Logic of Simpson paradox

Jacek Malinowski

DOI: http://dx.doi.org/10.12775/LLP.2005.013


The main aim of this paper is to elucidate, from a logical point of view, the phenomenon of Simpson reversal — the paradox of a statistical reasoning. We define a binary relation of supporting in the following way: a sentence A supports a sentence B if and only if the probability of B is higher when A is true, than when A is false. It appears that a statistical argument occurring in Simpson paradox cannot be formalized by means of a binary relation. We generalize the relation of support introducing the third parameter. Then we argue that it properly mirrors main features of the statistical argument occurring in Simpson paradox.


logical entailment; statistical inference; Bayesian inference; Simpson paradox

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ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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