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M. G. Kendall, Sheila F. H. Kendall, B. Babington Smith, The Distribution of Spearman's Coefficient of Rank Correlation in a Universe in which all Rankings Occur an Equal Number of Times:, Biometrika, Vol. 30, No. 3/4 (Jan., 1939), pp. 251-273
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Kendall et al. (1939) studied this question.
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