An Index of Agreement between a Hypothesized Partial Order and an Empirical Rank Order

Abstract

An index of agreement T between a hypothesized partial order of k groups on an independent variable X and the rank order of the observations on a dependent variable Y is proposed. The mean and variance of T under H 0 , including the cases of unequal group size and of ties in Y , are derived. Rapidity of convergence to normality is discussed and a z -test of the significance of T is given. The consistency of T and comparisons with ANOVA are considered. An illustrative example is given.