Cited by 945Statistical Methods and Bayesian InferenceOptimal Experimental Design MethodsStatistical Methods and Applications

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Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions

Huynh, Huynh, Feldt, Leonard S.·1970·Journal of the American Statistical Association

DOI 10.2307/2284340

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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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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
DOI: 10.2307/2284340
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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Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions

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