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.
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References
Bechtel, G. G. The analysis of variance and pairwise scaling.Psychometrika, 1967,32, 47–66. (a)
Bechtel, G. G.F tests for the absolute invariance of dominance and composition scales.Psychometrika, 1967,32, 157–182. (b)
Bechtel, G. G. A dual scaling analysis for paired compositions.Psychometrika, 1971,36, 135–154.
Gaylor, D. W., and Hopper, F. N. Estimating the degrees of freedom for linear combinations of mean squares by Satterthwaite's formula.Technometrics, 1969,11, 691–706.
Harris, W. P. A revised law of comparative judgements.Psychometrika, 1957,22, 189–198.
Laubscher, N. F. Interpolation inF tables.American Statistician, 1965,19, 28, 40.
Lev, J., and Kinder, E. F. New analysis of variance formulas for treating data from mutually paired subjects.Psychometrika, 1957,22, 1–15.
Lewis, P. A. W., Goodman, A. S., and Miller, J. M. A pseudo-random number generator for the System/360.IBM Systems Journal, 1969,2, 136–146.
Marsaglia, G., and Bray, T. A. A convenient method for generating normal variables.SIAM Review, 1964,6, 260–264.
Meyer, D. L. Methods of generating random normal numbers.Educational and Psychological Measurement, 1969,29, 193–198.
Rieder, C. A., and Lumia, A. R. Effects of olfactory bulb ablation on dominance-related behaviors of male Mongolian gerbils.Physiology and Behavior, 1973,11, 365–369.
Satterthwaite, F. E. An approximate distribution of estimates of variance components.Biometrics Bulletin, 1946,2, 110–114.
Scheffé, H. An analysis of variance for paired comparisons.Journal of the American Statistical Association, 1952,47, 381–400.
Scheffé, H.The analysis of variance. New York: Wiley, 1959.
Searle, S. R.Linear models. New York: Wiley, 1971.
Yates, F. Analysis of data from all possible reciprocal crosses between a set of parental lines.Heredity, 1947,1, 287–301.
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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.
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Gleason, J.R., Halperin, S. A paired compositions model for round-robin experiments. Psychometrika 40, 433–454 (1975). https://doi.org/10.1007/BF02291548
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DOI: https://doi.org/10.1007/BF02291548