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

Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the American Statistical Association Taylor & Francis

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

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

Journal of the American Statistical Association , Volume 65 (332): 8 – Dec 1, 1970

Abstract

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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References (13)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1537-274X
eISSN
0162-1459
DOI
10.1080/01621459.1970.10481187
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Journal of the American Statistical AssociationTaylor & Francis

Published: Dec 1, 1970

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