A relationship between a method of component analysis and univariate analysis of variance is presented. A data matrix consisting of Ss scores on independent variables, interaction terms, and a dependent variable is used to produce an average cross-product matrix, which in turn is “factored” by the method of triangular decomposition. The F statistics obtained are ratios of the appropriate elements of the component loading matrix times the reciprocals of their degrees of freedom. An example presents a component analysis of an experimental design including setting up the data matrix, decomposing the correlation matrix, and development of appropriate F statistics.
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