Subset selection for normal means in multi-factor experiments

The procedure of Gupta 1956], 1965] for selecting a random sized subset of k ≧ 2 normal populations which contains the population with the largest population mean when the populations have a common variance is generalized to multi-factor experiments. Two-factor experiments with equal replication on each factor-level combination are discussed in detail. The cases of zero and non-zero interactions between factor levels are considered. For the two-factor, zero interaction case with a common number of observations at each factor-level combination, a table of constants necessary to implement the procedure is provided for experiments having selected levels per factor; the constants are equi-coordinate upper percentage points of a multivariate Student t distribution.