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Global testing method for clustering means in ANOVA

机译：方差分析中聚类方法的全局测试方法

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Consider an experiment where m treatments are provided and there are n_i subjects receiving the treatment the outcome of the jth subject on treatment i is X_(ij) and it satisfies the ANOVA model where the error terms are independent with iid as unit normal distribution. There are many approaches available to handle this problem. Some are based on pair-wise comparisons using family wise error rate (FWER) such as Fisher's protected least significant difference test and Tukey's honestly significant difference test, or false discovery rate (FDR) like BH procedure (Benjamini and Hochberg, Ref. 1) and ssBH procedure (Yekutiyeli, Ref. 2) and many others. These tests focus on pair wise equality but ignore the overall characteristics of the testing results. The results obtained should be clear logical ones but this is not guaranteed by the available test methods. To overcome this drawback, cluster analysis can be used. In this approach, the treatments are divided in to several disjoint groups for which there is no significant difference in the means within a group. However there are differences among means between groups. This paper proposes a method to handle this approach using "all-down" and "all-up" and the propose algorithms are non-hierarchical as in every step all partitions are with the same number of groups are considered. The proposed procedure is applied to both homogenous and heterogeneous variance cases. (20 refs.)
机译：考虑一个提供m个治疗的实验，有n_i个受试者接受治疗，第i个受试者i的治疗结果为X_（ij），它满足ANOVA模型，其中误差项独立于iid作为单位正态分布。有许多方法可以解决此问题。有些是基于使用家庭明智错误率（FWER）进行的成对比较，例如Fisher的受保护的最低有效差异测试和Tukey的诚实有效差异测试，或基于BH程序的错误发现率（FDR）（Benjamini和Hochberg，参考资料1）。和ssBH程序（Yekutiyeli，参考文献2）等等。这些测试侧重于成对相等，但忽略了测试结果的总体特征。获得的结果应该是逻辑清晰的结果，但是可用的测试方法不能保证这一点。为了克服这个缺点，可以使用聚类分析。在这种方法中，将治疗分为几个不相交的组，对于这些组，一组内的方法没有显着差异。但是，各组之间的方法之间存在差异。本文提出了一种使用“ all-down”和“ all-up”处理该方法的方法，并且该提议算法是非分层的，因为在每个步骤中，所有具有相同数目组的分区都将被考虑。拟议的程序适用于均质和异质方差情况。 （20篇）

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