The efficiency of subset selection of an almost best treatment

A generalized goal using subset selection is discussed for the location parameter case. This goal is to select a non-empty subset from a set of k (k \geq 2) treatments that contains at least one \epsilon-best treatment with confidence level P*. For a set of treatments an \epsilon-best treatment is defined as a treatment with location parameter on a distance less than or equal to \epsilon (\epsilon \geq 0) from the best treatment, where best is defined as largest value of the location parameter. The efficiency of subset selection of an \epsilon-best treatment relative to subset selection of the best treatment is investigated and is computed for the Normal case as well as for the logistic case.