Using Bayes to get the most out of non-significant results
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It is argued Bayes factors allow theory to be linked to data in a way that overcomes the weaknesses of the other approaches, and provides a coherent approach to determining whether non-significant results support a null hypothesis over a theory, or whether the data are just insensitive.Abstract:
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.read more
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References
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Journal ArticleDOI
Bayesian statistical inference in psychology: comment on Trafimow (2003).
TL;DR: This comment, with the help of a simple example, explains the usefulness of Bayesian inference for psychology.
Book
Bayes' Rule: A Tutorial Introduction to Bayesian Analysis
TL;DR: A range of accessible examples are used to show how Bayes' rule is actually a natural consequence of commonsense reasoning, and Bayesian analysis is applied to parameter estimation using the MatLab programs provided.
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Understanding statistical power in the context of applied research
TL;DR: It is concluded that applied researchers should consider a broader range of factors (other than sample size) that influence statistical power, and that the use of standardized measures of effect size should be avoided.
Journal ArticleDOI
The Assessment of the Subjective Opinion and its Use in Relation to Stopping Rules for Clinical Trials
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A Default Bayesian Hypothesis Test for ANOVA Designs
TL;DR: In this article, a Bayesian hypothesis test for analysis of variance (ANOVA) designs is presented, which is an application of standard Bayesian methods for variable selection in regression models.