Abstract

The principle of least squares is applied to the selection of an optimum set of <i>n</i> response values, or of (<i>n</i>-1) basic response differences, corresponding to <i>n</i> stimuli, from <i>m</i> 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 <i>n</i>-1≦<i>m</i><½<i>n</i>(<i>n</i>-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 <i>a priori</i> ordering of the <i>n</i> stimuli, even in the incomplete-set case.

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