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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} $$\chi ^2 = n\Sigma(\theta '' - \theta ')^2 /821,$$ , 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.