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

Abstract

We study a generalisation of Simpson reversal (also known as Simpson's paradox or the Yule-Simpson effect) to $2\times 2\times 2$ 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.

16 pages, 4 figures, 4 tables