Stochastically Independent Components in the Analysis of Variance

Abstract In this paper an analysis of a sum of squares for linear hypothesis in a fixed linear model is presented. The analysis is based on a partition of sum of squares into independent components. These components are treated as sums of squares for hypotheses implied by an overall one. In the special case components of a sum of squares are distributed with one degree of freedom each and hypotheses concern single parametric functions. In the model not of full rank the form of a sum of squares is transformed before partitioning. The case of the model for cross classification is considered in details. Next the cases of the model of full rank and the one with restrictions on parameters are discussed. The model for balanced design with unweighted restrictions on parameters is considered in details. In this case sume of squares for orthogonal contrasts are obtained from analysis of the sum of squares for hypothesis concerning main or interaction effects.