# pingouin.bayesfactor_pearson

pingouin.bayesfactor_pearson(r, n)[source]

Bayes Factor of a Pearson correlation.

Parameters
rfloat

Pearson correlation coefficient

nint

Sample size

Returns
bfstr

Bayes Factor (BF10). The Bayes Factor quantifies the evidence in favour of the alternative hypothesis.

Notes

Adapted from a Matlab code found at https://github.com/anne-urai/Tools/blob/master/stats/BayesFactors/corrbf.m

If you would like to compute the Bayes Factor directly from the raw data instead of from the correlation coefficient, use the pingouin.corr() function.

The JZS Bayes Factor is approximated using the formula described in ref [1]:

$BF_{10} = \frac{\sqrt{n/2}}{\gamma(1/2)}* \int_{0}^{\infty}e((n-2)/2)* log(1+g)+(-(n-1)/2)log(1+(1-r^2)*g)+(-3/2)log(g)-n/2g$

where n is the sample size and r is the Pearson correlation coefficient.

References

1(1,2)

Wetzels, R., Wagenmakers, E.-J., 2012. A default Bayesian hypothesis test for correlations and partial correlations. Psychon. Bull. Rev. 19, 1057–1064. https://doi.org/10.3758/s13423-012-0295-x

Examples

Bayes Factor of a Pearson correlation

>>> from pingouin import bayesfactor_pearson
>>> bf = bayesfactor_pearson(0.6, 20)
>>> print("Bayes Factor: %s" % bf)
Bayes Factor: 8.221