Abstract
Consider a three-way classification with one observation per cell. In this paper, we propose a statistical test of three-factor interaction for the layout. For the purpose of testing, we present an ANOVA model which is an extension of the one given by Johnson and Graybill for the two-way classification. Under the ANOVA model, the likelihood ratio test statistics is driven. The approximation for a distribution of the test statistics is investigated, and a table of critical points for the statistics is constructed. It is seen that the power of this test is more than that of Milliken and Graybill for wide values of parameters in the model.
