title: Are multiple contrast tests superior to the ANOVA?
abstract: Multiple contrast tests can be used to test arbitrary linear hypotheses by providing local and global test decisions as well as simultaneous confidence intervals. The ANOVA-F-test on the contrary can be used to test the global null hypothesis of no treatment effect. Thus, multiple contrast tests provide more information than the analysis of variance (ANOVA) by offering which levels cause the significance. We compare the exact powers of the ANOVA-F-test and multiple contrast tests to reject the global null hypothesis. Hereby, we compute their least favorable configurations (LFCs). It turns out that both procedures have the same LFCs under certain conditions. Exact power investigations show that their powers are equal to detect their LFCs.
authors.affiliation: Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, Göttingen, Lower Saxony 37073, Germany. Frank.Konietschke@medizin.uni-goettingen.de
authors.forename: Frank
authors.initials: F
authors.lastname: Konietschke
authors.forename: Sandra
authors.initials: S
authors.lastname: Bösiger
authors.forename: Edgar
authors.initials: E
authors.lastname: Brunner
authors.forename: Ludwig A
authors.initials: LA
authors.lastname: Hothorn
mesh_terms: D000704:Analysis of Variance; D016001:Confidence Intervals; D006801:Humans; D015233:Models, Statistical; D012107:Research Design