New Method for the Assignment of Psychometric Scale Values from Incomplete Paired Comparisons*

The principle of least squares is applied to the selection of an optimum set of n response values, or of (n−1) basic response differences, corresponding to n stimuli, from m observed response differences provided by the paired-comparison method of psychometric measurement. This method of selection is shown to be the most appropriate generalization, to the case of a usable but incomplete set, i.e., with n-1≦ m<12n(n-1), of observed response differences, of a corrected form of the algorithm of J. P. Guilford. Unlike the Guilford algorithm, however, direct application of the least-squares principle implies response values which are independent of the a priori ordering of the n stimuli, even in the incomplete-set case.