On the Design of Experiments for Testing the Simultaneous Effects of a Treatment Against a Control at Different Locations.
GEORGE WASHINGTON UNIV WASHINGTON D C DEPT OF STATISTICS
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Testing the simultaneous effects of a treatment against a control when an experiment is conducted at each of several locations is studied in connection with design problems and sample allocation over the locations. This arises in clinical trials situations and other sampling settings. While the observations are binomial, the typical sample sizes are large enough to permit variance stabilizing transformations and the normal model. A balanced allocation arises under the criterion of minimal volumes for simultaneous confidence ellipsoids. This is analogous to testing the hypothesis of all differences equal to zero against the composite hypothesis that the differences between the experimental variable and the control variable are unequal. This balanced allocation is minimax under some general conditions but not necessarily Bayes. The composite hypothesis that all differences are equal to some value not zero is tested against the alternative that they are not equal. For the case of two locations, the balanced allocation is optimal for a large number of locations, the problem is still open. Author
- Statistics and Probability