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Biometrika 1979 66(1):7-15; doi:10.1093/biomet/66.1.7
© 1979 by Biometrika Trust
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A measure of the agreement between rankings

A. D. GORDON

Department of Statistics, University of St Andrews

A measure of the agreement between two rankings of a set of objects is proposed. This measure not only gives an indication of the overall correspondence of the rankings, but also specifies the objects in each sequence which are contributing to the agreement. The null distribution of the measure is found to be related to a standard problem in combinatorics: given a random permutation of the first N integers, what is the distribution of the length of a longest monotone subsequence? Algorithms are described for obtaining the set of objects contributing to the measure of agreement. Several extensions are considered, in particular the problem of preserving tied ranks, and an application to classification studies is noted.

Key Words: Classification • Cluster analysis • Combinatorial analysis • Comparing sequences • Rank correlation • Tied ranks • Ulam's problem • Young tableaux


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