Positive Association Among Three Binary Variables and Cross-Product Ratios |
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| Authors: | Fienberg Stephen E; Kim Sung-Ho |
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| Institution: | Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. fienberg{at}stat.cmu.edu |
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| Abstract: | We show that, when the three-way association level among thethree binary variables, X, U1 and U2 is fixed, DP = pr(X = 1¦U1= 1) – pr(X = 1¦U1 = 0) increases as the cross-productratio of U1 and U2 increases under the assumption that X ispositively associated with U1 and U2. We then discuss some implicationsof this property. |
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| Keywords: | Conditional probability Discriminating ability Prediction robustness Yule-Simpson paradox |
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