A Sequential Procedure for Selecting the Population with the Largest Mean from $k$ Normal Populations

In this paper sequential procedures are given for selecting the normal population with the greatest mean when (a) the $k$ populations have a common known variance or (b) the $k$ populations have a common but unknown variance, so that in each case the probability of making the correct selection exceeds a specified value when the greatest mean exceeds all other means by at least a specified amount. The procedures in the present paper all have the property that inferior populations can be eliminated from further consideration as the experiment proceeds.