ON THE CHOICE OF THE BEST AMONGST THREE NORMAL POPULATIONS WITH KNOWN VARIANCES

Abstract

Summary Statistical decisions to be taken in the case of three normal populations with known variances are investigated in the following two situations: (i)The problem of selecting the population with the largest mean (the case of the smallest is obviously similar), given a probability of taking a wrong decision. (ii) The problem of determining the smallest sample sizes required to detect the population with largest mean, in the case of some given values for the non-centrality parameters. These sample sizes depend on the probabilities of good and wrong decisions. The statistic used in connexion with these problems is the standardized difference between the two largest sample means.