Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T15:51:19.850Z Has data issue: false hasContentIssue false
  • English
  • Français

An Axiomatic Formulation and Generalization of Successive Intervals Scaling

Published online by Cambridge University Press:  01 January 2025

Ernest Adams  and
Samuel Messick
Ernest Adams
Affiliation:
University of California, Berkeley
Samuel Messick
Affiliation:
Educational Testing Service
Get access Rights & Permissions [Opens in a new window]

Abstract

A formal set of axioms is presented for the method of successive intervals, and directly testable consequences of the scaling assumptions are derived. Then by a systematic modification of basic axioms the scaling model is generalized to non-normal stimulus distributions of both specified and unspecified form.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 4 , December 1958 , pp. 355 - 368
Copyright
Copyright © 1958 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This paper was written while the authors were attending the 1957 Social Science Research Council Summer Institute on Applications of Mathematics in Social Science. The research was supported in part by Stanford University under Contract NR 171-034 with Group Psychology Branch, Office of Naval Research, by Social Science Research Council, and by Educational Testing Service. The authors wish to thank Dr. Patrick Suppes for his interest and encouragement throughout the writing of the report and Dr. Harold Gulliksen for his helpful and instructive comments on the manuscript.

References

Adams, E. and Messick, S. An axiomatization of Thurstone's successive intervals and paired comparisons scaling models, Stanford, Calif.: Stanford Univ., Applied Mathematics and Statistics Laboratory, 1957.Google Scholar
Attneave, F. A method of graded dichotomies for the scaling of judgments. Psychol. Rev., 1949, 56, 334–340.Google ScholarPubMed
Bishop, R. Points of neutrality in social attitudes of delinquents and non-delinquents. Psychometrika, 1940, 5, 35–45.CrossRefGoogle Scholar
Bock, R. D.. Note on the least squares solution for the method of successive categories. Psychometrika, 1957, 22, 231–240.CrossRefGoogle Scholar
Burros, R. H. The estimation of the discriminal dispersion in the method of successive intervals. Psychometrika, 1955, 20, 299–305.Google Scholar
Diederich, G., Messick, S., and Tucker, L. R. A general least squares solution for successive intervals. Psychometrika, 1957, 22, 159–173.CrossRefGoogle Scholar
Edwards, A. L. The scaling of stimuli by the method of successive intervals. J. appl. Psychol., 1952, 36, 118–122.CrossRefGoogle Scholar
Edwards, A. L. and Thurstone, L. L. An internal consistency check for scale values determined by the method of successive intervals. Psychometrika, 1952, 17, 169–180.CrossRefGoogle Scholar
Garner, W. R. and Hake, H. W. The amount of information in absolute judgments. Psychol. Rev., 1951, 58, 446–459.Google Scholar
Guilford, J. P. The computation of psychological values from judgments in absolute categories. J. exp. Psychol., 1938, 22, 32–42.CrossRefGoogle Scholar
Gulliksen, H. Paired comparisons and the logic of measurement. Psychol. Rev., 1946, 53, 199–213.CrossRefGoogle ScholarPubMed
Gulliksen, H. A least squares solution for successive intervals assuming unequal standard deviations. Psychometrika, 1954, 19, 117–139.CrossRefGoogle Scholar
Luce, R. D. A theory of individual choice behavior. Bureau Appl. Soc. Res., Columbia Univ., 1957. (Mimeo.)Google Scholar
Messick, S. Some recent theoretical developments in multidimensional scaling. Educ. psychol. Measmt, 1956, 16, 82–100.Google Scholar
Mosier, C. I. A modification of the method of successive intervals. Psychometrika, 1940, 5, 101–107.Google Scholar
Mosteller, F. Some miscellaneous contributions to scale theory: Remarks on the method of paired comparisons. Cambridge: Harvard Univ., Lab. Soc. Relations, Report No. 10. Ch. III.Google Scholar
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
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, 1951, 16, 207–218.CrossRefGoogle Scholar
Rimoldi, H. J. A. and Hormaeche, M. The law of comparative judgment in the successive intervals and graphic rating scale methods. Psychometrika, 1955, 20, 307–318.Google Scholar
Rozeboom, W. W. and Jones, L. V. The validity of the successive intervals method of psychometric scaling. Psychometrika, 1956, 21, 165–183.CrossRefGoogle Scholar
Saffir, M. A comparative study of scales constructed by three psychophysical methods. Psychometrika, 1937, 2, 179–198.Google Scholar
Stevens, S. S. Mathematics, measurement, and psychophysics. In Stevens, S. S. (Eds.), Handbook of experimental psychology, New York: Wiley, 1951.Google Scholar
Thurstone, L. L. A method of scaling psychological and educational tests. J. educ. Psychol., 1925, 16, 433–451.CrossRefGoogle Scholar
Thurstone, L. L. Psychophysical analysis. Amer. J. Psychol., 1927, 38, 368–389.CrossRefGoogle Scholar
Thurstone, L. L. A law of comparative judgment. Psychol. Rev., 1927, 34, 424–432.Google Scholar
Thurstone, L. L. The unit of measurement in educational scales. J. educ. Psychol., 1927, 18, 505–524.Google Scholar
Torgerson, W. S. A law of categorical judgment. In Clark, L. S. (Eds.), Consumer behavior, New York: New York Univ. Press, 1954.Google Scholar