An Empirical Study of Related Correlation Coefficients

Abstract

Tests for comparing the strength of association between a variable, X 1 , and each of two potential predictor variables, X 2 and X 3 , are proposed and examined in a simulation study. The variances of X 2 and X 3 and the correlation between X 2 and X 3 are nuisance parameters. A simple modification of a test proposed by Williams (1959) is found to have reasonable properties for a wide range of parameter values and both normal and nonnormal distributions.