Abstract
Consider a repeated measurements study in which a single observation is taken at each oft(t > 2) equally spaced time points for each ofn 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 observationsu time units apart is equal to ρu. For large values oft, the multiplicative correction has a lower bound approximately equal to 2.5/(t − 1).
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Box, G. E. P. Some theorems on quadratic forms applied in the study of analysis of variance problems. II. Effects of inequality of variance and of correlation between errors in the two-way classification.Annals of Mathematical Statistics, 1954,25, 484–498.
Collier, R. O., Baker, F. B. M., Mandeville, G. K., & Hayes, T. F. Estimates of test size for several test procedures based on conventional variance ratios in the repeated measures design.Psychometrika, 1967,32, 339–353.
Elston, R. C. & Grizzle, J. E. Estimation of time response curves and their confidence bands.Biometrics, 1962,18, 148–159.
Geisser, S. & Greenhouse, S. W. An extension of Box's results on the use of the F-statistic in multivariate analysis.Annals of Mathematical Statistics, 1958,29, 885–889.
Greenhouse, S. W. & Geisser, S. On methods in the analysis of profile data.Psychometrika, 1959,24, 95–112.
Huynh, H. Some approximate tests for repeated measurement designs.Psychometrika, 1978,43, 161–175.
Huynh, H. & Feldt, L. S. Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs.Journal of Educational Statistics, 1976,1, 69–82.
Machin, D. On a design problem in growth studies.Biometrics, 1975,31, 749–753.
Pothoff, R. F. & Roy, S. N. A generalized multivariate analysis of variance model useful especially for growth curve problems.Biometrika, 1964,51, 313–325.
Stoloff, P. H. Correcting for heterogeneity of covariance for repeated measures designs of the analysis of variance.Educational and Psychological Measurement, 1970,30, 909–924.
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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.
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Wallenstein, S., Fleiss, J.L. Repeated measurements analysis of variance when the correlations have a certain pattern. Psychometrika 44, 229–233 (1979). https://doi.org/10.1007/BF02293973
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DOI: https://doi.org/10.1007/BF02293973