Comparison of Correlation Coefficients

Alexei Stepanov ()
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Alexei Stepanov: Immanuel Kant Baltic Federal University

Sankhya A: The Indian Journal of Statistics, 2025, vol. 87, issue 1, No 8, 218 pages

Abstract: Abstract In the present paper, we discuss the Pearson $$\rho $$ ρ , Spearman $$\rho _S$$ ρ S , Kendall $$\tau $$ τ correlation coefficients and their statistical analogues $$\rho _n, \rho _{n,S}$$ ρ n , ρ n , S and $$\tau _n$$ τ n . We propose a new correlation coefficient r and its statistical analogue $$r_n$$ r n . The coefficient r is based on Kendal’s and Spearman’s correlation coefficients. In the situation when the second moments do not exist, we also offer a new extension of the Pearson correlation coefficient. We conduct simulation experiments and study the behavior of the above correlation coefficients. By these experiments, we show that the behavior of $$\rho _n$$ ρ n can be very different from the behavior of the rank correlation coefficients $$\rho _{n,S}, \tau _n$$ ρ n , S , τ n and $$r_n$$ r n , which, in turn, behave in a similar way in each discussed example. The question arises: which correlation coefficient best measures the dependence rate? We try to answer this question in our work.

Keywords: Bivariate distributions; Pearson; Kendall and Spearman correlation coefficients; 60G70; 62G30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13171-025-00378-w

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