The two-step approach-a significant ANOVA F-test before Dunnett's comparisons against a control-is not recommended

Decision-tree approaches are commonly used in the analysis of toxicological assays. This paper considers the widely-used and recommended approach of first applying the ANOVA F-test and, if it is significant, using the many-to-one comparison procedure of Dunnett (1955). Data configurations are provided for which the F-test is not significant, but the Dunnett-test is significant. Because a conditional F-test before the Dunnett-test may increase the false negative rate, it is recommended that the ANOVA F-test not be used at all as a global pre-test. In addition, related non-parametric tests are investigated.