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A Comparison of the Precision of Three Experimental Designs Employing a Concomitant Variable

Published online by Cambridge University Press:  01 January 2025

Leonard S. Feldt
Leonard S. Feldt*
Affiliation:
State University of Iowa
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Abstract

Three techniques are commonly employed to capitalize on a concomitant variate and improve the precision of treatment comparisons: (1) stratification of the experimental samples and use of a factorial design, (2) analysis of covariance, and (3) analysis of variance of difference scores. The purpose of this paper is to compare the effectiveness of these alternatives in improving experimental precision, to identify the most precise design and the conditions under which its advantage holds, and to derive, in the case of the factorial approach, recommendations as to the optimal numbers of levels.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 4 , December 1958 , pp. 335 - 353
Copyright
Copyright © 1958 The Psychometric Society

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References

Anderson, R. L. and Bancroft, T. A. Statistical theory in research, New York: McGraw-Hill, 1952.Google Scholar
Bartlett, M. S. The use of transformations. Biometrics, 1947, 3, 39–52.CrossRefGoogle ScholarPubMed
Box, G. E. P. Some theorems on quadratic form applied in the study of analysis of variance problems, I. Effects of inequality of variance in the one-way classification. Ann. math. Statist., 1954, 25, 290–302.CrossRefGoogle Scholar
Cochran, W. G. Some consequences when the assumptions for analysis of variance are not satisfied. Biometrics, 1947, 3, 22–28.CrossRefGoogle Scholar
Cochran, W. G. and Cox, G. M. Experimental designs, New York: Wiley, 1950.Google Scholar
Cox, D. R. The use of a concomitant variable in selecting an experimental design. Biometrika, 1957, 44, 150–158.Google Scholar
Eisenhart, C. The assumptions underlying the analysis of variance. Biometrics, 1947, 3, 1–21.CrossRefGoogle ScholarPubMed
Federer, W. T. Experimental design, New York: Macmillan, 1955.Google Scholar
Federer, W. T. and Schlottfeldt, C. S. The use of covariance to control gradients in experiments. Biometrics, 1954, 10, 282–290.Google Scholar
Finney, D. J. Standard errors of yields adjusted for regression on an independent measurement. Biometrics, 1946, 2, 53–55.Google Scholar
Fisher, R. A. Statistical methods for research workers 12th ed., London: Oliver and Boyd, 1952.Google Scholar
Fisher, R. A. The design of experiments 5th ed., London: Oliver and Boyd, 1949.Google Scholar
Gourlay, N. Covariance analysis and its applications in psychological research. Brit. J. statist. Psychol., 1953, 6, 25–34.CrossRefGoogle Scholar
Graybill, F. Variance heterogeneity in a randomized block design. Biometrics, 1954, 10, 516–520.CrossRefGoogle Scholar
Greenberg, B. G. Use of covariance and balancing in analytical surveys. Amer. J. publ. Hlth, 1953, 43, 692–699.CrossRefGoogle Scholar
Kempthorne, O. The design and analysis of experiments, New York: Wiley, 1952.CrossRefGoogle Scholar
Lindquist, E. F. Design and analysis of experiments in psychology and education, Boston: Houghton Mifflin, 1953.Google Scholar
Lucas, H. L. Design and analysis of feeding experiments with milking dairy cattle. Raleigh, N. C.: Inst. Statist. Mimeo. Series No. 18, Univ. North Carolina, 1951.Google Scholar
Norton, D. W. An empirical investigation of some effects of nonnormality and heterogeneity on the F-distribution. Unpublished doctoral dissertation, State Univ. Iowa, 1952.Google Scholar
Outhwaite, A. D. and Rutherford, A. Covariance analysis as an alternative to stratification in the control of gradients. Biometrics, 1955, 11, 431–440.CrossRefGoogle Scholar
Snedecor, G. W. Statistical methods 5th ed., Ames, Iowa: Iowa State College Press, 1956.Google Scholar