Generalized Odds Ratios for Ordinal Data

We consider properties of the ordinal measure of association defined by the ratio of the proportions of concordant and discordant pairs. For 2 x 2 cross-classification tables, the measure simplifies to the odds ratio. The generalized measure can be used to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable. The ratio of its values for two groups constitutes an odds ratio defined in terms of pairs of observations. Unlike the odds ratio measures proposed by Clayton (1974, Bionxetrika 61, 525-531) for similar purposes, this measure is not linked to specific model assumptions and hence it is more widely applicable as a descriptive measure.