Rank Correlations and the Analysis of Rank-Based Experimental Designs

The notion of distance between two permutations is used to provide a unified treatment for various problems involving ranking data. Using the distances defined by Spearman and Kendall, the approach is illustrated in terms of the problem of concordance as well as the problem of testing for agreement among two or more populations of rankers. An extension of the notion of distance for incomplete permutations is shown to lead to a generalization of the notion of rank correlation. Applications are given to the incomplete block design as well as to the class of cyclic designs.