A modified subset selection formulation with special reference to one-way and two-way layout experiments

The usual formulation of subset selection due to Gupta (1956) requires a minimum guaranteed probability of a correct selection. The modified formulation of the present paper includes an additional requirement that the expected number of the nonbest populations be bounded above by a specified constant when the best and the next best populations are ‘sufficiently’ apart. A class of procedures is defined and the determination of the minimum sample size required is discussed. The specific problems discussed for normal populations include selection in terms of means and variances, and selection in terms of treatment effects in a two-way layout.