Some properties of a test for concordance of two groups of rankings

Abstract

The statistic L, introduced to test for concordance within and between two groups of rankings of k objects is shown to be related to several measures of internal rank correlation. It has been previously shown that Kendall's W is proportional to the average of the rank correlations of all pairs of rankings in a single group and that Page's L is essentially the average of the rank correlations of an external ranking with each ranking in a group suggested by Lyerly. Similarly L is here shown to be directly related to the average of all rank correlations between a ranking from one group with a ranking from the other group. This statistic is also equal to the total of the L statistics calculated for each judge in one rroup with all judges in the other. The L statistic is shown to be uncorrelated with Kendall's W for concordance within either group. The asymptotic normality of L is established. A modification for ties is reported.