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Optimal Scaling for Ordered Categories

Published online by Cambridge University Press:  01 January 2025

R. A. Bradley ,
S. K. Katti  and
Irma J. Coons
R. A. Bradley
Affiliation:
The Florida State University
S. K. Katti
Affiliation:
The Florida State University
Irma J. Coons
Affiliation:
Research Center, The General Foods Corporation
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Abstract

This paper deals with the determination of optimal weights for points on scoring scales for subjective comparative experiments. A scoring scale with a specific number of points is considered, and it is assumed that verbal or other indications imply an order to the scale points. The optimal spacing for the scale points is obtained in the sense that treatment or item differences are maximized relative to error or within-treatment variation. The method is presented in sufficiently generalized form to be used directly with any experimental design leading to the analysis of variance. An iterative procedure, suitable for computer use, yields the optimal differences among the ordered scale points. Properties of this procedure are discussed.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 4 , December 1962 , pp. 355 - 374
Copyright
Copyright © 1962 The Psychometric Society

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Footnotes

*

Research sponsored in part by the Statistics Branch, Office of Naval Research, and in part by the Research Center, the General Foods Corporation. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

Bock, R. D. Note on the least squares solution for the method of successive categories. Psychometrika, 1957, 22, 231–240.CrossRefGoogle Scholar
Bock, R. D. Methods and applications of optimal scaling. Report No. 25, Psychometric Laboratory, Univ. of North Carolina, 1960.Google Scholar
Fisher, R. A. Statistical methods for research workers (10th ed.), Edinburgh: Oliver and Boyd, 1946.Google Scholar
Gulliksen, H. A least squares solution for successive intervals assuming unequal standard deviations. Psychometrika, 1954, 19, 117–139.CrossRefGoogle Scholar
Guttman, L. The quantification of a class of attributes: A theory and method of scale construction. In Horst, P. et al., The prediction of personal adjustment. New York: Social Science Research Council, 1941, 319–348..Google Scholar
Horst, P. The prediction of personal adjustment, New York: Social Science Research Council, 1941.Google Scholar
Mosteller, F. A theory of scalogram analysis, using noncumulative types of items: A new approach to Thurstone's method of scaling attitudes. Report No. 9, Laboratory of Social Relations, Harvard Univ., 1949.Google Scholar
Torgerson, W. S. Theory and methods of scaling, New York: Wiley, 1958.Google Scholar