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Summary Spearman's measure of disarray D is the sum of the absolute values of the difference between the ranks. We treat D as a metric on the set of permutations. The limiting mean, variance and normality are established. D is shown to be related to the metric I arising from Kendall's τ through the combinatorial inequality I ≤ D ≤ 2I.
Diaconis et al. (1977) studied this question.