Details
| Original language | English |
|---|---|
| Journal | International Journal of Biostatistics |
| Volume | 9 |
| Issue number | 1 |
| Publication status | Published - 1 Aug 2013 |
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.
Keywords
- Analysis of variance, Least favorable configuration, Multiple contrast tests, Multivariate t-distribution, One-way layout, Sample size computations
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: International Journal of Biostatistics, Vol. 9, No. 1, 01.08.2013.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Are multiple contrast tests superior to the ANOVA?
AU - Konietschke, Frank
AU - Bösiger, Sandra
AU - Brunner, Edgar
AU - Hothorn, Ludwig A.
N1 - Funding Information: Acknowledgments: The authors are grateful to an Associate Editor and two anonymous referees for helpful comments which considerably improved the article. This work was supported by the German Research Foundation projects DFG-Br 655/16–1 and Ho 1687/9–1.
PY - 2013/8/1
Y1 - 2013/8/1
N2 - 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.
AB - 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.
KW - Analysis of variance
KW - Least favorable configuration
KW - Multiple contrast tests
KW - Multivariate t-distribution
KW - One-way layout
KW - Sample size computations
UR - http://www.scopus.com/inward/record.url?scp=84881638141&partnerID=8YFLogxK
U2 - 10.1515/ijb-2012-0020
DO - 10.1515/ijb-2012-0020
M3 - Article
C2 - 23902695
AN - SCOPUS:84881638141
VL - 9
JO - International Journal of Biostatistics
JF - International Journal of Biostatistics
SN - 1557-4679
IS - 1
ER -