# A tutorial on Bayesian hypothesis testing of correlation coefficients using the BFpack-module in JASP

## TL;DR

This tutorial teaches how to use Bayesian methods in JASP to test correlation coefficients, offering an alternative to traditional p-values.

## Contribution

Introduces a new Bayesian hypothesis testing module (BFpack) in JASP for correlation coefficients.

## Key findings

- BFpack supports Bayesian testing for various correlation types, including product–moment and tetrachoric correlations.
- The module allows testing partial correlations while controlling for covariates.
- Researchers can test dependent and independent correlations for equality or against zero.

## Abstract

Correlation coefficients play a central role in scientific research to quantify the (linear) association between certain key variables of interest. Currently, hypothesis testing of correlation coefficients, such as whether a correlation equals zero or whether two correlations are equal, is mainly done using classical p values, despite their known limitations. An important cause of this problem is the limited availability of statistical software that supports alternative, Bayesian testing procedures. To address this shortcoming, the current tutorial paper showcases how to perform Bayesian hypothesis tests on correlation coefficients using the new BFpack module in the free and open-source software program JASP. The module supports Bayesian tests of various types of correlations such as product–moment correlations, polyserial correlations, or tetrachoric correlations, among others. Partial correlations can be tested by controlling for certain covariates. Moreover, both dependent and independent correlations can be tested to be zero or tested against each other. This tutorial aims to get researchers acquainted with this new flexible testing paradigm, which avoids the limitations of classical methods, and to make the methodology widely available to the research community.