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

Frederick Mosteller

doi:10.1007/bf02289116

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.

Keywords

Thurstone scaleMathematicsStatisticsPaired comparisonGoodness of fitStandard deviationTransformation (genetics)Degrees of freedom (physics and chemistry)ComputationInverseAlgorithmGeometryPhysics

Affiliated Institutions

Harvard University Press US

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Publication Info

Year: 1951
Type: article
Volume: 16
Issue: 2
Pages: 207-218
Citations: 218
Access: Closed

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APA Style

                            
                                    Frederick Mosteller
                                
                            (1951). 
                            Remarks on the Method of Paired Comparisons: III. A Test of Significance for Paired Comparisons when Equal Standard Deviations and Equal Correlations are Assumed. 
                            Psychometrika
                            , 16
                            (2)
                            , 207-218.
                            https://doi.org/10.1007/bf02289116

Identifiers

DOI: 10.1007/bf02289116