Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-27T02:41:27.591Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of Variance for Correlated Observations

Published online by Cambridge University Press:  01 January 2025

Raymond O. Collier Jr.
Raymond O. Collier Jr.*
Affiliation:
University of Minnesota
Get access Rights & Permissions [Opens in a new window]

Abstract

Two different linear models are presented for the four-dimensional classification system in which correlations exist between certain pairs of observations. Except for the assumption of correlated observations, classical assumptions associated with classification systems are made. The models considered are modifications of those which underlie the split-plot design and the split-split-plot design. In the first model the correlations between observations of the levels of one dimension are all set equal to ρ. In the second model the observations of the levels of one dimension are assumed correlated to degree ρ1, whereas the observations of a second dimension are correlated to degree ρ2. Analyses for the two models and tests of hypotheses for various parameters are indicated.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 3 , September 1958 , pp. 223 - 236
Copyright
Copyright © 1958 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Binder, A. The choice of an error term in analysis of variance designs. Psychometrika, 1955, 20, 29–50.CrossRefGoogle Scholar
Cochran, W. G. and Cox, G. M. Experimental designs 2nd ed., New York: Wiley, 1957.Google Scholar
Collier, R. O. Jr. Experimental designs in which the observations are assumed to be correlated. Unpublished doctoral dissertation, Univ. Minnesota, 1956.Google Scholar
Edwards, A. L. Experimental design in psychological research, New York: Rinehart, 1950.Google Scholar
Halperin, M. Normal regression theory in the presence of intraclass correlation. Ann. math. Statist., 1951, 22, 573–580.CrossRefGoogle Scholar
Hartley, H. O. Some recent developments in analysis of variance. Commun. pure appl. Math., 1955, 8, 47–57.CrossRefGoogle Scholar
Hoyt, C. J., Stunkard, C. L. et al. A comparison of two methods of instruction in beginning drawing. J. exp. Educ., 1952, 20, 265–279.CrossRefGoogle Scholar
Kempthorne, O. The design and analysis of experiments, New York: Wiley, 1952.CrossRefGoogle Scholar
Kogan, L. S. Analysis of variance—repeated measurements. Psychol. Bull., 1948, 45, 131–143.CrossRefGoogle ScholarPubMed
Kogan, L. S. Variance designs in psychological research. Psychol. Bull., 1953, 50, 1–40.CrossRefGoogle ScholarPubMed
Kramer, C. Y. Extension of multiple range tests to group correlated means. Biometrics, 1957, 13, 13–18.CrossRefGoogle Scholar
Lindquist, E. F. Design and analysis of experiments in psychology and education, Boston: Houghton Mifflin, 1953.Google Scholar
Moonan, W. J. Simultaneous examination and method analysis by variance algebra. J. exp. Educ., 1955, 23, 253–257.CrossRefGoogle Scholar
Moonan, W. J. An analysis of variance method for determining the external and internal consistency of an examination. J. exp. Educ., 1956, 24, 239–244.CrossRefGoogle Scholar
Nandi, H. K. A mathematical set-up leading to analysis of a class of designs. Sankhyā, 1947, 8, 172–176.Google Scholar
Taylor, J. The comparison of pairs of treatments in split-plot experiments. Biometrika, 1950, 37, 443–444.CrossRefGoogle ScholarPubMed
Wilks, S. S. Mathematical statistics, Princeton: Princeton Univ. Press, 1950.Google Scholar
Yates, F. The principles of orthogonality and confounding in replicated experiments. J. agric. Sci., 1933, 23, 109–145.CrossRefGoogle Scholar
Yates, F. Complex experiments. Suppl. J. roy. statist. Soc., 1935, 2, 181–223.CrossRefGoogle Scholar
Yates, F. The design and analysis of factorial experiments. Imp. Bur. soil Sci., Tech. Comm. No. 35, Harpenden, England, 1937.Google Scholar