Musca Serban C, Kamiejski Rodolphe, Nugier Armelle, Méot Alain, Er-Rafiy Abdelatif, Brauer Markus
Centre de Recherches en Psychologie, Cognition et Communication (EA1285), Université Rennes 2 Rennes, France.
Front Psychol. 2011 Apr 20;2:74. doi: 10.3389/fpsyg.2011.00074. eCollection 2011.
Least squares analyses (e.g., ANOVAs, linear regressions) of hierarchical data leads to Type-I error rates that depart severely from the nominal Type-I error rate assumed. Thus, when least squares methods are used to analyze hierarchical data coming from designs in which some groups are assigned to the treatment condition, and others to the control condition (i.e., the widely used "groups nested under treatment" experimental design), the Type-I error rate is seriously inflated, leading too often to the incorrect rejection of the null hypothesis (i.e., the incorrect conclusion of an effect of the treatment). To highlight the severity of the problem, we present simulations showing how the Type-I error rate is affected under different conditions of intraclass correlation and sample size. For all simulations the Type-I error rate after application of the popular Kish (1965) correction is also considered, and the limitations of this correction technique discussed. We conclude with suggestions on how one should collect and analyze data bearing a hierarchical structure.
对分层数据进行最小二乘法分析（例如方差分析、线性回归）会导致I型错误率严重偏离假定的名义I型错误率。因此，当使用最小二乘法分析来自某些组被分配到治疗条件而其他组被分配到对照条件的设计的分层数据时（即广泛使用的“治疗下嵌套组”实验设计），I型错误率会严重膨胀，导致经常错误地拒绝原假设（即错误地得出治疗有效果的结论）。为了突出问题的严重性，我们给出模拟结果，展示在不同组内相关条件和样本量下I型错误率是如何受到影响的。对于所有模拟，还考虑了应用流行的基什（1965年）校正后的I型错误率，并讨论了这种校正技术的局限性。我们最后就如何收集和分析具有分层结构的数据提出建议。
