A selection and testing procedure for comparing several experimental treatments with a control

We consider a selection and testing procedure for comparing k experimental treatments with a control treatment where the treatments are assumed to be normally distributed with unknown means and a common, unknown variance. Stein-type sampling is used in the selection phase to screen for an experimental treatment that exhibits evidence of bring better than the control treatment and each of the other experimental treatments. where better is defined in terms of the largest mean. In the testing phase, the best experimental treatment is compared to the control using a hypothesis test. If no experimental treatment indicates that it is an improvement over the control during the selection phase, our procedure allows for early termination. We provide definitions of level and power appropriate For our hybrid procedure and compute procedure parameters required to implement our procedure.