A weighted distance metric for assessing ranking dissimilarity and inter-group heterogeneity

In this paper, a weighted variant of the normalized pairwise angular distance metric is proposed. The inclusion of position weights aims at penalizing inversions in the top of the ranking more than inversions in the tail of the ranking. The performance of the proposed weighted distance metric for assessing ranking dissimilarity and its impact on a procedure for testing inter-group heterogeneity have been investigated via a Monte Carlo simulation study under several scenarios—differing for group size, number of ranked alternatives and system of hypotheses—and compared against those obtained for the unweighted variant.