J Austral Math Soc Ser A 44 pp362--388, 1988.

Cumulants and Partition Lattices VI. Variances and Covariances of Mean Squares

T. P. Speed and H. L. Silcock

Abstract

Formulae are given for the variances and covariances for mean squares is anova under the broadest possible assumptions. The results of authors are obtained by specializing appropriately: these include ones concerning randomization and/or random sampling models, as well as additive (linear) models consisting of mutually independent sets of exchangeable effects. Although the illustrations given refer only to doubly and triply-indexed arrays, the approach is quite general. Particular attention is drawn to the generalized cumulants (and their natural unbiased estimators) which vanish when additive models are assumed.

1980 AMS Subject Classification: 62A05, 62J10

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Authors

T. P. Speed

H. L. Silcock

Division of Mathematics and Statistics, CSIRO, Canberra 2601, Australia.