Journal article

CUMULANTS AND PARTITION LATTICES .6. VARIANCES AND COVARIANCES OF MEAN SQUARES

TP SPEED, HL SILCOCK

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS | AUSTRALIAN MATHEMATICS PUBL ASSOC INC | Published : 1988

Abstract

Formulae are given for the variances and covariances for mean squares in anova under the broadest possible assumptions. The results of other 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 curnulants (and their natural unbiased estimators) which vanish when additive models are assumed. 1980 Mathematics subject classification (Amer. Math. Soc.): 62 A 05, 62 ..

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