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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

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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\(\chi ^2 = n\Sigma (\theta '' - \theta ')^2 /821,\), wheren is the number of observations per pair, andθ″ andθ′ 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.

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References

  1. Bartlett, M. S. The square root transformation in analysis of variance.Suppl. J. roy. stat. Soc., 1936,3, 68–78.

    Google Scholar 

  2. Bartlett, M. S. The use of transformations.Biometrics Bull., 1947,3, 39–52.

    Google Scholar 

  3. Bliss, C. I. Plant protection, No. 12. Leningrad, 1937.

  4. Fisher, R. A. On the dominance ratio.Proc. roy. soc. Edinb., 1922,42, 321–341.

    Google Scholar 

  5. Mosteller, F. Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations.Psychometrika, 1951,16, 3–9.

    Google Scholar 

  6. Mosteller, F. Remarks on the method of paired comparisons: II. The effect of an aberrant standard deviation when equal standard deviations and equal correlations are assumed.Psychometrika, 1951,16, 203–206.

    Google Scholar 

  7. Mosteller, F, and Tukey, J. W. The uses and usefulness of binomial probability paper.J. Amer. statist. Ass., 1949,44, 174–212.

    Google Scholar 

  8. Statistical Research Group, Columbia University. Selected techniques of statistical analysis. New York: McGraw-Hill Book Co., 1947.

    Google Scholar 

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Authors and Affiliations

  1. Harvard University, USA

    Frederick Mosteller

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  1. Frederick Mosteller
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Additional information

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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Mosteller, F. 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, 207–218 (1951). https://doi.org/10.1007/BF02289116

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  • DOI: https://doi.org/10.1007/BF02289116

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