“实验心理学数据是否应该使用混合线性模型（LMM）”的讨论
Linear mixed-effects models for within-participant psychology experiments: an introductory tutorial and free, graphical user interface (LMMgui)
文章网址：https://www.frontiersin.org/articles/10.3389/fpsyg.2015.00002/full
”引子：
以上引自(Magezi, 2015).
张阳老师回答道：
实验中的正确率不适合作用ANOVA，不管实验设计多么经典（如2选迫选任务，2AFC），也不能使用。这样的数据在单个trial中是1/0的二分。
如何处理这个二分变量的问题？见如下引文：
It is worth noting that ANOVA may not be an appropriate method for accuracy data analysis because accuracy data is inherently categorical (a correct/wrong response in each trial) (Dixon, 2008; Jaeger, 2008)2. Therefore, to provide additional converging evidence, mixed logit models (a type of generalized linear mixed models; Dixon, 2008; Jaeger, 2008) with a maximal random effects structure (Barr, 2013; Barr et al., 2013) was carried out to analyze the accuracy data. The significance of the main effects and interactions was tested by comparing the model including the effects against a model without the effects using a χ2 test (the compare function in MATLAB 2015b; The MathWorks, Inc., Natick, MA, United States). The mixed logit models suggested a significant main effect of task difficulty, χ2(2) = 45.55, p < 0.001 (97.4%, 86.7%, and 74.6% in easy, medium, and hard condition, respectively). The main effect of cueing failed to reach significance, χ2(1) = 2.83, p = 0.09. The task difficulty × cueing interaction was confirmed to be significant, χ2(2) = 6.27, p < 0.05. Follow-up simple effect analyses identified a significant cueing effect in the medium condition only, χ2(2) = 11.46, p < 0.001.
――引自(Li, Miao, Han, He, & Zhang, 2018)
关于这个问题，Jaeger (2008)进行了非常清楚地说明。即使将正确率当作连续变量，进行ANOVA也不合适。比方说同样是 3%的差异， 80% 对 77% 同97% 对100% 显然是不一样的，然而，anova认为是一样的。另外，anova要求变量 正态分布，然而 acc并不是正态分布（范围也不是正无穷到负无穷，而是 0-1）。理论上，如果anova 一个条件下全对，另外一个条件哪怕只有一点点差异都有可能显著，因为标准误很小。
问题
正态分布是指样本均值（即所有被试的正确率的平均值）的分布是不是正态分布，不是原始的每个被试的正确率。通常样本量在30以上，样本均值的分布就是正态的，无论原始数据的分布是怎样的。所以可以对正确率的均值当作正态进行分析？
张阳老师回答道：可参考文章Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59(4), 434-446. doi:http://dx.doi.org/10.1016/j.jml.2007.11.007
用anova和用logit mixed model，p值结果有多大差异？ （(Li et al., 2018)里有两种方法的结果？）用这两种方法在统计结论（显著or不显著）上会多大概率有出入呢？
刘金婷老师观点认为：我觉得用anova不是用错了，而是logit mixed model在某些方面更好，相当于改进了。
相比于因变量测量上的误差，用ANOVA带来的统计误差算是小的，所以我觉得还是实验设计更为重要，而且更不可逆。统计错了可以重来，成本很低。数据收集出了问题，只能卷土重来了。
沈强老师观点认为：是误用，回归可以handle得很好，没必要守着anova不放。这种被试内有多个trial的data，就应该用mixed的回归，anova如果分两步走，是损失了信息的，而且data还不一定符合anova要求的假设。
两种观点的融合：
参考文献：
Dixon, P. (2008). Models of accuracy in repeated-measures designs. Journal of Memory and Language, 59(4), 447-456. doi:https://doi.org/10.1016/j.jml.2007.11.004
Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59(4), 434-446. doi:http://dx.doi.org/10.1016/j.jml.2007.11.007
Li, A.-S., Miao, C.-G., Han, Y., He, X., & Zhang, Y. (2018). Electrophysiological Correlates of the Effect of Task Difficulty on Inhibition of Return. Frontiers in Psychology, 9(2403). doi:10.3389/fpsyg.2018.02403
Magezi, D. A. (2015). Linear mixed-effects models for within-participant psychology experiments: an introductory tutorial and free, graphical user interface (LMMgui). Frontiers in Psychology, 6(2). doi:10.3389/fpsyg.2015.00002
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