Abstract: | Let π1…, πk denote k(≥ 2) populations with unknown means μ1 , …, μk and variances σ1 2 , …, σk 2 , respectively and let πo denote the control population having mean μo and variance σo 2 . It is assumed that these populations are normally distributed with correlation matrix {ρij}. The goal is to select a subset, of populations of π1 , …, πk which contains all the populations with means larger than or equal to the mean of the control one. Procedures are given for selecting such a subset so that the probability that all the populations with means larger than or equal to the mean of the control one are included in the selected subset is at least equal to a predetermined value P?(l/k < P? < 1). The goal treated here is a first step screening procedure that allows the experimenter to choose a subset and withhold judgement about which one has the largest mean. Then, if the one with the largest mean is desired it can be chosen from the selected subset on the basis of cost and other considerations. Percentage points are also included. |