On a Measure of Dependence Between two Random Variables

The properties of a measure of dependence $q'$ between two random variables are studied. It is shown (Sections 3-5) that $q'$ under fairly general conditions has an asymptotically normal distribution and provides approximate confidence limits for the population analogue of $q'$. A test of independence based on $q'$ is non-parametric (Section 6), and its asymptotic efficiency in the normal case is about 41% (Section 7). The $q'$-distribution in the case of independence is tabulated for sample sizes up to 50.