Selecting the Best Unknown Mean from Normal Populations Having a Common Unknown Coefficient of Variation

Abstract

This paper deals with the problem of selecting the population associated with the largest unknown mean from several normal populations having a common unknown coefficient of variation. Both subset selection and indifference zone approaches are studied. Based on the observed sample means and sample standard deviations, a subset selection rule is proposed. Some properties related to this selection rule are discussed. For the indifference zone approach, a two-stage elimination type selection rule is considered. If the experimenter has some prior knowledge about an upper bound on the unknown means, a modification is introduced to reduce the size of the selected subset at the first stage and also to reduce the sample size at the second stage. An example is provided which indicates that the saving in the total sample size is quite significant if this prior knowledge is taken into consideration in designing the selection rule. It is shown how to implement the above selection rules by using several existing tables.