Advertisement

Psychometrika

, Volume 19, Issue 2, pp 117–139 | Cite as

A least squares solution for successive intervals assuming unequal standard deviations

  • Harold Gulliksen
Article

Abstract

A least squares solution has been presented for the Law of Categorical Judgment and the Method of Successive Intervals, which is formally equivalent to Horst's solution for the matrix of incomplete data. A simplified approximation which is recommended for use with any matrix of complete data is also given. A procedure, analogous to that originally devised by Thurstone and presented by Saffir, is outlined for the typical experimental matrix of incomplete data. It is essentially a “point and slope” method of fitting a straight line which comes rather directly from the least squares solution.

Keywords

Standard Deviation Public Policy Statistical Theory Complete Data Incomplete Data 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Attneave, F. A method of graded dichotomies for the scaling of judgments.Psychol. Rev., 1949,56, 334–340.Google Scholar
  2. 2.
    Flanagan, J. C. A bulletin reporting the basic principles and procedures used in the development of their system of scaled scores. New York: Cooperative Test Service, American Council on Education, 1939.Google Scholar
  3. 3.
    Gulliksen, H. Paired comparisons and the logic of measurement.Psychol. Rev., 1946,53, 199–213.Google Scholar
  4. 4.
    Horst, P. The prediction of personal adjustment. Social Science Research Council Bulletin 48, 1941.Google Scholar
  5. 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. 6.
    Mosteller, F. Remarks on the method of paired comparisons. III. A test of significance for paired comparisons when equal standard deviations and equal intercorrelations are assumed.Psychometrika, 1951,16, 207–218.Google Scholar
  7. 7.
    Saffir, M. A. A comparative study of scales constructed by three psychophysical methods.Psychometrika, 1937,2, 179–198.Google Scholar
  8. 8.
    Stephenson, W. The inverted factor technique.Brit. J. Psychol., 1936,26, 344–361.Google Scholar
  9. 9.
    Stephenson, W. Methodological consideration of Jung's typology.J. Mental Sci., 1939,85, 185–205.Google Scholar
  10. 10.
    Stevens, S. S. On the problem of scales for the measurement of psychological magnitudes.J. of Unif. Sci., 1939,9, 94–99.Google Scholar
  11. 11.
    Stevens, S. S. and Volkmann, J. The relation of pitch to frequency: a revised scale.Amer. J. Psychol., 1940,53, 329–353.Google Scholar
  12. 12.
    Thurstone, L. L. A method of scaling psychological and educational tests.J. Educ. Psychol., 1925,16, 433–451.Google Scholar
  13. 13.
    Thurstone, L. L. Psychophysical analysis.Amer. J. Psychol., 1927,38, 368–389.Google Scholar
  14. 14.
    Thurstone, L. L. A law of comparative judgment.Psychol. Rev., 1927,34, 273–286.Google Scholar
  15. 15.
    Thursone, L. L. Three psychophysical laws.Psychol. Rev., 1927,34, 424–432.Google Scholar
  16. 16.
    Thurstone, L. L. Equally often noticed differences.J. Educ. Psychol., 1927,18, 289–293.Google Scholar
  17. 17.
    Thurstone, L. L. The unit of measurement in educational scales.J. Educ. Psychol., 1927,18, 505–524.Google Scholar
  18. 18.
    Torgerson, W. S. A theoretical and empirical investigation of multidimensional scaling. Research Bulletin (RB-51-14), Educational Testing Service. Ph.D. thesis, Princeton University, 1951. (AlsoPsychometrika, 1952,17, 401–419.)Google Scholar
  19. 19.
    Volkmann, J. The method of single stimuli.Amer. J. Psychol., 1932,44, 808–809.Google Scholar
  20. 20.
    Wever, E. G. and Zener, K. E. The method of absolute judgment in psychophysics.Psychol. Rev., 1928,35, 466–493.Google Scholar

Copyright information

© Psychometric Society 1954

Authors and Affiliations

  • Harold Gulliksen
    • 1
    • 2
  1. 1.Princeton UniversityUSA
  2. 2.Educational Testing ServiceUSA

Personalised recommendations