Selecting all treatments better than a control with a binomial prior distribution
Titel:
Selecting all treatments better than a control with a binomial prior distribution
Auteur:
Chen, Hubert J. Chen, Shun-Yi Sirichote, Jirawan
Verschenen in:
Communications in statistics
Paginering:
Jaargang 14 (1985) nr. 1 pagina's 187-221
Jaar:
1985
Inhoud:
Let π1,…,πk denote k treatment populations and let πk represent thex control population. It is assumed that data obtained from (π0, π1,…,πk) by a repeated measurements design follow a multivariate normal distribution with mean vector (π0, π1,…, πk) and covariance matrix £0. Then, if “better” is defined to mean “at least as good as” (πi > π0) we propose selection procedures for selecting a subset which includes all treatments better than the control. Due to the fact that the number of better populations is unknown, a binomial prior distribution on this unknown factor is assumed. Consequently, the exact infimum of probability of correct selection is obtained. Statistical tables to implement these procedure are extensively constructed and expected subset size is also considered.