A factorial design examines the effects of two independent variables on a single, continuous dependent variable. The statistical test employed to analyze the data is a two-way analysis of variance (ANOVA). This test yields three results: a main effect for each of the independent variables and an interaction effect between the two independent variables. This article explains factorial designs and two-way ANOVA with the help of a worked example using hypothetical data in a spreadsheet provided as a supplementary file. The main effects and interaction effects are explained and illustrated using tables and figures. A short discussion provides general notes about the concepts explained in this article, along with brief notes on repeated measures ANOVA and higher order ANOVAs. Many additional examples, with figures and explanations, are provided in the supplementary materials, which the reader is strongly encouraged to view.

中文翻译：

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了解因子设计、主效应和交互效应：通过一个示例进行简单解释

因子设计检查两个自变量对单个连续因变量的影响。用于分析数据的统计检验是双向方差分析 (ANOVA)。该检验产生三个结果：每个自变量的主效应以及两个自变量之间的交互效应。本文借助一个工作示例解释了因子设计和双向方差分析，该示例使用作为补充文件提供的电子表格中的假设数据。使用表格和图形来解释和说明主要效应和交互效应。简短的讨论提供了有关本文中解释的概念的一般说明，以及有关重复测量方差分析和高阶方差分析的简要说明。补充材料中提供了许多带有图表和解释的附加示例，强烈建议读者查看。