A studentized range test for the equivalency of normal means under heteroscedasticity

A studentized range test using a two-stage and a one-stage sampling procedures, respectively, is proposed for testing the null hypothesis that the average deviation of the normal means is falling into a practical indifference zone. Both the level and the power of the proposed test associated with the hypotheses are controllable and they are completely independent of the unknown variances. The two-stage procedure is a design-oriented procedure that satisfies certain probability requirements and simultaneously determines the required sample sizes for an experiment while the one-stage procedure is a data-analysis procedure after the data have been collected, which can supplement the two-stage procedure when the later has to end its experiment sooner than its required experimental process is completed. Tables needed for implementing these procedures are given. (c) 2005 Elsevier B.V. All rights reserved.