Simultaneous inferences: new method of maximum combination

Abstract

The Scheffé method is used to carry out simultaneous inferences on many linear combinations of K parameters. Frequently these combinations arise from the need to explain the causes of significance of the homogeneity test for all the parameters. This paper proposes an alternative methodology based on the maximization of the contrast statistic in the coefficient of the combination. This new method, compatible with Scheffé's method, in addition yields the statistic which should be used for the global test, as well as the combination of maximum significance. The method is illustrated in the cases of K means of normal distributions and K binomial proportions (independent samples). In the second case, the method allows a homogeneity test that is more powerful than Pearson's classic chi-squared test to be obtained. The program which determines this may be obtained at