Analysis of Variance for Correlated Observations

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Abstract
Two different linear models are presented for the four-dimensional classification system in which correlations exist between certain pairs of observations. Except for the assumption of correlated observations, classical assumptions associated with classification systems are made. The models considered are modifications of those which underlie the split-plot design and the split-split-plot design. In the first model the correlations between observations of the levels of one dimension are all set equal to ρ. In the second model the observations of the levels of one dimension are assumed correlated to degree ρ1, whereas the observations of a second dimension are correlated to degree ρ2. Analyses for the two models and tests of hypotheses for various parameters are indicated.