ten less focused and are designed to detect a broader range of departures from the null. For example, a simple Bonferroni correction places the primary comparison and the two versioned comparisons on equal footing. If the investigator does not suspect a priori that a particular alternative hypothesis is most likely, he may conduct an omnibus F-test, whose power is distributed over a broad range of alternative hypotheses. The researcher’s scientifc aim should determine which method for multiple comparisons is most appropriate. With this guidance in mind, we compare our method to the omnibus F-test and Bonferroni corrected intervals. In exploratory analyses, the F-test can be a useful “prelude to subsequent examinations of unplanned contrasts” (Steiger, 2004). However, in many studies, the researcher will have a particular contrast in mind. Several authors have argued that the omnibus hypothesis in ANOVA studies be replaced with hypotheses that focus on a substantive research question, often involving just a single contrast (Rosenthal et al., 2000; Steiger, 2004). In the football study, we suspect a priori that versions are not terribly consequential and proceed first with our primary investigation of whether playing high school football accelerates the onset of cognitive decline. The hypotheses about versions are secondary to our main inquiry and are treated as such in our method. The F-test does not lend itself to effect size estimates, but we can compare it to our method by evaluating it’s power to reject Fisher’s sharp null hypothesis and the probabil- ity that I c excludes τ = 0 under a variety of alternative hypotheses with vary degrees of “versioning.” If the primary goal of the study is less directed and detecting any departure from the null of no effect is of interest and the researcher suspects that versions may play an important role, the F-test may be more suitable. However, in a simulation study de- The omnibus F-test 18