Positive Association Among Three Binary Variables and Cross-Product Ratios

We show that, when the three-way association level among the three binary variables, X, U₁ and U₂ is fixed, D_P = pr(X = 1¦U₁ = 1) - pr(X = 1¦U₁ = 0) increases as the cross-product ratio of U₁ and U₂ increases under the assumption that X is positively associated with U₁ and U₂. We then discuss some implications of this property. Copyright 2007, Oxford University Press.