Simultaneous prediction intervals for all patrwise differences among several future sample means
Hahn (1977) suggested a procedure for constructing prediction intervals for the difference between the means of two future samples from normal populations having equal variance, based on past samples selected from both populations. In this paper, we extend Hahn's work by constructing simultaneous prediction intervals for all pairwise differences among the means of k ≥ 2 future samples from normal populations with equal variances, using past samples taken from each of the k populations. For K = 2, this generalization reduces to Hahn's special case. These prediction intervals may be used when one has sampled the performance of several products and wishes to simultaneously as- sess the differences in future sample mean performance of these products with a predetermined overall coverage probability. The use of the new procedure is demonstrated with a numerical example.