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Repeated Measurements Analysis of Variance when the Correlations have a Certain Pattern

Published online by Cambridge University Press:  01 January 2025

Sylvan Wallenstein and
Joseph L. Fleiss
Sylvan Wallenstein*
Affiliation:
Columbia University
Joseph L. Fleiss
Affiliation:
Columbia University
*
Reprint requests should be sent to Sylvan Wallenstein, Division of Biostatistics, Columbia University School of Public Health, 600 West 168 Street, New York, New York 10032.
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Abstract

Consider a repeated measurements study in which a single observation is taken at each of t(t > 2) equally spaced time points for each of n subjects. This paper uses a result of Box to find the appropriate multiplicative correction term for the degrees of freedom in the analysis of variance table for the case when there is equal variability per time point, and when the correlation between observations u time units apart is equal to ρu. For large values of t, the multiplicative correction has a lower bound approximately equal to 2.5/(t − 1).

Keywords

repeated measurementsanalysis of varianceadjusted degrees of freedompatterned correlation matrix

Information

Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 2 , June 1979, pp. 229 - 233
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

Dr. Fleiss is also with the Biometrics Research Unit of the New York State Psychiatric Institute. This work was supported in part by grant DE 04068 from the National Institute of Dental Research.

References

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