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Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables


  • Schaarschmidt, Frank


In biological and medical research, continuous, strictly positive, right-skewed data, possibly with heterogeneous variances, are common, and can be described by log-normal distributions. In experiments involving multiple treatments in a one-way layout, various sets of multiple comparisons among the treatments and corresponding simultaneous confidence intervals can be of interest. The focus is on multiple contrasts of the expected values of the treatments. Previously published methods based on normal approximations and generalized pivotal quantities are extended to the case of multiple contrasts. These methods are evaluated in a simulation study that involves comparisons to a control group, all pairwise comparisons and, to illustrate more general multiple contrast types, a non-standard type of contrast matrix. A method based on generalized pivotal quantities is recommended because it is superior to all other methods in terms of simultaneous coverage probability and because the type-I-errors are distributed almost equally between lower and upper confidence bounds. Methods based on normal approximations are found to be very liberal and biased with respect to directional type-I-errors. These methods are illustrated with an example from pharmaceutical research.

Suggested Citation

  • Schaarschmidt, Frank, 2013. "Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 265-275.
  • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:265-275
    DOI: 10.1016/j.csda.2012.08.011

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    References listed on IDEAS

    1. Mandel, Micha & Betensky, Rebecca A., 2008. "Simultaneous confidence intervals based on the percentile bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2158-2165, January.
    2. Li, Xinmin, 2009. "A generalized p-value approach for comparing the means of several log-normal populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1404-1408, June.
    3. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
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    Cited by:

    1. Sadooghi-Alvandi, S.M. & Malekzadeh, A., 2014. "Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 133-140.
    2. Schaarschmidt, Frank & Gerhard, Daniel & Vogel, Charlotte, 2017. "Simultaneous confidence intervals for comparisons of several multinomial samples," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 65-76.
    3. Tang, Nian-Sheng & Luo, Xian-Gui, 2015. "Confidence interval construction for sensitivity difference of two continuous-scale diagnostic tests at the fixed level of two specificities," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 32-40.


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