ABSTRACT
The association between two variables measured on the same set of objects is commonly referred to as their correlation and often measured by the Pearson product moment correlation coefficient. Specifically, suppose ZX1, . . . , ZXN and ZY1 , . . . , ZYN refer to zscores (that is, having mean zero and variance one) calculated for our original observational pairs, (Xi, Yi), i = 1, . . . , N ; then the correlation between the original variables, rXY , is defined as
rXY = ( 1
N )
ZXiZYi ,
or the average product of the z-scores. As usually pointed out early in any statistics course, rXY measures the linearity of any relation that might be present; thus, if some other (nonlinear) form of association exists, different means of assessing the latter are needed.
