Simpson’s Paradox for Kendall’s Rank Coefficient

Pierre Zuyderhoff; Michel Denuit; Julien Trufin

doi:10.1007/s11009-025-10161-x

Simpson’s Paradox for Kendall’s Rank Coefficient

Pierre Zuyderhoff, Michel Denuit, Julien Trufin

School of Mathematical Sciences

Research output: Journal Publication › Article › peer-review

Abstract

This note revisits Simpson’s paradox and discusses confounding effects of hidden covariates on Kendall’s tau. As a result, observed correlation may vanish or even revert. More specifically, a decomposition of Kendall’s tau in the presence of subgroups is established, a formal definition of Simpson’s paradox for Kendall’s tau is given and some simple examples of paradoxical situations in the insurance domain are provided. Finally, necessary and sufficient conditions for a Simpson’s paradox to occur are studied.

Original language	English
Article number	29
Journal	Methodology and Computing in Applied Probability
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s11009-025-10161-x
Publication status	Published - Jun 2025

Keywords

Covariates
Kendall’s tau
Simpson’s paradox

ASJC Scopus subject areas

Statistics and Probability
General Mathematics

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10.1007/s11009-025-10161-x

Cite this

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title = "Simpson{\textquoteright}s Paradox for Kendall{\textquoteright}s Rank Coefficient",

abstract = "This note revisits Simpson{\textquoteright}s paradox and discusses confounding effects of hidden covariates on Kendall{\textquoteright}s tau. As a result, observed correlation may vanish or even revert. More specifically, a decomposition of Kendall{\textquoteright}s tau in the presence of subgroups is established, a formal definition of Simpson{\textquoteright}s paradox for Kendall{\textquoteright}s tau is given and some simple examples of paradoxical situations in the insurance domain are provided. Finally, necessary and sufficient conditions for a Simpson{\textquoteright}s paradox to occur are studied.",

keywords = "Covariates, Kendall{\textquoteright}s tau, Simpson{\textquoteright}s paradox",

author = "Pierre Zuyderhoff and Michel Denuit and Julien Trufin",

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AU - Zuyderhoff, Pierre

AU - Denuit, Michel

AU - Trufin, Julien

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/6

Y1 - 2025/6

N2 - This note revisits Simpson’s paradox and discusses confounding effects of hidden covariates on Kendall’s tau. As a result, observed correlation may vanish or even revert. More specifically, a decomposition of Kendall’s tau in the presence of subgroups is established, a formal definition of Simpson’s paradox for Kendall’s tau is given and some simple examples of paradoxical situations in the insurance domain are provided. Finally, necessary and sufficient conditions for a Simpson’s paradox to occur are studied.

AB - This note revisits Simpson’s paradox and discusses confounding effects of hidden covariates on Kendall’s tau. As a result, observed correlation may vanish or even revert. More specifically, a decomposition of Kendall’s tau in the presence of subgroups is established, a formal definition of Simpson’s paradox for Kendall’s tau is given and some simple examples of paradoxical situations in the insurance domain are provided. Finally, necessary and sufficient conditions for a Simpson’s paradox to occur are studied.

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KW - Simpson’s paradox

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Simpson’s Paradox for Kendall’s Rank Coefficient

Abstract

Keywords

ASJC Scopus subject areas

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