Using Correlation in Studies of Studies

Abstract

Let $X$, $Y$, and $Z$ be random variables. If $X$ is positively correlated to $Y$ and $Y$ is positively correlated to $Z$, it does not necessarily follow that $X$ is positively correlated to $Z$. In this article we find ranges for the correlation coefficients $r_{XY}$ and $r_{YZ}$ that guarantee that $X$ and $Z$ have a specified level of correlation. We explore the implications of these results to finding relationships between variables investigated in different studies.