Multifactorial experimental designs allow us to assess the contribution of several factors, and potentially their interactions, to one or several responses of interests. Following the principles of the partition of the variance advocated by Sir R.A. Fisher, the experimental responses are factored into the quantitative contribution of main factors and interactions. A popular approach to perform this factorization in both ANOVA and ASCA(+) is through General Linear Models. Subsequently, different inferential approaches can be used to identify whether the contributions are statistically significant or not. Unfortunately, the performance of inferential approaches in terms of Type I and Type II errors can be heavily affected by missing data, outliers and/or the departure from normality of the distribution of the responses, which are commonplace problems in modern analytical experiments. In this paper, we study these problem and suggest good practices of application.

翻译：多因素实验设计使我们能够评估多个因素（及其潜在交互作用）对一个或多个关注响应的贡献。遵循R.A. Fisher爵士倡导的方差分解原则，实验响应可被分解为主因素与交互作用的量化贡献。在方差分析与ASCA(+)中实现此类分解的常用方法是通过广义线性模型。随后可采用不同的推断方法以判定这些贡献是否具有统计显著性。然而，现代分析实验中普遍存在的缺失数据、异常值及响应分布偏离正态性等问题，会严重影响推断方法在I类与II类错误方面的性能。本文系统研究这些问题并提出相应的应用实践建议。