Abstract
Publisher Summary This chapter focuses on the inference on the structure of interaction in a two-way classification model. Under the classical two-way classification model with one observation per cell, the hypotheses of no main effects are tested in practice by using the ratios of the mean squares associated with the main effects to the error mean square. But when the interaction among the main effects is present, these tests are no longer valid. So, there is quite a bit of interest in studying the structure of interaction term and the effect of interaction on the usual tests for main effects. The chapter discusses some early developments on tests for additivity, tests for the structure of interaction using the eigenvalues of a random matrix, and the problem of testing the main effects in the presence of interaction. It also illustrates the applications of certain tests for the hypotheses of no interaction with some data on animal models.
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