Positive Association Among Three Binary Variables and Cross-Product Ratios

Abstract

We show that, when the three-way association level among the three binary variables, X , U 1 and U 2 is fixed, D P = pr(X = 1¦ U 1 = 1) − pr( X = 1¦ U 1 = 0) increases as the cross-product ratio of U 1 and U 2 increases under the assumption that X is positively associated with U 1 and U 2 . We then discuss some implications of this property.