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

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Correlation coefficients are crucial for quantifying linear associations between variables in scientific research.
• Classical hypothesis testing using p-values for correlations has known limitations and limited software support for alternatives.
• Limited availability of statistical software hinders the adoption of Bayesian testing procedures for correlation coefficients.

Purpose of the Study:

• To demonstrate how to conduct Bayesian hypothesis tests on various correlation coefficients using the BFpack module in JASP.
• To provide researchers with a user-friendly, open-source tool for advanced correlation analysis, overcoming limitations of classical methods.

Main Methods:

• Utilized the BFpack module within the JASP software for performing Bayesian hypothesis tests.
• Showcased testing for product-moment, polyserial, and tetrachoric correlations, including partial correlations.
• Demonstrated Bayesian testing of zero correlations and comparisons between dependent and independent correlations.

Main Results:

• The BFpack module in JASP enables flexible Bayesian hypothesis testing for diverse correlation types.
• The tutorial successfully illustrates the application of Bayesian methods as an alternative to classical p-value approaches.
• The study highlights the accessibility of advanced Bayesian correlation testing through free, open-source software.

Conclusions:

• The BFpack module in JASP offers a powerful and accessible solution for Bayesian hypothesis testing of correlation coefficients.
• This approach provides researchers with a robust alternative to classical methods, mitigating known limitations.
• The tutorial facilitates wider adoption of Bayesian statistical methods in correlation analysis across research disciplines.