On Comparing the Correlations within Two Pairs of Variables

Abstract

Let Ai , 1 < i < n, be a random sample of observations on A = (G1 , G2), where Gk = (Xk , Yk), k = 1, 2, and Xk and Yk are at least ordinal. It is desired to test a hypothesis concerning, or place a confidence interval on, the difference between the correlation of variables X1 and Y, , and that of variables X2 and Y2 , when no assumption is made concerning the form of the underlying distribution. It is the purpose of this paper to indicate how this can be carried out for large samples. The measure of correlation used is the unconditional index of order association or Kendall's [1962] tau-a, hereafter referred to as the unconditional index, which we now define. A pair of bivariate observations Gki and Gki , i id j, is said to be: