A new approximation to the distribution function of the studentized maximum root

The Studentized maximum root (SMR) distribution is useful for constructing simultaneous confidence intervals around product interaction contrasts in replicated two-way ANOVA. A three-moment approximation to the SMR distribution is proposed. The approximation requires the first three moments of the maximum root of a central Wishart matrix. These values are obtained by means of numerical integration. The accuracy of the approximation is compared to the accuracy of a two-moment approximation for selected two-way table sizes. Both approximations are reasonably accurate. The three-moment approximation is generally superior.