, Volume 32, Issue 1, pp 47–65 | Cite as

The analysis of variance and pairwise scaling

  • Gordon G. Bechtel


Variance analyses are presented for two data layouts—each corresponding to the class of all ordered pairs from a single finite set. The analysis of the dominance layout is in terms of a fixed effects linear model which includes parameters representing the scale values of the elements of the set, response bias, and pairwise interactions. A parallel parametrization is carried out for the composition layout for which corresponding point estimates and hypothesis tests are given. A joint treatment of concurrently observed dominance and composition layouts is suggested and illustrative data are presented.


Linear Model Fixed Effect Public Policy Hypothesis Test Variance Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Binder, A. Statistical theory.Ann. Rev. Psychol., 1964,15, 277–310.Google Scholar
  2. [2]
    Coombs, C. H.A theory of data. New York: Wiley, 1964.Google Scholar
  3. [3]
    Cronbach, L. J. and Gleser, Goldine. Assessing similarity between profiles.Psychological Bulletin, 1953,50, 456–473.Google Scholar
  4. [4]
    David, H. A. The method of paired comparisons. In M. G. Kendall (Ed.)Griffin's statistical monographs and courses, No. 12. New York: Hafner, 1963.Google Scholar
  5. [5]
    Edwards, W. The theory of decision making.Psychol. Bull., 1954,51, 380–417.Google Scholar
  6. [6]
    Edwards, W. Behavioral decision theory.Ann. Rev. Psychol., 1961,12, 473–498.Google Scholar
  7. [7]
    Ekman, G. and Sjöberg, L. Scaling.Ann. Rev. Psychol., 1965,16, 451–475.Google Scholar
  8. [8]
    Goodman, N.The structure of appearance. Cambridge, Mass.: Harvard Univ. Press, 1951.Google Scholar
  9. [9]
    Harris, W. P. A revised law of comparative judgment.Psychometrika, 1957,22, 189–198.Google Scholar
  10. [10]
    Lee, M. C. Interactions, configurations, and nonadditive models.Educ. and Psychol. Measmt., 1961,21, 797–805.Google Scholar
  11. [11]
    Lev, J. and Kinder, E. F. New analysis of variance formulas for treating data from mutually paired subjects.Psychometrika, 1957,22, 1–15.Google Scholar
  12. [12]
    Quenouille, H. M.Design and analysis of experiments. New York: Hafner, 1953.Google Scholar
  13. [13]
    Scheffé, H. An analysis of variance for paired comparisons.J. of Amer. Statist. Assn., 1952,47, 381–400.Google Scholar
  14. [14]
    Scheffé, H.The analysis of variance. New York: Wiley, 1959.Google Scholar
  15. [15]
    Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.Google Scholar
  16. [16]
    Tucker, L. R. and Messick, S. An individual differences model for multidimensional scaling.Psychometrika, 1963,28, 333–367.Google Scholar
  17. [17]
    Yates, F. Analysis of data from all possible reciprocal crosses between a set of parental lines.Heredity, 1947,1, 287–301.Google Scholar

Copyright information

© Psychometric Society 1967

Authors and Affiliations

  • Gordon G. Bechtel
    • 1
  1. 1.Oregon Research InstituteUSA

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