Partitioning Normal Populations With Respect to a Control

Tong (1969) describes a two-stage procedure for partitioning k normal populations with respect to a control, the population having a common but unknown variance. This problem can be solved for unknown and unequal variances with a modification of a procedure given by Dudewicz and Dala (1975). This paper derives the appropriate probability equation to be solved so that a correct decision is made with probability at least P*. Tables of the required h values are given for k=1(1)24, P*=.75, .90, .95, .99 and n₀=2(1)15(5)30 where n₀ is the sample size in the first stage of the two-stage procedure.