On the Numerical Availability of Multiple Comparison Procedures

Abstract

In the past many multiple comparison procedure were difficult to perform. Usually, such procedures can be traced back to studentized multiple contrast tests. Numerical difficulties restricted the use of the exact procedures to simple, commonly balanced, designs. Conservative approximations or simulation based approaches have been used in the general cases. However, new efforts and results in the past few years have led to fast and efficient computations of the underlying multidimensional integrals. Inferences for any finite set of linear functions of normal means are now numerically feasible. These include all-pairwise comparisons, comparisons with a control (including dose-response contrasts), multiple comparison with the best, etc. The article applies the numerical progress on multiple comparisons procedures for common balanced and unbalanced designs within the general linear model.