全局检验与事后检验之间的联系:ANOVA方差分析中F检验结果的一项调查
Relationship between Omnibus and Post-hoc Tests: An Investigation of performance of the F test in ANOVA
Chen T 1Xu M 2Tu J 3Wang H 4Niu X5
作者信息
- 1. Department of Mathematics and Statistics, University of Toledo, OH, USA
- 2. Shanghai Mental Health Center, Shanghai Jiao Tong University Medical College, Shanghai, China
- 3. Department of Physical Medicine and Rehabilitation, University of Virginia School of Medicine, Charlottesville, VA, USA
- 4. Department of Biostatistics and Computational Biology, University of Rochester, NY, USA
- 5. College of Informatics, Huazhong Agriculture University, Wuhan, China
- 折叠
摘要
多组比较在许多生物医学和心理社会学研究中是一种常见的统计检验.当组数为两个以上时,首先对组间的整体差异进行全局检验.如果零假设被拒绝,则接着进行下一步的事后两两组间比较,以确定差异的来源.相反,第一步停止即可声明没有组间差异.一个共同认识是如果全局检测结果是显著的,那么至少存在两个组之间是有显著差异的,反之亦然.因此,当全局检测结果显著,但没有事后组间两两比较没有显著差异,人们会感到困惑发生了什么并想知道如何来解释该结果.总之,当全局检测结果不显著时,人们会想知道是否所有的事后检测也都不显著？同样,全局检测结果不显著而停止事后检测是否会导致发现组差差异的丢失？在这篇报告中,我们研究了这个令人费解的现象,并且讨论了如何解释这样的结果.
Abstract
Comparison of groups is a common statistical test in many biomedical and psychosocial research studies.When there are more than two groups,one first performs an omnibus test for an overall difference across the groups.If this null is rejected,one then proceeds to the next step of posthoc pairwise group comparisons to determine sources of difference.Otherwise,one stops and declares no group difference.A common belief is that if the omnibus test is significant,there must exist at least two groups that are significantly different and vice versa.Thus,when the omnibus test is significant,but no post-hoc between-group comparison shows significant difference,one is bewildered at what is going on and wondering how to interpret the results.At the end of the spectrum,when the omnibus test is not significant,one wonders if all post-hoc tests will be non-significant as well so that stopping after a nonsignificant omnibus test will not lead to any missed opportunity of finding group difference.In this report,we investigate this perplexing phenomenon and discuss how to interpret such results.
关键词
全局检测/事后检验、F检验、图基(Tukey)检验Key words
Omnibus test/post-hoc test/F test/Tukey's test引用本文复制引用
出版年
2018
NETL
NSTL
维普
万方数据