The ranking of means of normal populations for a generalized selection goal

This paper shows the possibility of achieving a generalized selection goal for a ranking problem, using some common decision procedures. Given k normal populations with unknown means and having properly specified two positive constants (δ*, P*), an experimenter wishes to select t populations which include all those having a population mean not smaller than the (t+ 1)th largest population mean plus δ*, and at the same time exclude all those having a population mean not greater than the tth largest population mean minus δ*, The probability of successfully making such a selection is shown to be at least P* if a single-stage procedure such as the one proposed by Bechhofer (1954), or a two-stage procedure such as the one proposed by Bechhofer, Dunnet & Sobel (1954), is used.