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)


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 


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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

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