Advertisement

Block Designs for Comparison of Two Test Treatments with a Control

  • Steven M. Bortnick
  • Angela M. Dean
  • Jason C. Hsu
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)

Abstract

In an experiment to compare p = 2 test treatments with a control, simultaneous confidence bounds (or intervals) for the amount by which each test treatment is better than (or differs from) the control are required. When an experiment is arranged in b blocks of size k, the optimal allocation of a fixed number of experimental units to the individual test treatments and the control within each block need to be determined. The optimality criteria of interest are the minimization of the expected average allowance (EAA) or the minimization of the expected maximum allowance (EMA) of the simultaneous confidence bounds for the p = 2 treatment-control mean contrasts. This paper provides bounds on the EAA and EMA which are then used in search algorithms for obtaining optimal or highly efficient experimental design solutions.

block design confidence bounds multiple comparisons optimal design treatment versus control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bortnick, S.B. (1999). Optimal Block Designs for Simultaneous Comparison of Test Treatments with a Control. PhD Dissertation, Ohio State University.Google Scholar
  2. Daly, D.A., Cooper, E.B, (1967). Rate of stuttering adaptation under two electro-shock conditions. Behaviour, Research and Therapy 5, 49–54.CrossRefGoogle Scholar
  3. Dunnett, C.W., (1955). A multiple comparison procedure for comparing several treatments with a control. JASA 50, 1096–1121.zbMATHCrossRefGoogle Scholar
  4. Hedayat, A., Jacroux, M., and Majumdar, D. (1988). Optimal designs for comparing test treatments with controls. Statistical Science 3, 462–476.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Hsu, J. C., Berger, R. L. (1999). Stepwise confidence intervals without multiplicity adjustment for dose response and toxicity studies. JASA 94, 468–482.Google Scholar
  6. John, P. W. M. (1961). An application of a balanced incomplete design, Technometrics 3, 51–54.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Marshall, A. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. N.Y.: Academic Press.zbMATHGoogle Scholar
  8. Spurrier, J.D., Nizam, A. (1990). Sample size allocation for simultaneous inference in comparison with control experiments. JASA 85, 181–186.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Tong, Y.L. (1980). Probability Inequalities in Multivariate Distributions. N.Y.: Academic Press.zbMATHGoogle Scholar
  10. Tukey, J.W. (1994). The problem of multiple comparisons. The Collected Works of John W. Tukey. N.Y., London: Chapman & Hall.Google Scholar
  11. US Environmental Protection Agency (1994) Short-term Methods for Estimating the Chronic Toxicity of Effluents and Receiving Waters to Freshwater Organisms, 3rd edn. Cincinnati, Ohio: Office of Research and Development, US Environmental Protection Agency.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Steven M. Bortnick
    • 1
  • Angela M. Dean
    • 2
  • Jason C. Hsu
    • 2
  1. 1.Battelle Memorial Institute ColumbusUSA
  2. 2.The Ohio State University ColumbusUSA

Personalised recommendations