Beyond Pearson’s Correlation: Modern Nonparametric Independence Tests for Psychological Research

Multivariate Behavioral Research, vol. 59, pp. 957–977

Abstract

When examining whether two continuous variables are associated, tests based on Pearson's, Kendall's, and Spearman's correlation coefficients are typically used. This paper explores modern nonparametric independence tests as an alternative, which, unlike traditional tests, have the ability to potentially detect any type of relationship. In addition to existing modern nonparametric independence tests, we developed and considered two novel variants of existing tests, most notably the Heller-Heller-Gorfine-Pearson (HHG-Pearson) test. We conducted a simulation study to compare traditional independence tests, such as Pearson's correlation, and the modern nonparametric independence tests in situations commonly encountered in psychological research. As expected, no test had the highest power across all relationships. However, the distance correlation and the HHG-Pearson tests were found to have substantially greater power than all traditional tests for many relationships and only slightly less power in the worst case. A similar pattern was found in favor of the HHG-Pearson test compared to the distance correlation test. However, given that distance correlation performed better for linear relationships and is more widely accepted, we suggest considering its use in place or additional to traditional methods when there is no prior knowledge of the relationship type, as is often the case in psychological research.

Authors 3

1. Julian David Karch corresponding Aachen Methodology and Statistics Department Institute of Psychology, Leiden University

   Leiden University

   Affiliation as printed

   Methodology and Statistics Department, Institute of Psychology, Leiden University

   Methodology and Statistics Department, Institute of Psychology, Leiden University, Leiden, the Netherlands

2. Andres F. Perez-Alonso

   Tilburg University

   Affiliation as printed

   Department of Methodology and Statistics, Tilburg School of Social and Behavioral Sciences Tilburg University, Tilburg, the Netherlands

3. Wicher Bergsma

   London School of Economics and Political Science

   Affiliation as printed

   Department of Statistics, London School of Economics and Political Science, London, United Kingdom