Measures of Ordinal Association I

Chapter 9 is the first of two chapters describing connections, equivalencies, and relationships relating to measures of ordinal association. First, Spearman’s rank-order correlation coefficient is presented and the connection linking Spearman’s rank-order correlation coefficient and Pearson’s product-moment correlation coefficient is described. Next, the connection linking Spearman’s rank-order correlation coefficient and Mielke and Berry’s ℜ $$\Re $$ chance-corrected measure is documented. Second, Kendall’s S test statistic is described and illustrated with an example analysis. Third, Mann’s test of randomness is described and the connection linking Mann’s test with Kendall’s S test statistic is described. Fourth, the connection linking Kendall’s S test statistic and Spearman’s rank-order correlation coefficient is described and illustrated. Next, the connection linking Kendall’s S and permutation test statistic δ $$\delta $$ is documented. Fifth, Spearman’s footrule measure of ordinal association is presented and the connection linking Spearman’s footrule with permutation test statistic δ $$\delta $$ is demonstrated with an example analysis. Sixth, the Benford probability distribution and Nigrini’s goodness-of-fit measure are introduced and the connection with Spearman’s footrule measure is demonstrated. Seventh, Kendall’s τ a $$\tau _{a}$$ measure is described and illustrated with an example analysis. Eighth, Kendall and Babington Smith’s u measure of ordinal association is described and the connection linking Kendall’s τ a $$\tau _{a}$$ and Babington Smith’s u is described. Finally, Kendall’s τ b $$\tau _{b}$$ measure of ordinal association is described and illustrated.