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 [12pt]{minimal} {amsmath} {wasysym} {amsfonts} {amssymb} {amsbsy} {mathrsfs} {upgreek} {}{-69pt} {document} χ ² = nΣ(θ '' - θ ')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.