In this paper we use a one-stage procedure described by Chen [Chen, S. Y. (2001). One-stage and two-stage statistical inference under heteroscedasticity. Commun. Statist. Simulation Computat. 30(4):991–1009] for testing the equality of normal means against an ordered alternative in one-way layout when variances are unknown and unequal. Tables of percentage points and the power under a specific alternative needed for implementation are given. The relationship between the one-stage and the two-stage test procedures is discussed. Comparison between the new procedure and the range test [Chen, S. Y. (2000). One-sided range test for testing against an ordered alternative under heteroscedasticity.
Communications in Statistics-Simulation and Computation 33(1), pp.49-67