CROSS‐COMPARISON OF ANOVA AND SCJM: A NEW APPROACH TO AXIOMATIC CONJOINT MEASUREMENT FOR NOISY DATA*

Abstract

ABSTRACTStochastic conjoint measurement (SCJM) diagnosis is a new methodology for the identification of descriptive models of subjective judgments of multiattribute alternatives. SCJM implements nonparametric statistical analogues of the Krantz, Luce, Suppes, and Tversky [5] independence and cancellation axioms on which the present theory of conjoint measurement is based. SCJM thus relaxes the assumption that the rank‐order data are error free. This paper describes the SCJM approach and applies both SCJM and classical ANOVA to the same factorial designs to obtain cross‐comparisons of the effectiveness of these methodologies for detecting interaction effects. The data are five cross‐section samples of the largest NYSE industrials drawn from Compustat tapes to explore financial leverage effects on E/P ratios during 1963–1973. Results indicate that the two methodologies usually reach similar conclusions regarding the appropriateness of a main effects additive model, but SCJM can detect interactions which would not be detected by ANOVA. Procedures for analyzing the sensitivity of SCJM conclusions are also illustrated.