IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i4p1530-1539.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00401-9
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Junfeng Shang & Joseph E. Cavanaugh & Farroll T. Wright, 2008. "A Bayesian Multiple Comparison Procedure for Order‐Restricted Mixed Models," International Statistical Review, International Statistical Institute, vol. 76(2), pages 268-284, August.
    2. Nashimoto, Kane & Wright, F.T., 2008. "Bayesian multiple comparisons of simply ordered means using priors with a point mass," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5143-5153, August.
    3. Jianan Peng & Chu‐In Charles Lee & Karelyn A. Davis & Weizhen Wang, 2008. "Stepwise Confidence Intervals for Monotone Dose–Response Studies," Biometrics, The International Biometric Society, vol. 64(3), pages 877-885, September.
    4. 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.
    5. Oh, Man-Suk & Shin, Dong Wan, 2011. "A unified Bayesian inference on treatment means with order constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 924-934, January.
    6. Nashimoto, Kane & Wright, F.T., 2010. "Marcus-Talpaz simultaneous lower confidence bounds for contrasts between treatment and control means," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 128-133, January.
    7. Manfred Horn & Rudiger Vollandt & Charles W. Dunnett, 2000. "Sample Size Determination for Testing Whether an Identified Treatment Is Best," Biometrics, The International Biometric Society, vol. 56(3), pages 879-881, September.
    8. Jacobson, Sheldon H. & McLay, Laura A., 2009. "Applying statistical tests to empirically compare tabu search parameters for MAX 3-SATISFIABILITY: A case study," Omega, Elsevier, vol. 37(3), pages 522-534, June.
    9. 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.
    10. Yuchung Wang, 1997. "Multivariate normal integrals and contingency tables with ordered categories," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 267-284, June.
    11. de Crombrugghe, D.P.I. & Espinoza, H. & Heijke, J.A.M., 2010. "Determinants of dropout behaviour in a job training programme for disadvantaged youth," ROA Research Memorandum 008, Maastricht University, Research Centre for Education and the Labour Market (ROA).
    12. 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.
    13. Pooja Soni & Isha Dewan & Kanchan Jain, 2019. "Nonparametric tests for ordered quantiles," Statistical Papers, Springer, vol. 60(3), pages 963-981, June.
    14. Paul Kabaila & Nishika Ranathunga, 2021. "Computation of the expected value of a function of a chi-distributed random variable," Computational Statistics, Springer, vol. 36(1), pages 313-332, March.
    15. Kwong, Koon Shing & Cheung, Siu Hung, 2012. "Optimal design for p-value consistent step-up procedures for multiple comparisons with a control in direction-mixed families," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4157-4164.
    16. Per A. Brodtkorb, 2006. "Evaluating Nearly Singular Multinormal Expectations with Application to Wave Distributions," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 65-91, March.
    17. J. Peng & C. I. C. Lee & L. Liu, 2006. "Max-min multiple comparison procedure for comparing several dose levels with a zero dose control," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(5), pages 549-555.
    18. Grechanovsky, Eugene & Pinsker, Ilia, 1995. "Conditional p-values for the F-statistic in a forward selection procedure," Computational Statistics & Data Analysis, Elsevier, vol. 20(3), pages 239-263, September.
    19. Tomasz Rychlik, 2019. "Sharp bounds on distribution functions and expectations of mixtures of ordered families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 166-195, March.
    20. Peng, J. & Lee, C.I.C. & Liu, L. & Jiang, J., 2006. "Orthogonal multiple contrast test for testing monotone on the average," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 161-168, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1530-1539. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.