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A Paired Compositions Model for Round-Robin Experiments

Published online by Cambridge University Press:  01 January 2025

John R. Gleason  and
Silas Halperin
John R. Gleason
Affiliation:
Syracuse University
Silas Halperin
Affiliation:
Syracuse University
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Abstract

Investigation of the effects of a series of treatment conditions upon some social behaviors may require observation of a set of subjects which have been mutually paired, in round-robin fashion. Data arising from such experiments are difficult to analyze, partly because they do not fit neatly into standard designs. A paired compositions scaling model due to Bechtel is adapted to provide a linear model for such round-robin experiments. Both fixed and mixed versions of the model are considered and some results of a Monte Carlo study of the mixed model are reported. The model is applied to illustrative data from the field of physiological psychology.

Information

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 4 , December 1975 , pp. 433 - 454
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

We wish to thank Corinne A. Rieder and Augustus R. Lumia for graciously making available their data, a portion of which serves as the example in Section 6. Portions of this paper were presented at the Psychometric Society meeting, Stanford, California, March 28, 1974.

References

Bechtel, G. G.. The analysis of variance and pairwise scaling. Psychometrika, 1967, 32, 47–66.CrossRefGoogle ScholarPubMed
Bechtel, G. G.. F tests for the absolute invariance of dominance and composition scales. Psychometrika, 1967, 32, 157–182.CrossRefGoogle ScholarPubMed
Bechtel, G. G.. A dual scaling analysis for paired compositions. Psychometrika, 1971, 36, 135–154.CrossRefGoogle Scholar
Gaylor, D. W., Hopper, F. N.. Estimating the degrees of freedom for linear combinations of mean squares by Satterthwaite's formula. Technometrics, 1969, 11, 691–706.CrossRefGoogle Scholar
Harris, W. P.. A revised law of comparative judgements. Psychometrika, 1957, 22, 189–198.CrossRefGoogle Scholar
Laubscher, N. F.. Interpolation in F tables. American Statistician, 1965, 19, 28–28.Google Scholar
Lev, J., Kinder, E. F.. New analysis of variance formulas for treating data from mutually paired subjects. Psychometrika, 1957, 22, 1–15.CrossRefGoogle Scholar
Lewis, P. A. W., Goodman, A. S., Miller, J. M.. A pseudo-random number generator for the System/360. IBM Systems Journal, 1969, 2, 136–146.CrossRefGoogle Scholar
Marsaglia, G., Bray, T. A.. A convenient method for generating normal variables. SIAM Review, 1964, 6, 260–264.CrossRefGoogle Scholar
Meyer, D. L.. Methods of generating random normal numbers. Educational and Psychological Measurement, 1969, 29, 193–198.CrossRefGoogle Scholar
Rieder, C. A., Lumia, A. R.. Effects of olfactory bulb ablation on dominance-related behaviors of male Mongolian gerbils. Physiology and Behavior, 1973, 11, 365–369.CrossRefGoogle ScholarPubMed
Satterthwaite, F. E.. An approximate distribution of estimates of variance components. Biometrics Bulletin, 1946, 2, 110–114.CrossRefGoogle ScholarPubMed
Scheffé, H.. An analysis of variance for paired comparisons. Journal of the American Statistical Association, 1952, 47, 381–400.Google Scholar
Scheffé, H.. The analysis of variance, 1959, New York: Wiley.Google Scholar
Searle, S. R.. Linear models, 1971, New York: Wiley.Google Scholar
Yates, F.. Analysis of data from all possible reciprocal crosses between a set of parental lines. Heredity, 1947, 1, 287–301.CrossRefGoogle Scholar