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Is the Property of Being Positively Correlated Transitive?

Eric Langford, Neil Schwertman and Margaret Owens
The American Statistician
Vol. 55, No. 4 (Nov., 2001), pp. 322-325
Stable URL: http://www.jstor.org/stable/2685695
Page Count: 4
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Is the Property of Being Positively Correlated Transitive?
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Abstract

Suppose that X, Y, and Z are random variables and that X and Y are positively correlated and that Y and Z are likewise positively correlated. Does it follow that X and Z must be positively correlated? As we shall see by example, the answer is (perhaps surprisingly) "no." We prove, though, that if the correlations are sufficiently close to 1, then X and Z must be positively correlated. We also prove a general inequality that relates the three correlations. The ideas should be accessible to students in a first (postcalculus) course in probability and statistics.

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