A default Bayesian hypothesis test for correlations and partial correlations

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Abstract

We propose a default Bayesian hypothesis test for the presence of a correlation or a partial correlation. The test is a direct application of Bayesian techniques for variable selection in regression models. The test is easy to apply and yields practical advantages that the standard frequentist tests lack; in particular, the Bayesian test can quantify evidence in favor of the null hypothesis and allows researchers to monitor the test results as the data come in. We illustrate the use of the Bayesian correlation test with three examples from the psychological literature. Computer code and example data are provided in the journal archives.

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A tutorial on a practical Bayesian alternative to null-hypothesis significance testing.

Michael Masson (2011)

Null-hypothesis significance testing remains the standard inferential tool in cognitive science despite its serious disadvantages. Primary among these is the fact that the resulting probability value does not tell the researcher what he or she usually wants to know: How probable is a hypothesis, given the obtained data? Inspired by developments presented by Wagenmakers (Psychonomic Bulletin & Review, 14, 779-804, 2007), I provide a tutorial on a Bayesian model selection approach that requires only a simple transformation of sum-of-squares values generated by the standard analysis of variance. This approach generates a graded level of evidence regarding which model (e.g., effect absent [null hypothesis] vs. effect present [alternative hypothesis]) is more strongly supported by the data. This method also obviates admonitions never to speak of accepting the null hypothesis. An Excel worksheet for computing the Bayesian analysis is provided as supplemental material.

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Mixtures ofgPriors for Bayesian Variable Selection

Qi-Feng Liang, Rui Paulo, German Molina … (2008)

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Intensive meditation training improves perceptual discrimination and sustained attention.

Katherine Maclean, Emilio Ferrer, Stephen R. Aichele … (2010)

The ability to focus one's attention underlies success in many everyday tasks, but voluntary attention cannot be sustained for extended periods of time. In the laboratory, sustained-attention failure is manifest as a decline in perceptual sensitivity with increasing time on task, known as the vigilance decrement. We investigated improvements in sustained attention with training (approximately 5 hr/day for 3 months), which consisted of meditation practice that involved sustained selective attention on a chosen stimulus (e.g., the participant's breath). Participants were randomly assigned either to receive training first (n = 30) or to serve as waiting-list controls and receive training second (n = 30). Training produced improvements in visual discrimination that were linked to increases in perceptual sensitivity and improved vigilance during sustained visual attention. Consistent with the resource model of vigilance, these results suggest that perceptual improvements can reduce the resource demand imposed by target discrimination and thus make it easier to sustain voluntary attention.