Statistical selection: Main approaches and a modification with a preference threshold

Statistical selection is discussed in general terms. In a certain selection procedures are often more realistic than the usual testing and multiple comparison procedures in answering question like "Which treatment can be considered to be the best?. The approach of Bechhofer, the so-called Indifference Zone approach, as well as the approach of Gupta, the so-called Subset Selection approach, are presented. A comparison of these approaches is made using qualitative terms. A short review is given on the use of a loss function as a generalization of selection of an épsilon-best treatment is a generalization of a best treatment and is defined as a treatment on a "distance" less than épsilon of the best treatment. Finally, a generalization of the concept of the Indifference Zone selection is presented. The Indifference Zone approch is generalized by introducing a preference threshold. By this way there are three possibilities of decision: correct selection, false selection and no selection.