pingouin.bayesfactor_pearson

pingouin.
bayesfactor_pearson
(r, n, tail='twosided', method='ly', kappa=1.0)[source] Bayes Factor of a Pearson correlation.
 Parameters
 rfloat
Pearson correlation coefficient.
 nint
Sample size.
 tailstr
Tail of the alternative hypothesis. Can be ‘twosided’, ‘onesided’, ‘greater’ or ‘less’. ‘greater’ corresponds to a positive correlation, ‘less’ to a negative correlation. If ‘onesided’, the directionality is inferred based on the
r
value (= ‘greater’ ifr
> 0, ‘less’ ifr
< 0). methodstr
Method to compute the Bayes Factor. Can be ‘ly’ (default) or ‘wetzels’. The former has an exact analytical solution, while the latter requires integral solving (and is therefore slower). ‘wetzels’ was the default in Pingouin <= 0.2.5. See notes for details.
 kappafloat
Kappa factor. This is sometimes called the rscale parameter, and is only used when
method
is ‘ly’.
 Returns
 bfstr
Bayes Factor (BF10). The Bayes Factor quantifies the evidence in favour of the alternative hypothesis.
See also
corr
(Robust) correlation between two variables
pairwise_corr
Pairwise correlation between columns of a pandas DataFrame
bayesfactor_ttest
Bayes Factor of a Ttest
bayesfactor_binom
Bayes Factor of a binomial test
Notes
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 twosided Wetzels Bayes Factor (also called JZS Bayes Factor) is calculated using the equation 13 and associated R code of Wetzels & Wagenmakers (2012):
\[\text{BF}_{10}(n, r) = \frac{\sqrt{n/2}}{\gamma(1/2)}* \int_{0}^{\infty}e((n2)/2)* log(1+g)+((n1)/2)log(1+(1r^2)*g)+(3/2)log(g)n/2g\]where \(n\) is the sample size, \(r\) is the Pearson correlation coefficient and \(g\) is is an auxiliary variable that is integrated out numerically. Since the Wetzels Bayes Factor requires solving an integral, it is slower than the analytical solution described below.
The twosided Ly Bayes Factor (also called Jeffreys exact Bayes Factor) is calculated using equation 25 of Ly et al, 2016:
\[\text{BF}_{10;k}(n, r) = \frac{2^{\frac{k2}{k}}\sqrt{\pi}} {\beta(\frac{1}{k}, \frac{1}{k})} \cdot \frac{\Gamma(\frac{2+k(n1)}{2k})}{\Gamma(\frac{2+nk}{2k})} \cdot 2F_1(\frac{n1}{2}, \frac{n1}{2}, \frac{2+nk}{2k}, r^2)\]The onesided version is described in eq. 27 and 28 of Ly et al, 2016. Please take note that the onesided test requires the mpmath package.
Results have been validated against JASP and the BayesFactor R package.
References
 1
Ly, A., Verhagen, J. & Wagenmakers, E.J. Harold Jeffreys’s default Bayes factor hypothesis tests: Explanation, extension, and application in psychology. J. Math. Psychol. 72, 19–32 (2016).
 2
Wetzels, R. & Wagenmakers, E.J. A default Bayesian hypothesis test for correlations and partial correlations. Psychon. Bull. Rev. 19, 1057–1064 (2012).
Examples
Bayes Factor of a Pearson correlation
>>> from pingouin import bayesfactor_pearson >>> r, n = 0.6, 20 >>> bf = bayesfactor_pearson(r, n) >>> print("Bayes Factor: %s" % bf) Bayes Factor: 10.634
Compare to Wetzels method:
>>> bf = bayesfactor_pearson(r, n, method='wetzels') >>> print("Bayes Factor: %s" % bf) Bayes Factor: 8.221
Onesided test
>>> bf10pos = bayesfactor_pearson(r, n, tail='greater') >>> bf10neg = bayesfactor_pearson(r, n, tail='less') >>> print("BFpos: %s, BFneg: %s" % (bf10pos, bf10neg)) BFpos: 21.185, BFneg: 0.082
We can also only pass
tail='onesided'
and Pingouin will automatically infer the directionality of the test based on ther
value.>>> print("BF: %s" % bayesfactor_pearson(r, n, tail='onesided')) BF: 21.185