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Spearman's Footrule as a Measure of Disarray

Persi Diaconis and R. L. Graham
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 39, No. 2 (1977), pp. 262-268
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2984804
Page Count: 7
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Spearman's Footrule as a Measure of Disarray
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Abstract

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.

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