## Abstract

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
$n-1\leqq m<{\scriptstyle \frac{1}{2}}n(n-1)$, 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.

© 1955 Optical Society of America

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