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A Dual Scaling Analysis for Paired Compositions

Published online by Cambridge University Press:  01 January 2025

Gordon G. Bechtel
Gordon G. Bechtel*
Affiliation:
Oregon Research Institute
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Abstract

A paired composition is a response (upon a dependent variable) to the ordered pair <j, k> of stimuli, treatments, etc. The present paper develops an alternative analysis for the paired compositions layout previously treated by Bechtel's [1967] scaling model. The alternative model relaxes the previous one by including row and column scales that provide an expression of bias for each pair of objects. The parameter estimation and hypothesis testing procedures for this model are illustrated by means of a small group analysis, which represents a new approach to pairwise sociometrics and personality assessment.

Keywords

Parameter EstimationSmall GroupPublic PolicyHypothesis TestingTesting Procedure

Information

Type
Original Paper
Information
Psychometrika , Volume 36 , Issue 2 , June 1971, pp. 135 - 154
Copyright
Copyright © 1971 The Psychometric Society

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Footnotes

*

This study was supported by Grant Nos. MH 12972, MH 10822, and MH 15506 from the National Institute of Mental Health, U. S. Public Health Service. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by N.I.H. special research resources Grant RR-3.

The motivation of this effort has been enhanced by Gerald Patterson and his associates, who have kindly provided the illustrative data at the end of the paper. The author would also like to express his appreciation to Wei-Ching Chang of the Oregon Research Institute and the University of Oregon for his substantive contributions to the paper, and to William Chaplin and Mark Layman of the Oregon Research Institute for the programming of the data analytic method. FORTRAN IV program listings for this analysis are available upon request to the author.

References

Bechtel, G. G. The analysis of variance and pairwise scaling. Psychometrika, 1967, 32, 47–65.CrossRefGoogle ScholarPubMed
Bock, R. D., & Jones, L. V. The measurement and prediction of judgment and choice, 1968, San Francisco: Holden-Day.Google Scholar
Gulliksen, H. Measurement of subjective values. Psychometrika, 1956, 21, 229–244.CrossRefGoogle Scholar
Hicks, J. M., & Campbell, D. T. Zero-point scaling as affected by social object, scaling method, and context. Journal of Personality and Social Psychology, 1965, 2, 793–808.CrossRefGoogle ScholarPubMed
Horst, P. A method for determining the absolute affective value of a series of stimulus situations. The Journal of Educational Psychology, 1932, 23, 418–440.CrossRefGoogle Scholar
Jones, L. V. Invariance of zero-point scaling over changes in stimulus context. Psychological Bulletin, 1967, 67, 153–164.CrossRefGoogle ScholarPubMed
Lev, J., & Kinder, E. F. New analysis of variance formulas for treating data from mutually paired subjects. Psychometrika, 1957, 22, 1–15.CrossRefGoogle Scholar
Patterson, G. R., Ray, R., & Shaw, D. Reprogramming in the families of deviant children, In Jessen, M. (Ed.), Increasing educational effectiveness: Sensitivity, creativity, innovation. Published proceedings of California Association of School Psychologists and Psychometrists, 1968.Google Scholar
Patterson, G. R., & Reid, J. Reciprocity and coercion: Two facets of social systems. In Michaels, J., Neuringer, C. (Eds.), Behavior modification for clinical psychologists, 1970, New York: Appleton-Century-Crofts.Google Scholar
Quenouille, H. M. Design and analysis of experiments, 1953, New York: Hafner.Google Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: Wiley.Google Scholar
Scheffe, H. The analysis of variance, 1959, New York: Wiley.Google Scholar
Thurstone, L. L., & Jones, L. V.. The rational origin for measuring subjective values. Journal of the American Statistical Association, 1957, 52, 458–471.CrossRefGoogle Scholar
Yates, F. Analysis of data from all possible reciprocal crosses between a set of parental lines. Heredity, 1947, 1, 287–301.CrossRefGoogle Scholar