is also not limited to one degree of freedom contrasts, as the Dienes (2008) calculator is (see Hoijtink et al, 2008, for Bayes factors on complex hypotheses involving a set of inequality constraints). However, pin point tests of theoretical predictions are generally one degree of freedom contrasts (e.g., Lewis, 1993; Rosenthal et al, 2000).…”

Section: Some General Considerations In Using Bayes Factorsmentioning

confidence: 99%

“…However, pin point tests of theoretical predictions are generally one degree of freedom contrasts (e.g., Lewis, 1993; Rosenthal et al, 2000). Multiple degree of freedom tests usually serve as precursors to one degree of freedom tests simply to control familywise error rates (though see Hoijtink et al, 2008). But for a Bayesian analysis one should not correct for what other tests are conducted (only data relevant to a hypothesis should be considered to evaluate that hypothesis), so one can go directly to the theoretically relevant specific contrasts of interest (Dienes, 2011; for more extended discussion see Dienes, forthcoming; and Kruschke, 2010a for the use of hierarchical modeling for dealing with multiple comparisons).…”

Section: Some General Considerations In Using Bayes Factorsmentioning

confidence: 99%

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Using Bayes to get the most out of non-significant results

2014

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No scientific conclusion follows automatically from a statistically non-significant result, yet people routinely use non-significant results to guide conclusions about the status of theories (or the effectiveness of practices). To know whether a non-significant result counts against a theory, or if it just indicates data insensitivity, researchers must use one of: power, intervals (such as confidence or credibility intervals), or else an indicator of the relative evidence for one theory over another, such as a Bayes factor. I argue Bayes factors allow theory to be linked to data in a way that overcomes the weaknesses of the other approaches. Specifically, Bayes factors use the data themselves to determine their sensitivity in distinguishing theories (unlike power), and they make use of those aspects of a theory’s predictions that are often easiest to specify (unlike power and intervals, which require specifying the minimal interesting value in order to address theory). Bayes factors provide a coherent approach to determining whether non-significant results support a null hypothesis over a theory, or whether the data are just insensitive. They allow accepting and rejecting the null hypothesis to be put on an equal footing. Concrete examples are provided to indicate the range of application of a simple online Bayes calculator, which reveal both the strengths and weaknesses of Bayes factors.

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Section: Some General Considerations In Using Bayes Factorsmentioning

confidence: 99%

Section: Some General Considerations In Using Bayes Factorsmentioning

confidence: 99%

Using Bayes to get the most out of non-significant results

2014

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“…Yet, inference is surprisingly convenient from a Bayesian perspective (Gelfand, Smith, & Lee, 1992). And the computation of Bayes factors-the strength of evidence from data for one model relative to another-is relatively straightforward for the inequality constraints in the positive model (Hoijtink, Klugkist, & Boelen, 2008;Klugkist & Hoijtink, 2007;Klugkist, Laudy, & Hoijtink, 2005). In our previous work, we provide the development of Bayes factor solutions .…”

Section: Comparing Modelsmentioning

confidence: 99%

Are There Reliable Qualitative Individual Difference in Cognition?

Rouder

Haaf

2021

Journal of Cognition

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In this paper we propose a new set of questions that focus on the direction of effects.In almost all studies the direction is important. For example, in a Stroop task we expect responses to incongruent items to be slower than those to congruent ones, and this direction implies one theoretical explanation. Yet, if congruent words are slowed down relative to incongruent words we would have a completely different theoretical explanation. We ask a 'does everybody' question, such as, 'does every individual show a Stroop effect in the same direction?' Or, 'does every individual respond faster to loud tones than soft tones?' If all individuals truly have effects in the same direction that implicate a common theory, we term the differences among them as quantitative individual differences. Conversely, if all individuals truly have effects in different directions that implicate different theories, we term the differences among them as qualitative individual differences. Here, we provide a users guide to the question of whether individual differences are qualitative or quantitative. We discuss theoretical issues, methodological advances, new software for assessment, and, most importantly, how the question impacts theory development in cognitive science. Our hope is that this mode of analysis is a productive tool in researchers' toolkits.

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“…From a broader perspective, our findings illustrate that despite of methodological differences and occasional heated debates between frequentist and Bayesian methods and their respective proponents (see e.g., Wagenmakers, et al, 2008), often relevant insights can be gained from describing the world from both perspectives. We hope that by showing how the notion of power equivalence and the BFDA method can be combined, we will have made a contribution towards an increased feasibility of Bayesian experimental planning.…”

Section: Discussionmentioning

confidence: 73%

Bayesian power equivalence in latent growth curve models

Stefan

Oertzen

2019

Brit J Math & Statis

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Longitudinal studies are the gold standard for research on time-dependent phenomena in the social sciences. However, they often entail high costs due to multiple measurement occasions and a long overall study duration. It is therefore useful to optimize these design factors while maintaining a high informativeness of the design. Von Oertzen and Brandmaier (2013, Psychology and Aging, 28, 414) applied power equivalence to show that Latent Growth Curve Models (LGCMs) with different design factors can have the same power for likelihood-ratio tests on the latent structure. In this paper, we show that the notion of power equivalence can be extended to Bayesian hypothesis tests of the latent structure constants. Specifically, we show that the results of a Bayes factor design analysis (BFDA; Sch€ onbrodt & Wagenmakers (2018, Psychonomic Bulletin and Review, 25, 128) of two power equivalent LGCMs are equivalent. This will be useful for researchers who aim to plan for compelling evidence instead of frequentist power and provides a contribution towards more efficient procedures for BFDA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Bayesian Evaluation of Informative Hypotheses

Cited by 75 publications

References 39 publications

Using Bayes to get the most out of non-significant results

Using Bayes to get the most out of non-significant results

Are There Reliable Qualitative Individual Difference in Cognition?

Bayesian power equivalence in latent growth curve models

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