An algorithm and program for calculation of Kendall’s rank correlation coefficient

Abstract

Although less widely used than Spearman's rho, Kendall's (1938, 1975) rank correlation coefficient (tau) possesses advantages that may make it a preferred statistic: Its distribution under the null hypothesis is approximately normal even when the sample size (n) is fairly small'; it allows determination of confidence interval bounds; and it can be applied to partial correlation (Kendall, 1975). Nevertheless, many statistics texts do not discuss tau, and some that do offer only fragmentary information. A few texts (e.g., McCall, 1980; Walker & Lev, 1953) present rho in considerable detail, mention the advantages of tau, and then ironically say nothing more about the use or calculation of tau. Kendall (1975) described the calculation of tau as involving comparison of every pair of ranks within each of the two distributions being studied. For a given pair of ranks Xi and Xi> where i Xj; and a score of 0 is assigned if r, = x; The statistic S, which is linearly related to tau, is then obtained by summing the products of the resulting scores for each corresponding pair of ranks in the two distributions. After a little simplification, the calculations can be summarized by the equation