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Are Multiple Contrast Tests Superior to the ANOVA?

Author

Listed:
  • Konietschke Frank

    (Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, Göttingen, Lower Saxony 37073, Germany)

  • Bösiger Sandra

    (Siemens – Siemens Healthcare Diagnostics Products GmbH, Marburg, Germany)

  • Brunner Edgar

    (Department of Medical Statistics, University Medical Center Göttingen, Göttingen, Lower Saxony, Germany)

  • Hothorn Ludwig A.

    (Institute of Biostatistics, Leibniz University Hannover, Hannover, Lower Saxony, Germany)

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.

Suggested Citation

  • Konietschke Frank & Bösiger Sandra & Brunner Edgar & Hothorn Ludwig A., 2013. "Are Multiple Contrast Tests Superior to the ANOVA?," The International Journal of Biostatistics, De Gruyter, vol. 9(1), pages 63-73, August.
    • Handle: RePEc:bpj:ijbist:v:9:y:2013:i:1:p:11:n:2
    DOI: 10.1515/ijb-2012-0020
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    References listed on IDEAS

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    1. Esther Herberich & Johannes Sikorski & Torsten Hothorn, 2010. "A Robust Procedure for Comparing Multiple Means under Heteroscedasticity in Unbalanced Designs," PLOS ONE, Public Library of Science, vol. 5(3), pages 1-8, March.
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    Cited by:

    1. Gunawardana, Asanka & Konietschke, Frank, 2019. "Nonparametric multiple contrast tests for general multivariate factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 165-180.
    2. Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.
    3. Philip Pallmann & Ludwig A. Hothorn, 2016. "Analysis of means: a generalized approach using R," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1541-1560, June.
    4. Konietschke, Frank & Placzek, Marius & Schaarschmidt, Frank & Hothorn, Ludwig A., 2015. "nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i09).

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