The Comparison of Single Item Constructs by Relative Mean and Relative Variance

Abstract

This article discusses the use of an approach advocated in the psychometrics and statistics literature for analyzing square contingency tables with ordered and comparable categories. Assuming that observed ordinal categorical variables are manifestations of underlying continuous variables, a model is formulated to compare the variables by studying the relative location and the relative dispersion of the underlying continuous variables. The formulation, interpretation, and analysis of the model are discussed, and the implementation of the proposed procedure using easily accessible software is addressed. The proposed approach is then compared with a widely adopted simple method that treats the ordinal measures as if they were interval scales. Analyses of real data and simulation results show that the simple method can be misleading and that the proposed approach is preferable in detecting variable differences.