Computation of the distribution of the maximum studentized range statistic with application to multiple significance testing of simple effects

We consider the probability distribution of the maximum of r statistics each distributed as the Studentized range of means calculated from c random samples of size n from normal populations. The rc samples are assumed to be mutually independent and a common pooled—within—samplevariance is used throughout. An algorithm using Gaussian quadrature and the secant method is presented for calculating the upper lOO∝ percentage points for this distribution. We discuss the application in a new procedure for constructing multiple significance tests and simultaneous confidence limits for simple effects in multiway Analysis of Variance.