The Effect of Category Choice on Some Ordinal Measures of Association

Abstract

Several ordinal measures of association for cross-classification tables are compared with respect to their stability when various grids are placed on a bivariate normal distribution. Kendall's tau b usually fares better than Kendall's tau c, Goodman and Kruskal's gamma, and three extensions of Spearman's rho for cross-classification tables, in terms of approximating an associated measure for ungrouped data. The loss of efficiency of tau b due to grouping in testing the hypothesis of no association is considered and observed to be strongly related to the proportion of tied pairs of observations.