This paper identifies several serious problems with the widespread use of ANOVAs for the analysis of categorical outcome variables such as forced-choice variables, question-answer accuracy, choice in production (e.g. in syntactic priming research), et cetera. I show that even after applying the arcsine-square-root transformation to proportional data, ANOVA can yield spurious results. I discuss conceptual issues underlying these problems and alternatives provided by modern statistics. Specifically, I introduce ordinary logit models (i.e. logistic regression), which are well-suited to analyze categorical data and offer many advantages over ANOVA. Unfortunately, ordinary logit models do not include random effect modeling. To address this issue, I describe mixed logit models (Generalized Linear Mixed Models for binomially distributed outcomes, Breslow & Clayton, 1993), which combine the advantages of ordinary logit models with the ability to account for random subject and item effects in one step of analysis. Throughout the paper, I use a psycholinguistic data set to compare the different statistical methods.

中文翻译：

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分类数据分析：远离 ANOVA（转换与否）并转向 logit 混合模型

本文确定了广泛使用方差分析的几个严重问题，用于分析分类结果变量，例如强制选择变量、问答准确性、生产选择（例如，在句法启动研究中）等。我表明，即使在对比例数据应用反正弦平方根变换后，方差分析也会产生虚假结果。我讨论了这些问题背后的概念问题以及现代统计提供的替代方案。具体来说，我介绍了普通的 logit 模型（即逻辑回归），它们非常适合分析分类数据，并且比 ANOVA 具有许多优势。不幸的是，普通的 logit 模型不包括随机效应建模。为了解决这个问题，我描述了混合 logit 模型（二项分布结果的广义线性混合模型，Breslow & Clayton, 1993)，它结合了普通 logit 模型的优点和在一步分析中考虑随机主题和项目效应的能力。在整篇论文中，我使用心理语言学数据集来比较不同的统计方法。