On a Two-Stage Selection Procedure for the Largest Mean when between Group Variances are Unknown and Unequal

N. Mukhopadhyay (1995). On a Two-Stage Selection Procedure for the Largest Mean when between Group Variances are Unknown and Unequal. Journal of Statistical Research, Vol. 29, No. 1, pp. 15-20.

Abstract

Consider Independent $N(\mu_{ij},\sigma_i^2)$ populations, $j=1,\ldots, k_i$ and $i=1,\ldots,b (\geq 2)$ , with $\sum k_i\gt b$ where $\mu$ 's are assumed unknown while $\sigma$ 's are assumed unknown and unequal. Under the indifference zone formulation, we construct a two-stage sampling strategy to select the population associated with $\mu_{[bk_b]}$ , the largest mean, so that the probability of correct selection exceeds $P^\star$ , a preassigned number between $(\sum k_i)^{-1}$ and unity, whenever $\mu$ 's belong to the preference zone.