A comparison of the eigenvalue method and the geometric mean procedure for ratio scaling

Abstract

This article evaluates and compares the performance of two ratio scaling methods, the eigenvalue method proposed by Saaty (1977, 1980) and the geometric mean procedure advocated by Williams and Crawford (1980), given random data. The two methods were examined in a series of monte carlo simulations for two response methods (direct estimation and constant sum) and various numbers of stimuli and response scales. The sampling distributions of the measures of consistency of the two methods were tabulated, rules for detecting and rejecting inconsistent respondents are outlined, and approximation formulas for other designs are derived. Overall, there was a high level of agreement and correspondence between the results from the two scaling techniques even when the data were random.