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心理科学进展  2018, Vol. 26 Issue (6): 951-965    DOI: 10.3724/SP.J.1042.2018.00951
     研究方法 本期目录 | 过刊浏览 | 高级检索 |
贝叶斯因子及其在JASP中的实现
胡传鹏1,2(),孔祥祯3,Eric-Jan Wagenmakers4,Alexander Ly4,5,彭凯平1()
1 清华大学心理学系, 北京 100084
2 Neuroimaging Center, Johannes Gutenberg University Medical Center, 55131 Mainz, Germany
3 Language and Genetics Department, Max Planck Institute for Psycholinguistics, 6500 AH Nijmegen, The Netherlands
4 Department of Psychological Methods, University of Amsterdam, 1018 VZ Amsterdam, The Netherlands
5 Centrum Wiskunde & Informatica, 1090 GB Amsterdam, The Netherlands
The Bayes factor and its implementation in JASP: A practical primer
Chuan-Peng HU1,2(),Xiang-Zhen KONG3,WAGENMAKERS Eric-Jan4,LY Alexander4,5,Kaiping PENG1()
1 Department of Psychology, School of Social Science, Tsinghua University, Beijing 100084, China
2 Neuroimaging Center, Johannes Gutenberg University Medical Center, 55131 Mainz, Germany
3 Language and Genetics Department, Max Planck Institute for Psycholinguistics, 6500 AH Nijmegen, The Netherlands
4 Department of Psychological Methods, University of Amsterdam, 1018 VZ Amsterdam, The Netherlands
5 Centrum Wiskunde & Informatica, 1090 GB Amsterdam, The Netherlands
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摘要 

统计推断在科学研究中起到关键作用, 然而当前科研中最常用的经典统计方法——零假设检验(Null hypothesis significance test, NHST)却因难以理解而被部分研究者误用或滥用。有研究者提出使用贝叶斯因子(Bayes factor)作为一种替代和(或)补充的统计方法。贝叶斯因子是贝叶斯统计中用来进行模型比较和假设检验的重要方法, 其可以解读为对零假设H0或者备择假设H1的支持程度。其与NHST相比有如下优势:同时考虑H0H1并可以用来支持H0、不“严重”地倾向于反对H0、可以监控证据强度的变化以及不受抽样计划的影响。目前, 贝叶斯因子能够很便捷地通过开放的统计软件JASP实现, 本文以贝叶斯t检验进行示范。贝叶斯因子的使用对心理学研究者来说具有重要的意义, 但使用时需要注意先验分布选择的合理性以及保持数据分析过程的透明与公开。

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胡传鹏
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Alexander Ly
彭凯平
关键词 贝叶斯因子贝叶斯学派频率学派假设检验JASP    
Abstract

Statistical inference plays a critical role in modern scientific research, however, the dominant method for statistical inference in science, null hypothesis significance testing (NHST), is often misunderstood and misused, which leads to unreproducible findings. To address this issue, researchers propose to adopt the Bayes factor as an alternative to NHST. The Bayes factor is a principled Bayesian tool for model selection and hypothesis testing, and can be interpreted as the strength for both the null hypothesis H0 and the alternative hypothesis H1 based on the current data. Compared to NHST, the Bayes factor has the following advantages: it quantifies the evidence that the data provide for both the H0 and the H1, it is not “violently biased” against H0, it allows one to monitor the evidence as the data accumulate, and it does not depend on sampling plans. Importantly, the recently developed open software JASP makes the calculation of Bayes factor accessible for most researchers in psychology, as we demonstrated for the t-test. Given these advantages, adopting the Bayes factor will improve psychological researchers’ statistical inferences. Nevertheless, to make the analysis more reproducible, researchers should keep their data analysis transparent and open.

Key wordsBayes factor    Bayesian statistics    Frequentist    NHST    JASP
收稿日期: 2017-10-10      出版日期: 2018-04-28
ZTFLH:  B841  
通讯作者: 胡传鹏,彭凯平     E-mail: hcp4715@hotmail.com;pengkp@mail.tsinghua.edu.cn
引用本文:   
胡传鹏,孔祥祯,Eric-Jan Wagenmakers,Alexander Ly,彭凯平. 贝叶斯因子及其在JASP中的实现[J]. 心理科学进展, 2018, 26(6): 951-965.
Chuan-Peng HU,Xiang-Zhen KONG,WAGENMAKERS Eric-Jan,LY Alexander,Kaiping PENG. The Bayes factor and its implementation in JASP: A practical primer. Advances in Psychological Science, 2018, 26(6): 951-965.
链接本文:  
http://journal.psych.ac.cn/xlkxjz/CN/10.3724/SP.J.1042.2018.00951      或      http://journal.psych.ac.cn/xlkxjz/CN/Y2018/V26/I6/951
假设检验中的问题 贝叶斯因子 传统推理 参考文献
1. 同时考虑H0H1的支持证据 × 10, 11
2. 可以用来支持H0 × 12, 13
3. 不“严重”地倾向于反对H0 × 14, 15, 16
4. 可以随着数据累积来监控证据的强度 × 17, 18
5. 不依赖于未知的或者不存在的抽样计划 × 19, 20
  假设检验中贝叶斯推断与传统NHST推断的比较
贝叶斯因子, BF10 解释
> 100 极强的证据支持H1
30 ~ 100 非常强的证据支持H1
10 ~ 30 较强的证据支持H1
3 ~ 10 中等程度的证据支持H1
1 ~ 3 较弱的证据支持H1
1 没有证据
1/3 ~ 1 较弱的证据支持H0
1/10 ~ 1/3 中等程度的证据支持H0
1/30 ~ 1/10 较强的证据支持H0
1/100 ~ 1/30 非常强的证据支持H0
< 1/100 极强的证据支持H0
  贝叶斯因子决策标准
  柯西分布与正态分布的对比
  使用JASP进行贝叶斯独立样本t检验时的操作截屏。软件左侧是数据; 中间为数据分析选项; 右侧为结果输出。
  使用JASP对Wagenmakers等人(2015)数据进行贝叶斯单侧独立样本t检验的示意图。左侧是数据, 中间为操作过程, 右侧为结果输出。细节见文中的描述。
  使用JASP进行贝叶斯因子的稳健性分析
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