Comparing three groups

For multiple comparisons in analysis of variance, practitioners’ handbooks generally advocate standard methods such as Bonferroni, or an <i>F</i>-test followed by Tukey’s honest significant difference method. These methods are known to be suboptimal compared to closed testing procedures, but improved methods can be complex in the general multi-group set-up. In this note we argue that the case of three-groups is special: with three groups, closed testing procedures are powerful and easy to use. We describe four different closed testing procedures specifically for the three-group set-up. The choice of method should be determined by assessing which of the comparisons are considered primary and which are secondary, as dictated by subject-matter considerations. We describe how all four methods can be used with any standard software.

在方差分析的多重比较场景中，从业者参考手册通常推荐标准方法，例如邦费罗尼（Bonferroni）校正法，或是先开展F检验（F-test），再采用图基（Tukey）诚实显著差异法。相较于闭合检验（closed testing）流程，上述方法已被证实并非最优；但在通用多组实验设置下，改进后的方法往往较为复杂。在本注记中，我们提出：三组分组场景具有特殊性——针对三组分组的情况，闭合检验流程兼具高效性与易用性。我们针对三组设置场景，详细介绍了四种不同的闭合检验流程。方法的选择应依据研究领域的具体考量，通过判定哪些比较属于首要检验、哪些属于次要检验来确定。此外，我们还说明了如何在任意标准统计软件中实现这四种方法的应用。