如何在析因设计中分析数据？广泛的模拟研究
How to analyze data in a factorial design? An extensive simulation study
摘要：
析因设计经常用于不同的科学领域，例如心理学，医学或生物统计学研究。标准方法，如ANOVA $F$检验，对不同组中误差项、方差或样本量的分布做出不同的假设。由于时间限制或缺乏统计背景，许多用户不检查这些假设;增加了潜在膨胀的类型- $I$错误率或功率大幅损失的风险。本文件的目的是，在没有这种限制性假设的情况下，概述不同的方法，并确定其中一种方法优于其他方法的情况。特别是，在总结了他们的基本假设，不同的方法进行了比较，在广泛的模拟。为了解决当前关于重新定义统计显著性水平的讨论，我们还包括了0.5%水平的模拟。
英文摘要：
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the variances or the sample sizes in the different groups. Because of time constraints or a lack of statistical background, many users do not check these assumptions; enhancing the risk of potentially inflated type-$I$ error rates or a substantial loss of power. It is the aim of the present paper, to give an overview of different methods without such restrictive assumptions and to identify situations in which one method is superior compared to others. In particular, after summarizing their underlying assumptions, the different approaches are compared within extensive simulations. To also address the current discussion about redefining the statistical significance level, we also included simulations for the 0.5\% level.
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