Tables of the Studentized Maximum Modulus Distribution and an Application to Multiple Comparisons Among Means

Abstract

Tables of the upper α-points m α; k*, v of the studentized maximum modulus distribution with parameter k* and v degrees of freedom are given for α = .01, .05, 10, and .20, twelve values 01 V, and k* = k(k − 1)/2 for k = 3(1)20. The tables are of use in applying Hochberg's GT2-Method [6] of multiple comparison and extend the use of this method to cases with k ≤ 20 means. As conjectured in [15]. the GT2-Method is in almost all cases the strongest of several competitors of Spodtvoll and Stoline's T′-Method [11] for carrying out the set of k* pairwise comparisons between the means of k groups with arbitrary sample sizes. The auxiliary tables of [15], in which the T′-Method and other procedures are compared, are extended here. These tables should aid the user in choosing between the T′ and GT2-Methods. The results of the comparisons continue to support the fact that the T-Method is preferred if the unbalance of the sample sizes is slight and that T becomes a stronger competitor as α increases.