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

Abstract

To examine whether two continuous variables are associated, tests based on Pearson’s,Kendall’s, and Spearman’s correlation coefficients are typically used. This paper examinesmodern nonparametric independence tests as an alternative, which, unlike traditional tests,have the ability to potentially detect any type of relationship. In addition to existing modernnonparametric independence tests, we developed and considered two novel variants ofexisting tests, most notably the Heller-Heller-Gorfine-Pearson (HHG-Pearson) test. Weconducted a simulation study to compare traditional independence tests, like Pearson’scorrelation, and the modern nonparametric independence tests in situations commonlyencountered in psychological research. As expected, no test had the highest power across allrelationships. However, the distance correlation and the HHG-Pearson tests were found tohave substantially greater power than all traditional tests for many relationships and onlyslightly less power in the worst case. A similar pattern was found in favor of theHHG-Pearson test compared to the distance correlation test. However, given that distancecorrelation performed better for linear relationships and is more widely accepted, we suggestconsidering its use in place of traditional methods when there is no prior knowledge of therelationship type, as is often the case in psychological research.