Simpson’s paradox, a tale of causality

Chambaz, Antoine; Drouet, Isabelle

Journal de la société française de statistique, Causality, Tome 161 (2020) no. 1, pp. 42-66.

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.

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.

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