18.2 - Spearman Correlation Coefficient

The Spearman rank correlation coefficient, \(r_s\), is a nonparametric measure of correlation based on data ranks. It is obtained by ranking the values of the two variables (X and Y) and calculating the Pearson \(r_p\) on the resulting ranks, not the data itself. Again, PROC CORR will do all of these actual calculations for you.

The Spearman rank correlation coefficient has properties similar to those of the Pearson correlation coefficient, although the Spearman rank correlation coefficient quantifies the degree of linear association between the ranks of X and the ranks of Y. Also, \(r_s\) does not estimate a natural population parameter (unlike Pearson's \(r_p\) which estimates \(\rho_p\) ).

An advantage of the Spearman rank correlation coefficient is that the X and Y values can be continuous or ordinal, and approximate normal distributions for X and Y are not required. Similar to the Pearson \(r_p\), Fisher's Z transformation can be applied to the Spearman \(r_s\) to get a statistic, \(z_s\), that has an asymptotic normal distribution for calculating an asymptotic confidence interval. Again, PROC CORR will do this as well.