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I'm wondering whether anyone knows whether it is possible to directly calculate a Bayes Factor (comparing null model of zero correlation to non-zero correlation) given just a correlation coefficient and sample size.

I've found this site that allows you to calculate the Bayes factor from t-test or regression coefficients and am hoping that a similar thing could be done with correlation coefficients.

Many thanks.

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  • $\begingroup$ The question is unclear as asked: if your observation is the empirical correlation coefficient, and if you know the distribution of this empirical correlation coefficient under both models being compared, you can compute the Bayes factor. Else you presumably cannot. $\endgroup$
    – Xi'an
    Commented Dec 4, 2015 at 10:16

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You could convert the Pearson's $r$ value to its corresponding $t$-statistic and then use the app that you found. The conversion is $$ t=\sqrt{\frac{(n-2)r^2}{1-r^2}} $$ where $n$ is the sample size.

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  • $\begingroup$ Thanks, that's almost an embarrassingly simply solution. $\endgroup$
    – Cam
    Commented Dec 7, 2015 at 2:00
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Here is a paper that has some derivations of Bayes factors for correlations (starting on page 21). This paper has some examples of the Bayes factors being used, and there is a link in that paper for the supporting R code. The R code requires just the sample size and the observed correlation.

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  • $\begingroup$ Awesome, these papers are excellent! Don't know why I didn't find them in my searches. Thanks so much! $\endgroup$
    – Cam
    Commented Dec 7, 2015 at 2:01
  • $\begingroup$ No problem. I should add that the calculations can also be done easily in a free software called JASP. $\endgroup$
    – Alexander Etz
    Commented Dec 7, 2015 at 2:03

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