A Comparison of the “Sometimes Pool”, “Sometimes Switch” and “Never Pool” Procedures in the Two-Way ANOVA Random Effects Model

Abstract

In the replicated two-way random-effects model, the “Sometimes Pool” (SP) procedure is employed for the specification of the appropriate model and the subsequent test of the main effects. The “Sometimes Switch” (SW) procedure is introduced and shown to be a limiting form of SP as the cell size increases. This article concerns itself with the question of whether to pool interaction and error mean squares in order to get better tests for the main effects. The significance levels and the powers of the “sometimes” procedures are compared with those of the “Never Pool” (NP). The SP and SW procedures rarely have control over the main test significance level. We recommend modifying the experimental design, when possible, to maximize the interaction degrees of freedom and employing the “Never Pool” procedure.