Consider k(2) normal populations with unknown means 1,., k, and a common known variance σ2. Let  ṡṡṡ [k] denote the ordered i.The populations associated with the t(1 t k-1) largest means are called the t best populations. Hsu and Panchapakesan (2004) proposed and investigated a procedure RHpfor selecting a non empty subset of the k populations whose size is at most m(1 m k-t) so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whenever [k-t + 1]-[k-t] δ*, where P* and δ* are specified in advance of the experiment. This probability requirement is known as the indifference-zone probability requirement. In the present article, we investigate the same procedure RHp for the same goal as before but when k-t < m k-1 so that at least one of the t best populations is included in the selected subset with a minimum guaranteed probability P* whatever be the configuration of the unknown i. The probability requirement in this latter case is termed the subset selection probability requirement. Santner (1976) proposed and investigated a different procedure (RS) based on samples of size n from each of the populations, considering both cases, 1 m k-t and k-t < m k. The special case of t = 1 was earlier studied by Gupta and Santner (1973) and Hsu and Panchapakesan (2002) for their respective procedures.
- Restricted subset size
- Selecting normalmeans
- Subset selection probability requirement
ASJC Scopus subject areas
- Statistics and Probability