The average spearman rank correlation coefficient

A method is derived for finding the average Spearman rank correlation coefficient ofN sets of ranks with a single dependent or criterion ranking ofn items without computing any of the individual coefficients. Procedures for calculating the exact distribution of_av for small values ofN andn are described for the null case. The first four moments about zero of this distribution are derived, and it is concluded that for samples as small asN=4 andn=4 the normal distribution can be used safely in testing the hypothesis_av=0.This problem first came to the writer's attention in discussions with Dr. Dean J. Clyde.