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One-sided multiple comparisons for treatment means with a control mean

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  • Wright, F.T.
  • Nashimoto, Kane

Abstract

We study comparisons of several treatments with a common control when it is believed a priori that the treatment means, [mu]i, are at least as large as the control mean, [mu]0. In this setting, which is called a tree ordering, we study multiple comparisons that determine whether [mu]i>[mu]0 or [mu]i=[mu]0 for each treatment. The classical procedure by Dunnett (1955) and the step-down and step-up techniques by (Dunnett and Tamhane, 1991) and (Dunnett and Tamhane, 1992) are well known. The results in Marcus and Talpaz (1992) provide multiple comparisons based on the maximum likelihood estimates restricted by the tree ordering. We also study two-stage procedures that consist of the likelihood ratio test of homogeneity with the alternative constrained by the tree ordering followed by two-sample t comparisons with possibly different critical values for the two-sample comparisons. Marcus et al. (1976) discuss the use of closed tests in such situations and propose using a closed version of the restricted likelihood ratio test. We describe step-down versions of the Marcus-Talpaz, the two-stage, and the likelihood ratio procedures, as well as a closed version of the Marcus-Talpaz multiple comparison procedure. Using Monte Carlo techniques, we study the familywise errors and powers of these procedures and make some recommendations concerning techniques that perform well for all tree ordered mean vectors.

Suggested Citation

  • Wright, F.T. & Nashimoto, Kane, 2011. "One-sided multiple comparisons for treatment means with a control mean," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1530-1539, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1530-1539
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    References listed on IDEAS

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    1. Nashimoto, Kane & Wright, F.T., 2005. "A note on multiple comparison procedures for detecting differences in simply ordered means," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 393-401, July.
    2. Charles W. Dunnett, 1989. "Multivariate Normal Probability Integrals with Product Correlation Structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(3), pages 564-579, November.
    3. Nashimoto, Kane & Wright, F.T., 2007. "Nonparametric multiple-comparison methods for simply ordered medians," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5068-5076, June.
    4. Lee, Chu-In Charles & Peng, Jianan & Liu, Lin, 2006. "Statistical Inference for the Difference Between the Best Treatment Mean and a Control Mean," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1050-1058, September.
    5. Nashimoto, Kane & Wright, F.T., 2005. "Multiple comparison procedures for detecting differences in simply ordered means," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 291-306, February.
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    Cited by:

    1. Li, Yang & Zhao, Hui & Sun, Jianguo & Kim, KyungMann, 2014. "Nonparametric tests for panel count data with unequal observation processes," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 103-111.

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