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针对Null Hypothesis Significance Testing (NHST)在统计学理论与实践中所起到的作用/扮演的角色,我的观点十分明确,那就是:NHST不应该在统计推断或科学发现推论过程中有立足之地。因为在NHST的推断/推理框架下连续型的统计检验量(如p-值,置信区间,贝叶斯因子)被人为地两分化/离散化以达到划分‘统计显著性’的目的并以此作为评判科学发现假设真伪(拒绝/接受)的标准。这个统计推断范式在逻辑上站不住脚,在技术层面上漏洞百出,在实践上造成了科研工作者忽视科学内涵/相关学科机理、盲目接受统计检验结果的严重后果。我们应该谦虚地承认,在只有一组样本数据的条件下统计抽样分布根本无从谈起,统计数据分析充其量能做到的只是给出“在给定假设条件下的数据模型”分析结果(what-if analysis),而不是所谓的能确认科学发现假设真伪的分析(confirmatory analysis)。这样的结论是在我收集、阅读、思考及消化了尽可能多的相关参考资料后逐渐形成的。
以下是一份截至2020年底我所收集的有关NHST这个对统计学理论与实践都十分重要的话题的不完整的参考资料清单(按时间顺序排列)。公平起见,我已尽量把正反两方的资料都收集,但我能查到的大部分的都是指出NHST种种问题的资料。我给对统计假设检验问题有兴趣的博友的阅读建议是:如果您只有时间读一篇文章,请选择下述资料清单的第146项;如果您有时间读两篇文章,请考虑下述资料清单的第141 和146项;如果您有时间读一本书的话,我强力推荐资料清单的第2项 - (The Lady Tasting Tea) – 中国统计出版社译为“女士品茶”(链接https://www.bookresource.net/pdf/151336.html);如果您有半个小时,我建议您看看Geoff Cumming教授的这段关于p-值话题的精彩视频https://www.youtube.com/watch?v=iJ4kqk3V8jQ (资料清单的第152项)。我相信您一定会觉得花一点时间关注一下这个对统计学理论与实践都十分重要的话题实在是值得的。
第一部分:参考书籍(Part I: Books)
1. Edited by Denton E. Morrison and Ramon E. Henkel (1970). The Significance Test Controversy. Routledge, Taylor & Francis Group.
2. David Salsburg (2001). The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. Henry Holt and Company.
3. Burham, K. and Anderson, D. (2002). Model Selection and Multimodel Inference: a practical information-theoretic approach. Springer.
4. E.T. Jaynes (edited by G. Larry Bretthorst) (2003). Probability Theory: the logic of science. Cambridge University Press.
5. Richard A. Berk (2004). Regression Analysis: A Constructive Critique. SAGE.
6. Stephen T. Ziliak and Deirdre N. McCloskey (2008). The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives. The University of Michigan Press.
7. Raymond Hubbard (2015). Corrupt Research: The case for reconceptualizing empirical management and social science. SAGE Publications, Inc.
8. Richard McElreath (2016). Statistical Rethinking: A Bayesian Course with Examples in R and Stan. CRC Press, Taylor & Francis Group.
9. Weichung Joe Shih and Joseph Aisner (2016). Statistical Design and Analysis of Clinical Trials: Principles and Methods. CRC Press, Taylor & Francis Group.
10. Geoff Cumming and Robert Calin-Jageman (2017). Introduction to The New Statistics: Estimation, Open Science, & Beyond. Routledge.
11. Hadley Wickham & Garrett Grolemund (2017). R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. O’Reilly.
12. Richard F. Harris (2017). Rigor Mortis: How Sloppy Science Creates Worthless Cures, Crushes Hope, and Wastes Billions. BASIC BOOKS.
13. Edited by Vladik Kreinovich, Nguyen Ngoc Thach, Nguyen Duc Trung, and Dang Van Thanh (2019). Beyond Traditional Probabilistic Methods in Economics. Springer
14. David Spiegelhalter (2019). The Art of Statistics: How to learn from data. BASIC BOOKS, New York.
第二部分:期刊文章(或参考书的章节)(Part II: Articles (including book chapters if any))
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30. E.L. Lehmann (1993). The Fisher, Neyman-Peerson Theories of Testing Hypotheses: One Theory or Two? Journal of the American Statistical Association, Vol. 88, No. 424, 201-208.
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33. Rama Menon (1993). Statistical Significance Testing Should be Discontinued in Mathematics Education Research. Mathematics Education Research Journal, Vol. 5, No. 1, 4-18.
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35. Jacob Cohen (1994). The Earth Is Round (p < .05). American Psychologist, Vol.49, No. 12, 997-1003.
36. Bruce Thompson (1994). The Concept of Statistical Significance Testing. Practical Assessment, Research & Evaluation, Vol. 4, No. 5, Available online: http://PAREonline.net/getvn.asp?v=4&n=5.
37. Bruce Thompson (1994). The Pivotal Role of Replication in Psychological Research: Empirically Evaluating the Replicability of Sample Results. Journal of Personality 62:2, 157-176.
38. Ruma Falk & Charles W. Greenbaum (1995). Significance Test Die Hard: The Amazing Persistence of a Probabilistic Misconception. Theory & Psychology 5(1), 75-98.
39. R.E. Kirk (1996). Practical significance: A concept whose time has come. Educational and Psychological Measurement, 56, 746-759.
40. Marks R. Nester (1996). An Applied Statistician’s Creed. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 45, No. 4, 401-410.
41. Frank L. Schmidt (1996). Statistical Significance Testing and Cumulative Knowledge in Psychology: Implications for Training of Researchers. Psychological Methods, Vol. 1, No. 2, 115-129.
42. Bruce Thompson (1996). AERA Editorial Policies Regarding Statistical Significance Testing: Three Suggested Reforms. Educational Researcher, Vol. 25, No. 2, pp. 26-30.
43. Robert P. Abelson (1997). On the Surprising Longevity of Flogged Horses: Why There Is a Case for the Significance Test. Psychological Science, Volume 8 issue 1, pp. 12-15.
44. Patrick E. Shrout (1997). Should Significance Tests Be Banned? Introduction to a Special Section Exploring the Pros and Cons. Psychological Sciences, Vol. 8, No. 1, 1-2.
45. Frank L. Schmidt (1997). Eight common but false objections to the discontinuation of significance testing in the analysis of research data, in book: What if there were no significance tests? Editors: Lisa L. Harlow, Stanley A. Mulaik, James H.Steiger, Publisher: Lawrence Erlbaum Associates.
46. Janet M. Lang, Kenneth J. Rothman, and Cristina I. Cann (1998). That Confounded P-Value. Epidemiology, Volume 9, Number 1, 7-8.
47. James E. McLean and James M. Ernest (1998). The Role of Statistical Significance Testing In Educational Research. Research in the Schools, Vol. 5, No. 2, 15-22.
48. James Currall (1998). Review on the book ‘Statistical Significance: Rationale, Validity and Utility’ (Siu L. CHOW, 1996). Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 47, No. 2, pp. 394-395
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50. Tapan K. Nayak (1998). Review on the book ‘Statistical Significance: Rationale, Validity and Utility’ (Siu L. CHOW, 1996). TECHNOMETRICS, MAY 1998, VOL. 40, NO. 2
51. David H. Krantz (1999). The Null Hypothesis Testing Controversy in Psychology. Journal of the American Statistical Association, Vol. 44, No. 448, pp. 1372-1381.
52. Douglas H. Johnson (1999). The Insignificance of Statistical Significance Testing. Journal of Wildlife Management, 63(3): 763-772.
53. Howard Wainer (1999). One Cheer for Null Hypothesis Significance Testing. Psychological Methods, Vol. 4, No. 2, 212-213.
54. Anderson, D. R., Burnham, K. P., and Thompson, W. L. (2000). Null Hypothesis Testing: Problems, Prevalence, and an Alternative. Journal of Wildlife Management, 64, 912–923.
55. John I. Marden (2000). Hypothesis Testing: From p Values to Bayes Factors. Journal of the American Statistical Association, Vol. 95, No. 452, 1316-1320.
56. Raymond S. Nickerson (2000). Null Hypothesis Significance Testing: A Review of an Old and Continuing Controversy. Psychological Methods, Vol. 5, No. 2, 241-301.
57. Charles Poole (2001). Low P-values or Narrow Confidence Intervals: Which Are More Durable? Epidemiology, Vol. 12, No. 3, 291-294.
58. Joachim Krueger (2001). Null Hypothesis Significance Testing: On the Survival of a Flawed Method. American Psychologist, Vol. 56, No. 1, 16-26. DOI: 10.1037//0003-066X.56.1.16.
59. Jonathan A. C. Sterne and George Davey Smith (2001). Sifting the evidence-what’s wrong with significance tests? BMJ, 322:226-31.
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61. Jeffrey A. Gliner, Nancy L. Leech, and George A. Morgan (2002). Problems With Null Hypothesis Significance Testing (NHST): What Do the Textbooks Say? The Journal of Experimental Education, 71(1), 83-92.
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63. Michael D. Jennions and Anders Pape Moller (2003). A survey of the statistical power of research in behavioral ecology and animal behaviour. Behavioral Ecology Vol. 14 No. 3: 438–445.
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66. Gerd Gigerenzer (2004). Mindless statistics. The Journal of Socio-Economics 33, 587–606.
67. Ioannidis JPA (2005). Why most published research findings are false. PLoS Med 2: e124. doi:10.1371/journal.pmed.0020124
68. Nekane Balluerka, Juana Gomez, and Dolores Hidalgo (2005). The Controversy over Null Hypothesis Significance Testing Revisited. Methodology European Journal of Research Methods for the Behavioral and Social Sciences, Vol. 1(2):55–70, DOI 10.1027/1614-1881.1.2.55
69. Editorial (2006). Some experimental design and statistical criteria for analysis of studies in manuscripts submitted for consideration for publication. Animal Feed Science and Technology 129, 1-11.
70. Andrew Gelman and Hal Stern (2006). The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant. The American Statistician, November 2006, Vol. 60, No. 4, 328-331.
71. Stephen Gorard (2006). Towards a judgement-based statistical analysis. British Journal of Sociology of Education, 27:1, 67-80, DOI: 10.1080/01425690500376663
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73. Raymond Hubbard and J. Scott Armstrong (2006). Why We Don't Really Know What Statistical Significance Means: A Major Educational Failure. Journal of Marketing Education, Vol. 28, pp. 114-120.
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127. Benjamin et al. (2018). Redefine Statistical Significance. Nature Human
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128. Jeffrey R. Spence and David J. Stanley (2018). Concise, Simple, and Not Wrong: In Search of a Short-Hand Interpretation of Statistical Significance. Frontiers in Psychology, Volume 9, Article 2185.
129. Harry Crane (2018). The Impact of P-hacking on “Redefine Statistical Significance”. Basic and Applied Social Psychology, 40:4, 219-235, DOI: 10.1080/01973533.2018.1474111.
130. Gerd Gigerenzer (2018). Statistical Rituals: The Replication Delusion and How We Got There. Advances in Methods and Practices in Psychological Science, Vol. 1(2) 198 –218.
131. Van Calster B, Steyerberg, EW, Collins GS, and Smits T. (2018). Consequences of relying on statistical significance: Some illustrations. Eur J Clin Invest. 48:e12912. https://doi.org/10.1111/eci.12912 .
132. Valentin Amrhein, Sander Greenland, Blake McShane (2019). Retire statistical significance. Nature, Vol. 567, 305: Comment.
133. Ronald D. Fricker Jr., Katherine Burke, Xiaoyan Han & William H. Woodall (2019). Assessing the Statistical Analyses Used in Basic and Applied Social Psychology After Their p-Value Ban. The American Statistician, 73:sup1, 374-384, DOI: 10.1080/00031305.2018.1537892
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135. Christopher Tong (2019). Statistical Inference Enables Bad Science; Statistical Thinking Enables Good Science. The American Statistician, Vol. 73, No. S1, 246-261: Statistical Inference in the 21st Century.
136. Dana P. Turner, Hao Deng and Timothy T. Houle (Guest Editorial, 2019). Statistical Hypothesis Testing: Overview and Application. Headache, pages 302-307. doi: 10.1111/head.13706.
137. Deborah G. Mayo (2019). P‐value thresholds: Forfeit at your peril. Eur J Clin Invest., 49:e13170. https://doi.org/10.1111/eci.13170
138. Andrew Gelman (2019). When we make recommendations for scientific practice, we are (at best) acting as social scientists. Eur J Clin Invest., 49:e13165. DOI: 10.1111/eci.13165
139. Tom E. Hardwicke & John P.A. Ioannidis (2019). Petitions in scientific argumentation: Dissecting the request to retire statistical significance. Eur J Clin Invest., 49:e13162. https://doi.org/10.1111/eci.13162
140. Horbert Hirschauer, Sven Gruner, oliver Muβhoff and Claudia Becker (2019). Twenty Steps Towards an Adequate Inferential Interpretation of p-Values in Econometrics. Journal of Economics and Statistics, 239(4):703–721
141. Raymond Hubbard, Brian D. Haig & Rahul A. Parsa (2019). The Limited Role of
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142. Raymond Hubbard (2019). Will the ASA's Efforts to Improve Statistical Practice be Successful? Some Evidence to the Contrary. The American Statistician, 73:sup1, 31-35, DOI:
10.1080/00031305.2018.1497540
143. Rob Herbert (2019). Research Note: Significance testing and hypothesis testing: meaningless, misleading and mostly unnecessary. Journal of Physiotherapy, 65, 178-181.
144. Valentin Amrhein, David Trafimow & Sander Greenland (2019). Inferential Statistics as Descriptive Statistics: There Is No Replication Crisis if We Don’t Expect Replication. The American Statistician, Vol. 73, No. S1, 262-270: Statistical Inference in the 21st Century.
145. Vincent S. Staggs (2019). Why statisticians are abandoning statistical significance. Guest Editorial, Res Nurs Health, 42:159–160, DOI: 10.1002/nur.21947.
146. Ronald L. Wasserstein, Allen L. Schirm & Nicole A. Lazar (2019). Moving to a World Beyond “p<0.05”. The American Statistician, Vol. 73, No. S1, 1-19: Editorial.
147. Caiyun Liao, Andrew L. Speirs, Sierra Goldsmith, & Sherman J. Silber (2020). When “facts” are not facts: what does p value really mean, and how does it deceive us? Journal of Assisted Reproduction and Genetics, 37:1303-1310, https://doi.org/10.1007/s10815-020-01751-4.
第三部分:网上资料(Part III: Online materials)
148. http://www.stats.org.uk/statistical-inference/ the link for Statistical Inference (and What is Wrong With Classical Statistics) – a long list of references.
149. https://fionaresearch.files.wordpress.com/2013/06/fidler-phd-2006.pdf Fiona Fidler’s PhD thesis “FROM STATISTICAL SIGNIFICANCE TO EFFECT ESTIMATION: STATISTICAL REFORM IN PSYCHOLOGY, MEDICINE AND ECOLOGY.”
150. https://learningstatisticswithr.com/book/ Learning statistics with R: A tutorial for paychology students and other beginners (Version 0.6.1). 2019-01-11, Danielle Navarro (UNSW, Australia)
151. https://www.fharrell.com/post/introduction/ Frank Harrell, author of an influential book on regression modeling and currently both a biostatistics professor and a statistician at the Food and Drug Administration sums up “some of his personal philosophy of statistics” here.
152. https://www.youtube.com/watch?v=iJ4kqk3V8jQ online video presented by Professor Geoff Cumming, La Trobe University, Australia
(注:上述NHST问题参考资料清单最早发表在我的researchgate的个人网页上https://www.researchgate.net/project/Say-NO-to-Null-Hypothesis-Significance-Testing )
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