Some Contributions to Average Rank Correlation Methods and to the Distribution of the Average Rank Correlation Coefficient

Abstract

This report concerns the method and distribution of “average rho” or , the algebraic mean of M independent Spearman rank correlation coefficients based on equal N 's of objects ranked on each of two variables. Included is a reference table of those values and probabilities of most closely associated with four conventional levels of significance, .01, .02, .05, and .10, two-tailed. Most of this table is derived from the construction of 58 exact frequency distributions of for M 's > 1. Also presented are (a) general formulas for the computation of , with comparisons between the method and distribution of and Lyerly's “average Spearman rank correlation coefficient,” (b) formulas for the computation of corrected for continuity, , and of the standard score z of (c) a comparison of the results of exact computation and normal approximation which illustrates the tendency of the distribution of to approach normality as M, N , and both M and N increase, but that caution should be used when M or N is small.