Multivariate Analysis of Ordinal Variables

This article examines the assumptions underlying two multivariate strategies commonly used in analyzing ordinal data. Both strategies employ as a descriptive tool the ordinary multiple regression algorithms; the crucial difference between the two is that the first, ordinal strategy, uses the matrix of Kendall's 's as the building block of multivariate analysis, while the second, parametric strategy, uses the matrix of Pearson's 's. These two strategies are evaluated and constrasted in terms of their usefulness in answering basic research questions that arise in multivariate analysis. One overriding conclusion is that, contrary to the claims of its proponents, the ordinal strategy is no better than the parametric strategy at meeting some of the basic requirements of multivariate analysis. It is argued that parametric strategy, when accompanied by careful evaluation of the validity of the implict quantification of ordinal variables, is more amenable to one of the goals of scientific research: successive approximation and refinement.