Simpson’s paradox, a tale of causality
Journal de la société française de statistique, Volume 161 (2020) no. 1, pp. 42-66.

For the mathematically wary and unwary alike, Simpson’s paradox may well function as a permanent invitation to error. We present Simpson’s paradox and discuss its nature based on three examples. It appears that to run afoul of Simpson’s paradox it suffices to (a) conflate an invalid probabilistic reasoning with a valid instance of unassailable causal reasoning, or (b) confuse the evidential concept of learning from observation, which for rational agents proceeds by conditioning on the evidence, with the causal concept of acting, represented in causal analysis by the operation of intervening in a causal graph.

Le paradoxe de Simpson peut induire en erreur jusqu’au mathématicien prudent. Nous présentons le paradoxe de Simpson et discutons sa nature en nous appuyant sur trois exemples. Il apparaît que pour se faire prendre à son piège, il suffit (a) de combiner un raisonnement probabiliste hasardeux avec un raisonnement causal inattaquable, ou bien (b) de confondre le concept évidentiel d’apprentissage à partir de l’observation, qui pour des agents rationnels procède par conditionnement selon les données, avec le concept causal d’action tel qu’il est représenté en analyse causale par une intervention dans un graphe.

Classification: 60-01, 62A01
Keywords: causality, Simpson’s paradox
Mot clés : causalité, paradoxe de Simpson
Chambaz, Antoine 1; Drouet, Isabelle 2

1 MAP5 (UMR CNRS 8145), Université Paris Descartes, 45 rue des Saints-Pères, 75270 Paris cedex 06.
2 Sciences, Normes, Décision (SND, FRE CNRS 3593), Sorbonne Université.
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Chambaz, Antoine; Drouet, Isabelle. Simpson’s paradox, a tale of causality. Journal de la société française de statistique, Volume 161 (2020) no. 1, pp. 42-66. http://archive.numdam.org/item/JSFS_2020__161_1_42_0/

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