Logic of Simpson paradox
DOI:
https://doi.org/10.12775/LLP.2005.013Słowa kluczowe
logical entailment, statistical inference, Bayesian inference, Simpson paradoxAbstrakt
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.Bibliografia
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Simpson, E.H. [1951], “The Interpretation of Interaction in Contingency Table”, Journal of Royal Statistical Society, Series B, vol. 13, 238–241.
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