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Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions
Abstract
Investigation is made of the character of the covariance matrix which will result in exact F-distributions for the treatments and interaction variance ratios in repeated measurements designs. It is shown, assuming multivariate normality, that the matrix may exhibit a more general character than is typically implied to be essential. Equality of variances and equality of covariances, with identical matrices for all levels of a second treatment factor, are sufficient but not necessary conditions. The necessary and sufficient condition is the equality of variances of differences for all pairs of treatment measures assumed to be correlated. An alternative statement is that the Box-Geisser-Greenhouse parameter ε = 1.0. A test is described which bears on the tenability of this condition.
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Citations
Cites
An Extension of Box's Results on the Use of the $F$ Distribution in Multivariate Analysis
Geisser, S., & Greenhouse, S. W. (1958) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177706545 · Cited by 1,098
Cited by
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007) · Behavior Research Methods · doi:10.3758/bf03193146 · Cited by 65,971
Mixed-effects modeling with crossed random effects for subjects and items
Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008) · Journal of Memory and Language · doi:10.1016/j.jml.2007.12.005 · Cited by 8,540
Friederici, A. D., Pfeifer, E., & Hahne, A. (1993) · Cognitive Brain Research · doi:10.1016/0926-6410(93)90026-2 · Cited by 820
(2004) · Springer Texts in Statistics · doi:10.1007/b98963 · Cited by 517
Heterogeneous Variance: Covariance Structures for Repeated Measures
Wolfinger, R. D. (1996) · Journal of Agricultural, Biological, and Environmental Statistics · doi:10.2307/1400366 · Cited by 401
Metadata
- Authors
- Huynh, H., & Feldt, L. S.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1970-12
- Volume
- 65
- Issue
- 332
- Pages
- 1582-1589
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1976429900
- Cited by
- 946
- References
- 1
- FWCI
- 1.39
- Type
- journal article
- Language
- en
- Open access
- closed
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- Huynh, H., & Feldt, L. S. (1970). Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1970.10481187
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