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Positive Association Among Three Binary Variables and Cross-Product Ratios
Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. fienberg{at}stat.cmu.edu
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea shkim{at}amath.kaist.ac.krs
Received for publication 1 July 2006. Revision received 1 May 2007.
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.
Key Words: Conditional probability • Discriminating ability • Prediction robustness • Yule–Simpson paradox
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