An Empirical Comparison of the Large Sample Approximations for the Coefficient of Concordance and Weighted Average Tau

Carol Lee Stamm

Journal of Educational and Behavioral Statistics, 1978, vol. 3, issue 3, 253-264

Abstract: Two rather similar statistics, the coefficient of concordance (W) and weighted average tau (W a ), have been suggested for estimating the communality between rankings. Two large sample tests have been suggested for each statistic when the values of m (the number of judges) and n (the number of objects) are larger than tabled values. The purpose of this study was to determine empirically which of the large sample approximations for the statistic, W or W a , was more appropriate for selected values of m and n . The procedures for the investigation involved manipulating m × n rankings using generated data sets. The results of the comparisons of the distributions of the large sample approximations for W and W a with their empirical distributions indicated that neither approximation was better for all sets of value m and n that were examined. However, the results suggest that the computationally simple approximation, χ 2 r for W and χ 2 n for W a , are appropriate for values of m and n chat are smaller than those recommended previously.

Keywords: Large Sample Approximations; Coefficient of Concordance; Average Tau; Nonparametric Tests (search for similar items in EconPapers)
Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:3:y:1978:i:3:p:253-264

DOI: 10.3102/10769986003003253

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