## The Annals of Mathematical Statistics

### On a Measure of Dependence Between two Random Variables

Nils Blomqvist

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist., Volume 21, Number 4 (1950), 593-600.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177729754

Digital Object Identifier
doi:10.1214/aoms/1177729754

Mathematical Reviews number (MathSciNet)
MR39190

Zentralblatt MATH identifier
0040.22403

JSTOR