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Some optimal designs for comparing a set of test treatments with a set of controls

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Abstract

In this paper, we give a detailed study of the problem of optimally comparing a set of t test treatments to a set of s controls under a 0-way elimination of heterogeneity model. The relationships between designs that are A and MV-optimal for comparing the test treatments to the controls and those that are A and MV-optimal for comparing all treatments are also studied.

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References

  • Bechhofer, R. E. and Tamhane, A. C. (1981). Incomplete block designs for comparing treatments with a control; General theory, Technometrics, 23, 45–57.

    Google Scholar 

  • Cheng, C. S., Majumdar, D., Stufken, J. and Ture, T. E. (1988). Optimal step type designs for comparing test treatments with a control, J. Amer. Statist. Assoc., 83, 477–482.

    Google Scholar 

  • Hedayat, A. S. and Majumdar, D. (1984). A-optimal incomplete block designs for control-test treatment comparisons, Technometrics, 26, 360–370.

    Google Scholar 

  • Hedayat, A. S. and Majumdar, D. (1985). A-optimal incomplete block designs for comparing test treatments with a control, Ann. Statist., 13, 757–767.

    Google Scholar 

  • Hedayat, A. S., Jacroux, M. and Majumdar, D. (1988). Optimal designs for comparing test treatments with controls, Statist. Sci., 3, 462–491.

    Google Scholar 

  • Jacroux, M. (1986). On the usage of refined linear models for determining N-way classification designs which are optimal for comparing test treatments with a standard treatment, Ann. Inst. Statist. Math., 38, 569–581.

    Google Scholar 

  • Jacroux, M. (1987a). On the determination and construction of MV-optimal block designs for comparing test treatments with a standard treatment, J. Statist. Plann. Inference, 15, 205–225.

    Google Scholar 

  • Jacroux, M. (1987b). Some MV-optimal block designs for comparing test treatments with a standard treatment. Sankhyā Ser. B, 49, 239–261.

    Google Scholar 

  • Jacroux, M. (1989). On the A-optimality of block designs for comparing test treatment with a control, J. Amer. Statist. Assoc., 84, 310–317.

    Google Scholar 

  • Majumdar, D. (1986). Optimal designs for comparisons between two sets of treatments, J. Statist. Plann. Inference, 14, 359–377.

    Google Scholar 

  • Majumdar, D. and Notz, W. (1983). Optimal incomplete block designs for comparing treatments with a control, Ann. Statist., 11, 258–266.

    Google Scholar 

  • Notz, W. (1985). Optimal designs for treatment-control comparisons in the presence of two-way heterogeneity, J. Statist. Plann. Inference, 12, 61–73.

    Google Scholar 

  • Stufken, J. (1987). A-optimal block designs for comparing test treatments with a control, Ann. Statist., 15, 1629–1638.

    Google Scholar 

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Research is sponsored by NSF Grant No. DMS-8700945.

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Jacroux, M. Some optimal designs for comparing a set of test treatments with a set of controls. Ann Inst Stat Math 42, 173–185 (1990). https://doi.org/10.1007/BF00050788

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  • DOI: https://doi.org/10.1007/BF00050788

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