The Carroll-Green-Schaffer Scaling in Correspondence Analysis: A Theoretical and Empirical Appraisal

In two recent JMR articles, Carroll, Green, and Schaffer have proposed an alternative scaling of the coordinates in the correspondence analysis of a contingency table. This “CGS scaling” is claimed to allow interpoint distance comparisons both “within sets” (i.e., row-to-row and column-to-column distances) and “between sets” (i.e., row-to-column distances). The author shows by a theoretical argument and by means of a simple practical example that the rationale on which this scaling is based is incorrect.