Selecting the best population in comparison with a control: The normal case with common unknown variance

We propose a two-stage procedure for comparing k normal populations with a normal control, when the populations have a common, unknown variance. The population with the largest mean is selected, if it is larger than the control's mean; otherwise, the control is selected. The proposed procedure is shown to satisfy the requirements: (1) the probability of selecting the control treatment is at least P0*, whenever the control's mean is larger than the k population means, and (2) the probability of selecting the population with the largest mean is at least P1*, whenever its mean is larger than the control's mean and the means of the other populations under consideration. The procedure has the attractive feature that it allows for a different sample size to be assigned to the control than is assigned to the other populations.