On Multiple Decision Methods for Ranking Population Means

Abstract

(i) In the case of the choice of the largest among $k$ population means (special case $\mathscr a$ of the use of ranking methods) the assertion of Bechhofer's method ([1], [2], [3]) can be strengthened without decreasing the probability of a correct decision (Sec. 3). (ii) Bechhofer's concept of the "least favorable configuration of the population means" is studied (Sec. 4.). The result suggests at the concept is not always in accord with the underlying practical problem, but that it is in accord in the important case $\mathscr a$. (iii) an approximation is suggested for use in the case of normal populations with a common unknown variance (Sec. 5).