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

Abstract

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} \begin{document} $$\chi ^2 = n\Sigma(\theta '' - \theta ')^2 /821,$$ \end{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.