Another measure of the agreement between rankings

Abstract

A measure of the agreement between the rankings of N objects by k observers is proposed which indicates the extent to which the objects may be divided into groups of objects such that each object in a group is preferred by all k observers to each object in subsequent groups. Some results are obtained on the distribution of the statistic under the null hypothesis of random permutations of the first N integers, and a simulation study is described which investigated the power of the test under an hypothesis of positive association. Several possible extensions are noted.