贝叶斯因子及其在JASP中的实现

doi:10.3724/SP.J.1042.2018.00951

摘要/Abstract

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H₀和H₁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。

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 words: Bayes factor, Bayesian statistics, Frequentist, NHST, JASP

中图分类号:

B841

胡传鹏, 孔祥祯, Eric-Jan Wagenmakers, Alexander Ly, 彭凯平. (2018). 贝叶斯因子及其在JASP中的实现. 心理科学进展 , 26(6), 951-965.

HU Chuan-Peng, KONG Xiang-Zhen, Eric-Jan WAGENMAKERS, Alexander LY, PENG Kaiping. (2018). The Bayes factor and its implementation in JASP: A practical primer. Advances in Psychological Science, 26(6), 951-965.

图/表 6

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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H₀和H₁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

假设检验中的问题	贝叶斯因子	传统推理	参考文献
1. 同时考虑H₀和H₁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

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, 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