The adaptation and use of Kendall's Coefficient of Concordance (W) to sociometric-type rankings.

Suppose the members of a group are asked to rank all the members including themselves according to some criterion such as social influence or cooperativene ss. It may be desirable to know how much agreement is present in the rankings. Rho's could be computed for the n(n —l)/2 pairs of rankings and an average rho would represent the extent of agreement. This becomes time consuming when the N of the group gets large. Kendall's W (2, 3) is an ideal measure for this situation and it is relatively rapid to compute. To obtain W, the ranks received by each individual are summed and the squared deviations of these sums from the mean computed. This quantity is then divided by the sum of the squared deviations which would result from perfect agreement among the rankers. W requires that all members be ranked. But in sociometric situations this would mean that the rank a member assigns to himself would have to be included or that he be assigned some rank. If either of these procedures were followed, the index of agreement would be difficult to interpret. It would, therefore, be desirable if a W could be computed which would omit the ranker's selfrank.