Conjoint Measurement and the Canonical Analysis of Contingency Tables

Abstract

The simultaneous conjoint model of measurement is first briefly outlined and its relevance to the problems of measurement level in sociological research discussed. The canonical correlation approach to the analysis of contingency tables is then presented as a simultaneous conjoint model solution to the problem of providing a more adequate representation than a traditional X 2 -based measure of association of more complex sets of frequency data.-. n this paper I outline a method for decomposing the conventional X2 test measure into a number of additive components. I then intend to show that this provides a quite general way for extracting metric information from contingency tables. THE PROBLEM OF MEASUREMENT LEVELClearly the single most important factor the researcher has to consider at the analysis stage is scale, or level, of measurement, since the range and power of the techniques that are open to him at this stage are largely determined by the assumptions he is