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<p>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.</p>

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Simpson’s Paradox for Kendall’s Rank Coefficient

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Pierre Zuyderhoff,
  • Michel Denuit,
  • Julien Trufin

摘要

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.