Intergroup Diversity and Concordance for Ranking Data: An Approach via Metrics for Permutations

Motivated by the apportionment of diversity analysis due to C. R. Rao, a general approach to comparing populations of rankers is proposed. Each permutation metric corresponds to a particular population characteristic that forms the basis of the comparison. Tests of hypotheses concerning equality of characteristics are developed. Throughout, comparison is made with earlier work, most of which is based on the use of only the Spearman metric. Extension to tied rankings is discussed. Examples for two groups are presented which illustrate the computational feasibility as well as the value of the proposed procedures.