The Average Spearman Rank Correlation Coefficient

Abstract

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 ρav 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 ρav = 0.

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