Some results on step-up tests for comparing treatments with a control in unbalanced one-way layouts

The basic problem is to compare several treatments with a control in the standard unbalanced one-way layouts. Step-up tests were considered by Dunnett and Tamhane (1995, Biometrics 51, 217-227). In this paper, a method of calculating the critical values of step-up tests is proposed so that the Type I family wise error (FWE) is controlled at a prespecified level alpha. It is also pointed out that the equivalence of a step-up test and the test based on the correspondingly adjusted p-values requires implicitly a monotone property. A practical example is used for illustration.