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We say that the signs of association measures among three variables {X, Y, Z}are transitive if a positive association measure between the variable X and theintermediate variable Y and further a positive association measure between Yand the endpoint variable Z imply a positive association measure between X andZ. We introduce four association measures with different stringencies, anddiscuss conditions for the transitivity of the signs of these associationmeasures. When the variables follow exponential family distributions, theconditions become simpler and more interpretable. Applying our results to twodata sets from an observational study and a randomized experiment, wedemonstrate that the results can help us to draw conclusions about the signs ofthe association measures between X and Z based only on two separate studiesabout {X, Y} and {Y, Z}.

Qualitative Evaluation of Associations by the Transitivity of the Association Signs