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A Covariance Analysis of Multiple Paired Comparisons

Published online by Cambridge University Press:  01 January 2025

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

In the method of multiple paired comparisons the dominance of object j over object k is observed upon p attributes. The present paper develops a covariance analysis for these paired comparisons in terms of a linear model which includes scale, bias, and interaction effects, along with s covariants upon which the comparisons are presumably dependent. The covariance model gives rise to adjusted parameter estimates and hypothesis tests for the residual pairwise layout from which the effects of the s covariants have been removed. These estimation and testing procedures are illustrated with an analysis of political judgment data, and their relevance to the general problem of residual scaling is discussed.

Keywords

CovarianceLinear ModelParameter EstimateInteraction EffectPublic Policy
Type
Original Paper
Information
Psychometrika , Volume 36 , Issue 1 , March 1971 , pp. 35 - 55
Copyright
Copyright © 1971 The Psychometric Society

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Footnotes

*

This research was supported by National Institute of Mental Health grants MH 12972 and MH 15506. The author would like to express his appreciation to Jerry Solomon and Wei-Ching Chang of the Oregon Research Institute for the data analysis reported at the end of the paper. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by N.I.H. Grant FR-3.

References

Bechtel, G. G. The multivariate analysis of variance and multi-attribute scaling. Oregon Research Institute Research Bulletin, 8(2), 1968.Google Scholar
Rao, C. R. An asymptotic expansion of the distribution of Wilk's Criterion. Bulletin of the International Statistical Institute, 1951, 33(2), 177–180Google Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: WileyGoogle Scholar
Scheffé, H. The analysis of variance, 1959, New York: WileyGoogle Scholar