Circular triad distributions with applications to complete paired comparisons data

Abstract

This work is concerned with the probability distributions of circular triads and the application of knowledge of these distributions to the study of behavior. Several approximations to distributions of the total number of circular triads produced by one judge are compared. Formulas for the means and variances of the distributions of circular triads for one object, across judges, are also derived. A computer program written to perform object: and subject scaling based upon circular triads is applied to four kinds of data. Analysis summaries of the results of scaling random data, social desirability word data, alphabetic visual similarity data, and Edwards Personal Preference Schedule data are produced. Research is restricted to the study of complete paired comparisons situations.