Abstract
SUMMARY A consideration of the purpose of some one-way classification experiments leads us to introduce a criterion of F-optimality of design, a compromise measure which concentrates on the detection of certain specified effects while allowing at least the inspection of a wider class of effects. to give added validity to this notion we first establish its equivalence to a min–max weighted variance design criterion. The actual construction of F-optimal designs is our main purpose. The direct min–max approach is difficult, and so our next main result directs attention to the equivalent problem of finding optimal strategies for a certain two-person zero-sum non-matrix game. Finally, we provide a computational scheme for the solution of this game and illustrate the technique by examples.
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