The Hypotheses That Can be Tested When There are Interactions in an Analysis of Variance Model

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Abstract
In order to test hypotheses in the analysis of variance certain sums of squares are computed. When interactions are assumed in the model, the sums of squares for testing the "main effects" depend on how these main effects are defined. This is clarified by expressing the testable hypotheses in terms of the true subclass means; it then becomes possible to devise suitable tests when one or more subclasses are empty. A general method is illustrated, suitable for programming on a large-scale electronic computer, for obtaining the sum of squares appropriate for testing any testable hypothesis.

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