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

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  • Carol Lee Stamm

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.

Suggested Citation

  • Carol Lee Stamm, 1978. "An Empirical Comparison of the Large Sample Approximations for the Coefficient of Concordance and Weighted Average Tau," Journal of Educational and Behavioral Statistics, , vol. 3(3), pages 253-264, September.
    • Handle: RePEc:sae:jedbes:v:3:y:1978:i:3:p:253-264
    DOI: 10.3102/10769986003003253
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