Positive Association Among Three Binary Variables and Cross–Product Ratios

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We show that, when the three-way association level among the three binary variables, X, U1 and U2 is fixed, DP=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.

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