| Abstract: | The problem of comparing several treatments with a control is considered. It is formulated as a test of homogeneity with one-sided alternatives that at least one treatment is better than the control, while no treatment is worse than the control. A class of linear rank tests for the simple tree alternatives is proposed, assuming a location model. The most efficient test of the proposed class for detecting a specified pattern is derived. Two optimal tests for use in the case of vaguely specified tree alternatives are derived. In a simulation study the power of these two tests are compared with the power of Kruskal-Wallis test. Recommendations about the use of the proposed tests are made. |
