Skip to main content
SpringerLink
Log in

The analysis of variance and pairwise scaling

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Binder, A. Statistical theory.Ann. Rev. Psychol., 1964,15, 277–310.

    Google Scholar 

  2. Coombs, C. H.A theory of data. New York: Wiley, 1964.

    Google Scholar 

  3. Cronbach, L. J. and Gleser, Goldine. Assessing similarity between profiles.Psychological Bulletin, 1953,50, 456–473.

    Google Scholar 

  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. Edwards, W. The theory of decision making.Psychol. Bull., 1954,51, 380–417.

    Google Scholar 

  6. Edwards, W. Behavioral decision theory.Ann. Rev. Psychol., 1961,12, 473–498.

    Google Scholar 

  7. Ekman, G. and Sjöberg, L. Scaling.Ann. Rev. Psychol., 1965,16, 451–475.

    Google Scholar 

  8. Goodman, N.The structure of appearance. Cambridge, Mass.: Harvard Univ. Press, 1951.

    Google Scholar 

  9. Harris, W. P. A revised law of comparative judgment.Psychometrika, 1957,22, 189–198.

    Google Scholar 

  10. Lee, M. C. Interactions, configurations, and nonadditive models.Educ. and Psychol. Measmt., 1961,21, 797–805.

    Google Scholar 

  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. Quenouille, H. M.Design and analysis of experiments. New York: Hafner, 1953.

    Google Scholar 

  13. Scheffé, H. An analysis of variance for paired comparisons.J. of Amer. Statist. Assn., 1952,47, 381–400.

    Google Scholar 

  14. Scheffé, H.The analysis of variance. New York: Wiley, 1959.

    Google Scholar 

  15. Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.

    Google Scholar 

  16. Tucker, L. R. and Messick, S. An individual differences model for multidimensional scaling.Psychometrika, 1963,28, 333–367.

    Google Scholar 

  17. Yates, F. Analysis of data from all possible reciprocal crosses between a set of parental lines.Heredity, 1947,1, 287–301.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Oregon Research Institute, USA

    Gordon G. Bechtel

Authors
  1. Gordon G. Bechtel
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by National Institutes of Health Grant MH-04439-06. The author would like to express his appreciation to Richard Beatty of the University of Toronto, James Baker and William Carroll of Oregon Research Institute, and J. E. Keith Smith of the University of Michigan, for their helpful comments concerning aspects of this work. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bechtel, G.G. The analysis of variance and pairwise scaling. Psychometrika 32, 47–65 (1967). https://doi.org/10.1007/BF02289404

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289404

Keywords

Search

Navigation