© 1975 by Biometrika Trust
Some properties of a test for concordance of two groups of rankings
Bishop College Dallas, Texas
Department of Statistics, Southern Methodist University Dallas, Texas
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.
Key Words: Asymptotic normality • Concordance • Friedman statistic • Interaction • Internal rank correlation • Rank test • Tied rankings
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