Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1988 - Volume 44, Issue 03  

Research Article

Cumulants and partition lattices VI. variances and covariances of mean squares

T. P. Speeda1 and H. L. Silcocka1

a1 Division of Mathematics and Statistics CSIRO Canberra 2601, Australia

Abstract

Formulae are given for the variances and covariances for mean squares in anova under the broadest possible assumptions. The results of ther 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.

(Received October 01 1985)

(Revised January 05 1987)

1980 Mathematics subject classification (Amer. Math. Soc.)

  • 62 A 05;
  • 62 J 10

Keywords and phrases

  • cumulant;
  • k-statistic;
  • anova model;
  • component of variance;
  • designed experiment;
  • treatment mean square;
  • randomization.