Estimating Concordance in a Set of Rank Orders

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Abstract
Kendall's W coefficient and Willerman's adaptation of W for sociometric rankings are difficult to interpret since these indices are different both from the average intercorrelation in a set of rank orders and from the reliability of the average order. A substitute coefficient called a is presented, being a special case of coefficient alpha, which relates to the average rho according to the Spearman-Brown formula, a w is easier to interpret than W, while W has no special advantages over a w. By analogy, a coefficient called aw is developed for the case of sociometric rankings.