Two rather similar statistics, the coefficient of concordance (W) and weighted average tau (Wa), 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 Wa, 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 Wa 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, χ2
r for W and χ2
n for Wa, are appropriate for values of m and n chat are smaller than those recommended previously.
