Remarks on the Method of Paired Comparisons: III. A Test of Significance for Paired Comparisons when Equal Standard Deviations and Equal Correlations are Assumed

A test of goodness of fit is developed for Thurstone's method of paired comparisons, Case V. The test involves the computation of 12ptminimal amsmath wasysym amsfonts amssymb amsbsy mathrsfs upgreek -69pt document ² = n ('' - ') ² /821, document, where n is the number of observations per pair, and θ ″ and θ ′ are the angles obtained by applying the inverse sine transformation to the fitted and the observed proportions respectively. The number of degrees of freedom is (k −1) (k −2) /2.