Simultaneous confidence intervals for pairwise multiple comparisons in a two-way unbalanced design

Turkey's (1953, The Problem of Multiple Comparisons, unpublished report, Princeton University) procedure is widely used for pairwise multiple comparisons in one-way ANOVA. It provides exact simultaneous pairwise confidence intervals (SPCI) for balanced designs and conservative SPCI for unbalanced designs. In this paper, we will extend Turkey's procedure to two-way unbalanced designs. Both the exact and the conservative methods will be introduced. The application of the new procedure is illustrated with sample data from two experiments.