On the Problem of Interactions in the Analysis of Variance
本文批评了在双向方差分析中先检验交互作用是否为零、若不显著则忽略交互作用的常见做法，指出该做法可能以大概率导致错误决策，并论证了改进建议（考虑检验功效）在实际应用中并不优于直接使用单因素模型。
Abstract For the two-way analysis of variance without the assumption of zero interactions, consider the following recommendation: Test the zero-interactions hypothesis and, if the hypothesis is not rejected, proceed as if the interactions were zero. This recommendation is unwarranted and may give incorrect decisions with a large probability, as has been pointed out in several articles beginning in the year 1935. Despite such isolated criticism, it is a recommendation suggested in most applied books in the field and used in countless applications. An apology for the recommendation is that it can be easily improved by considering the power of the test and thus obtaining information on the interactions neglected. We consider this improved recommendation for the goals of (i) an interval estimate of one of the cell expectations, (ii) a simultaneous interval estimate of the cell expectations, and (iii) an estimate of the cell with the largest expectation. We show that the improved recommendation leads to methods inferior to methods based on the replacement of the two-way model by the one-way model in cases (ii) and (iii) and to a method not better in case (i). This refutes the apology for the original unwarranted recommendation: the improved recommendation is not easy to apply and does not always lead to good methods.