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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In order to compensate for adverse effects in tests of within effects or between-within interactions, the noncentrality parameter and the degrees of freedom of the F distribution can be multiplied by a correction factor.
“In order to compensate for such adverse effects in tests of within effects or between-within interactions, the noncentrality parameter and the degrees of freedom of the F distribution can be multiplied by a correction factor (Geisser & Greenhouse, 1958;Huynh & Feldt, 1970).”
From G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences (2007) · cites this paper as Huynh & Feldt, 1970
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Schutz, R. W., & Gessaroli, M. E. (1987) · Research Quarterly for Exercise and Sport · doi:10.1080/02701367.1987.10605437 · Cited by 187 · see citing works
- Authors
- Huynh, H., & Feldt, L. S.
- Affiliations
- University of Iowa (US)
- 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
- 945
- References
- 18
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 5 · 2023: 9 · 2022: 9 · 2021: 13 · 2020: 16 · 2019: 17 · 2018: 17 · 2017: 18 · 2016: 25 · 2015: 19 · 2014: 29 · 2013: 24 · 2012: 28
- FWCI
- 1.48
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- repeated measures designs, covariance matrix, multivariate normality, equality of variances, variance ratio
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