Abstract
Hartley [1967] has given a general procedure for finding directly the numerical values in the formulas for expectations, variances and covariances of ANOVA mean squares. His procedure is applicable for any analysis of variance and any unbalanced random model with design matrices having exactly one 1 in each row and the remaining elements zero. This paper extends these results to general design matrices and also to any unbalanced mixed model. Generalization to correlated errors and/or correlated random components is also considered. Simple and direct proofs are provided with the help of the 'trace' of a matrix.
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