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Beyond Pearson’s correlation: modern nonparametric independence tests for psychological research

Author

Listed:
  • Karch, Julian D.
  • Perez-Alonso, Andres F.
  • Bergsma, Wicher P.

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.

Suggested Citation

  • Karch, Julian D. & Perez-Alonso, Andres F. & Bergsma, Wicher P., 2024. "Beyond Pearson’s correlation: modern nonparametric independence tests for psychological research," LSE Research Online Documents on Economics 124587, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:124587
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    File URL: http://eprints.lse.ac.uk/124587/
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    References listed on IDEAS

    as
    1. X. Wang & B. Jiang & J. S. Liu, 2017. "Generalized R-squared for detecting dependence," Biometrika, Biometrika Trust, vol. 104(1), pages 129-139.
    2. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    3. Fang Han & Shizhe Chen & Han Liu, 2017. "Distribution-free tests of independence in high dimensions," Biometrika, Biometrika Trust, vol. 104(4), pages 813-828.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    correlation; hypothesis test; independence; nonparametric; relationship;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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