Optimum Experiments with Sets of Treatment Combinations

  • Anthony C. AtkinsonEmail author
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Response surface designs are investigated in which points in the design region corresponds to single observations at each of s distinct settings of the explanatory variables. An extension of the “General Equivalence Theorem” for D-optimum designs is provided for experiments with such sets of treatment combinations. The motivation was an experiment in deep-brain therapy in which each patient receives a set of eight distinct treatment combinations and provides a response to each. The experimental region contains sixteen different sets of eight treatments.



I am grateful to Dr David Pedrosa of the Nuffield Department of Clinical Neurosciences, University of Oxford, for introducing me to the experimental design problem in deep-brain therapy that provided the motivation for this work.

I am also grateful to the referees whose comments strengthened and clarified the results of §3.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of StatisticsLondon School of EconomicsLondonUK

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