A PATH-LENGTH INEQUALITY FOR THE MULTIVARIATE-T DISTRIBUTION, WITH APPLICATIONS TO MULTIPLE COMPARISONS

This article presents a new inequality for the multivariate-t distribu tion, which implies a new method for multiple comparisons whose founda tion rests on a recent inequality due to Naiman. The new method is pro mising in view of the fact that it utilizes information (estimator int ercorrelations) ignored by the most widely used multiple comparison me thods yet is not computationally prohibitive, requiring only the numer ical evaluation of a single one-dimensional integral. In this article the validity of the new method in the normal-theoretic general linear model is established, and efficiency studies relative to the methods o f Scheffe, Bonferroni, Sidak, and Hunter-Worsley are presented. The ne w method is shown to always improve on Scheffe's method. The new metho d is also shown to perform well; that is, to lead to a smaller critica l point than its competitors, with low degrees of freedom. But the met hod is not as efficient as the Hunter-Worsley method for high degrees of freedom. In addition, the method appears to increase in relative ef ficiency as the number of comparisons increases relative to the rank o f the correlation matrix of the estimators.