方差分析--为什么它比以往任何时候都重要
Analysis of variance--why it is more important than ever
摘要：
方差分析（ANOVA）是探索性和验证性数据分析中一种非常重要的方法。在复杂的问题中（例如，裂区设计），并不总是容易建立一个适当的方差分析。我们提出了一种层次分析，即使在复杂的情况下，也能自动给出正确的ANOVA比较。所有均值和方差的推断均在模型下进行，ANOVA表的每行具有单独的效应批次。我们通过处理有限样本方差分量连接到经典ANOVA：固定和随机效应模型的特征分别是对因子现有水平和新水平的推断。我们还引入了一个新的图形显示，显示关于每批效应的标准差的推断。我们从我们的应用数据分析的两个例子说明，首先说明我们的分层计算和显示的有用性，第二个显示方差分析的想法是如何帮助理解以前适合分层模型。
英文摘要：
Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a hierarchical analysis that automatically gives the correct ANOVA comparisons even in complex scenarios. The inferences for all means and variances are performed under a model with a separate batch of effects for each row of the ANOVA table. We connect to classical ANOVA by working with finite-sample variance components: fixed and random effects models are characterized by inferences about existing levels of a factor and new levels, respectively. We also introduce a new graphical display showing inferences about the standard deviations of each batch of effects. We illustrate with two examples from our applied data analysis, first illustrating the usefulness of our hierarchical computations and displays, and second showing how the ideas of ANOVA are helpful in understanding a previously fit hierarchical model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
