A method is derived for finding the average Spearman rank correlation coefficient of N sets of ranks with a single dependent or criterion ranking of n items without computing any of the individual coefficients. Procedures for calculating the exact distribution of ρ av for small values of N and n 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 as N = 4 and n = 4 the normal distribution can be used safely in testing the hypothesis ρ av = 0.
Samuel B. Lyerly (1952) studied this question.