# On relationships between Chatterjee's and Spearman's correlation coefficients

arXiv: https://arxiv.org/abs/2302.10131 · HTML: https://mlsanity.com/paper/2302.10131/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Kernel Integrated R2: A Measure of Dependence](https://mlsanity.com/paper/2602.22985/) (2026)

## Abstract (arXiv)

In his seminal work, Chatterjee (2021) introduced a novel correlation measure which is distribution-free, asymptotically normal, and consistent against all alternatives. In this paper, we study the probabilistic relationships between Chatterjee's correlation and the widely used Spearman's correlation. We show that, under independence, the two sample-based correlations are asymptotically joint normal and asymptotically independent. Under dependence, the magnitudes of two correlations can be substantially different. We establish some extremal cases featuring large differences between these two correlations. Motivated by these findings, a new independence test is proposed by combining Chatterjee's and Spearman's correlations into a maximal strength measure of variable association. Our simulation study and real data application show the good sensitivity of the new test to different correlation patterns.