[Study of statistical test connections in non-orthogonal analysis of variance]

In the Analysis of Variance, we quite often split up the model to test different hypotheses about the model. However, when we analyse the results, we must not forget that the statistics used for the tests are not stochastically independent, either for an orthogonal design, because the test statistics have the same denominator, or for non-orthogonal design. In the latter case, test statistics have not only the same denominator but also not-independent numerators. The links between test statistics have been studied for orthogonal designs (Dall'Aglio, 1962) and for symmetrical Incomplete Block Design (Ballas and Webster, 1966). We shall give here results for the general case of the Analysis of Variance, treat more particularly the case of the Incomplete Block Design and show the joint distribution of two test statistics and, more simply, their correlation coefficient.