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On p-Values and Bayes Factors


Held, Leonhard; Ott, Manuela (2018). On p-Values and Bayes Factors. Annual Review of Statistics and Its Application, 5(1):593-419.

Abstract

The p-value quantifies the discrepancy between the data and a null hypothesis of interest, usually the assumption of no difference or no effect. A Bayesian approach allows the calibration of p-values by transforming them to direct measures of the evidence against the null hypothesis, so-called Bayes factors. We review the available literature in this area and consider two-sided significance tests for a point null hypothesis in more detail. We distinguish simple from local alternative hypotheses and contrast traditional Bayes factors based on the data with Bayes factors based on p-values or test statistics. A well-known finding is that the minimum Bayes factor, the smallest possible Bayes factor within a certain class of alternative hypotheses, provides less evidence against the null hypothesis than the corresponding p-value might suggest. It is less known that the relationship between p-values and minimum Bayes factors also depends on the sample size and on the dimension of the parameter of interest. We illustrate the transformation of p-values to minimum Bayes factors with two examples from clinical research.

Abstract

The p-value quantifies the discrepancy between the data and a null hypothesis of interest, usually the assumption of no difference or no effect. A Bayesian approach allows the calibration of p-values by transforming them to direct measures of the evidence against the null hypothesis, so-called Bayes factors. We review the available literature in this area and consider two-sided significance tests for a point null hypothesis in more detail. We distinguish simple from local alternative hypotheses and contrast traditional Bayes factors based on the data with Bayes factors based on p-values or test statistics. A well-known finding is that the minimum Bayes factor, the smallest possible Bayes factor within a certain class of alternative hypotheses, provides less evidence against the null hypothesis than the corresponding p-value might suggest. It is less known that the relationship between p-values and minimum Bayes factors also depends on the sample size and on the dimension of the parameter of interest. We illustrate the transformation of p-values to minimum Bayes factors with two examples from clinical research.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:2018
Deposited On:22 Feb 2018 14:49
Last Modified:31 Jul 2018 04:36
Publisher:Annual Reviews
ISSN:2326-8298
OA Status:Closed
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1146/annurev-statistics-031017-100307
Related URLs:http://www.annualreviews.org/eprint/dH3IEypty6E2Tr5Auu5j/full/10.1146/annurev-statistics-031017-100307 (Publisher)

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