On Correlation Coefficients

TL;DR

This paper reviews existing correlation coefficients, introduces a new one based on Kendall's and Spearman's, and compares their behaviors through simulations to determine which best measures dependence.

Contribution

It proposes a new correlation coefficient and its statistical analogue, extending the Pearson correlation, and compares their performance with existing coefficients.

Findings

Pearson's correlation can behave differently from rank correlations.

Rank correlations tend to behave similarly to each other.

The paper discusses which coefficient better measures dependence.

Abstract

In the present paper, we discuss the Pearson, Spearman, Kendall correlation coefficients and their statistical analogues. We propose a new correlation coefficient r and its statistical analogue. The coefficient r is based on Kendal's and Spearman's correlation coefficients. A new extension of the Pearson correlation coefficient is also discussed. We conduct simulation experiments and study the behavior of the above correlation coefficients. We observe that the behavior of Pearson's sample correlation coefficient can be very different from the behavior of the rank correlation coefficients, which, in turn, behave in a similar way. The question arises: which correlation coefficient better measures the dependence rate? We try to answer this question in the final conclusion.