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

Published online by Cambridge University Press:  01 January 2025

Frederick Mosteller
Frederick Mosteller*
Affiliation:
Harvard University
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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.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 2 , June 1951 , pp. 207 - 218
Copyright
Copyright © 1951 The Psychometric Society

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Footnotes

*

This research was performed in the Laboratory of Social Relations under a grant made available to Harvard University by the RAND Corporation under the Department of the Air Force, Project RAND.

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