Is the Property of Being Positively Correlated Transitive?

2001/11/01 by Eric Langford, Neil C. Schwertman, Margaret Ann Owens · 1 voice · 4 citations
Mathematics · Physics and Astronomy · #Mathematical and Theoretical Analysis #Probability and Statistical Research #Statistical Mechanics and Entropy

paper · doi:10.1198/000313001753272286

openalex publication_date 2001/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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, thenX 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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Discussions

• Somewhat related: correlation is not transitive doi.org/10.1198/0003... if I recall correctly Corr(X,Z)>0 only follows if both Corr(X,Y)>0.7 and Corr(Y,Z)>0.7, but I might be misremembering and the th [bsky, 3 points, 1 comments]

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