#### Vol. 12, No. 1, 2021

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Association and Simpson conversion in $2 \times 2 \times 2$ contingency tables

### Svante Linusson and Matthew T. Stamps

Vol. 12 (2021), No. 1, 57–74
##### Abstract

We study a generalisation of Simpson reversal (also known as Simpson’s paradox or the Yule–Simpson effect) to $2×2×2$ contingency tables and characterise the cases for which it can and cannot occur with two combinatorial-geometric lemmas. We also present a conjecture based on some computational experiments on the expected likelihood of such events.

##### Keywords
Simpson's paradox, correlation reversal, association, triangulations
##### Mathematical Subject Classification
Primary: 62P99, 52B10