Power of the lack-of-fit test in designed experiments: Guidance on sample size and the distribution of replicates
针对未重复的基础设计（如因子设计、响应曲面设计），提出基于标准失拟检验的功效和样本量计算方法，并探讨重复模式对功效的影响，为实验扩充提供指南。
Although there exists substantial literature on lack-of-fit tests for normal linear models, there is scant literature for determining the number or distribution of points to replicate when starting with an un-replicated base design like a factorial, response surface, or related constructions. In this article, we provide an easy-to-implement approach to determining power and sample size based on the standard lack-of-fit test. The method employs simply stated bounds on the null model in order to obtain the non-centrality parameter. We also explore the effect of different patterns of replication on power. Our approach results in guidelines for augmentation of designed experiments. For example, we show that, as the replications increase, the non-centrality parameter grows without bound if and only if the number of replicated treatments is greater than the number of terms in the null model. We also find guidelines for the standard practice of placing all replicates at the center point in factorial-type experiments with continuous factors. Although our approach is not restricted to any particular class of designs, we emphasize factorial, screening and response surface designs.