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Exact simultaneous confidence intervals for a finite set of contrasts of three, four or five generally correlated normal means


  • Liu, W.
  • Ah-Kine, P.
  • Bretz, F.
  • Hayter, A.J.


The construction of a set of simultaneous confidence intervals for any finite number of contrasts of p generally correlated normal means is considered. It is shown that the simultaneous confidence level can be expressed as a (p−2)-dimensional integral for a general p≥3. This expression allows one to compute quickly and accurately, by using numerical quadrature, the required critical constants and multiplicity adjusted p-values for at least p=3, 4 and 5, involving only one-, two- and three-dimensional integrals, respectively. Real data examples from a drug stability study and a dose response study are used to illustrate the method.

Suggested Citation

  • Liu, W. & Ah-Kine, P. & Bretz, F. & Hayter, A.J., 2013. "Exact simultaneous confidence intervals for a finite set of contrasts of three, four or five generally correlated normal means," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 141-148.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:141-148 DOI: 10.1016/j.csda.2012.06.007

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    References listed on IDEAS

    1. F. Bretz & J. C. Pinheiro & M. Branson, 2005. "Combining Multiple Comparisons and Modeling Techniques in Dose-Response Studies," Biometrics, The International Biometric Society, vol. 61(3), pages 738-748, September.
    2. Somerville, Paul N., 1997. "Multiple testing and simultaneous confidence intervals: calculation of constants," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 217-233, July.
    3. Hayter, A. J. & Liu, W., 1996. "Exact calculations for the one-sided studentized range test for testing against a simple ordered alternative," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 17-25, June.
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