Distribution Function for Similarity Estimates

Abstract

With the increasing use of similarity analysis as a technique for the study of multidimensional problems, properties of similarity estimates deserve increasing interest. The paper reports an investigation of the inter-individual variation of similarity estimates. Data from a previous large-scale study by Kuennapas were used for this purpose. Similarity estimates were available for 378 stimulus pairs judged by 57 Ss. The standard deviation was shown to vary regularly with the mean similarity estimate. A function derived from the binomial distribution function was found to describe the trend highly satisfactorily. As a further illustration of the same principle, it was shown that the binomial function describes the frequency distributions of similarity estimates in close approximation. It is suggested that similar simple principles may describe the data obtained in experiments involving conventional uni-dimensional scaling techniques, e.g., magnitude and ratio estimation.