| '''辛普森悖论 Simpson's paradox'''是一个统计学悖论。它是以Edward H. Simpson的名字命名的,他是一位英国统计学家,在1951年第一次描述了它<ref>Simpson, Edward H. (1951). "The Interpretation of Interaction in Contingency Tables". ''Journal of the Royal Statistical Society, Ser. B''. '''13''': 238–241</ref>。统计学家卡尔·皮尔森在1899年描述了一个非常相似的效应<ref>Pearson, Karl; Lee, A.; Bramley-Moore, L. (1899). "Genetic (reproductive) selection: Inheritance of fertility in man". ''Philosophical Translations of the Royal Statistical Society, Ser. A''. '''173''': 534–539</ref>。- Udny Yule 的描述可以追溯到1903年<ref>G. U. Yule (1903). "Notes on the Theory of Association of Attributes in Statistics". ''Biometrika''. '''2''' (2): 121–134. doi:10.1093/biomet/2.2.121</ref>。有时,这种现象被称为“尤尔-辛普森效应”。当观察小组的统计分数时,这些分数可能会发生变化,这取决于小组是逐一观察,还是将它们合并成一个更大的小组。这种情况经常发生在社会科学和医学统计中<ref>Clifford H. Wagner (February 1982). "Simpson's Paradox in Real Life". ''The American Statistician''. '''36''' (1): 46–48. doi:10.2307/2684093. JSTOR 2684093.</ref>。如果用频率数据来解释因果关系<ref>Judea Pearl. ''Causality: Models, Reasoning, and Inference'', Cambridge University Press (2000, 2nd edition 2009). <nowiki>ISBN 0-521-77362-8</nowiki>.</ref>,人们可能会感到困惑。悖论的其他名称还包括反转悖论和合并悖论<ref>I. J. Good, Y. Mittal (June 1987). "The Amalgamation and Geometry of Two-by-Two Contingency Tables". ''The Annals of Statistics''. '''15''' (2): 694–711. doi:10.1214/aos/1176350369. ISSN 0090-5364. JSTOR 2241334.</ref>. | | '''辛普森悖论 Simpson's paradox'''是一个统计学悖论。它是以Edward H. Simpson的名字命名的,他是一位英国统计学家,在1951年第一次描述了它<ref>Simpson, Edward H. (1951). "The Interpretation of Interaction in Contingency Tables". ''Journal of the Royal Statistical Society, Ser. B''. '''13''': 238–241</ref>。统计学家卡尔·皮尔森在1899年描述了一个非常相似的效应<ref>Pearson, Karl; Lee, A.; Bramley-Moore, L. (1899). "Genetic (reproductive) selection: Inheritance of fertility in man". ''Philosophical Translations of the Royal Statistical Society, Ser. A''. '''173''': 534–539</ref>。- Udny Yule 的描述可以追溯到1903年<ref>G. U. Yule (1903). "Notes on the Theory of Association of Attributes in Statistics". ''Biometrika''. '''2''' (2): 121–134. doi:10.1093/biomet/2.2.121</ref>。有时,这种现象被称为“尤尔-辛普森效应”。当观察小组的统计分数时,这些分数可能会发生变化,这取决于小组是逐一观察,还是将它们合并成一个更大的小组。这种情况经常发生在社会科学和医学统计中<ref>Clifford H. Wagner (February 1982). "Simpson's Paradox in Real Life". ''The American Statistician''. '''36''' (1): 46–48. doi:10.2307/2684093. JSTOR 2684093.</ref>。如果用频率数据来解释因果关系<ref>Judea Pearl. ''Causality: Models, Reasoning, and Inference'', Cambridge University Press (2000, 2nd edition 2009). <nowiki>ISBN 0-521-77362-8</nowiki>.</ref>,人们可能会感到困惑。悖论的其他名称还包括反转悖论和合并悖论<ref>I. J. Good, Y. Mittal (June 1987). "The Amalgamation and Geometry of Two-by-Two Contingency Tables". ''The Annals of Statistics''. '''15''' (2): 694–711. doi:10.1214/aos/1176350369. ISSN 0090-5364. JSTOR 2241334.</ref>. |
| 这是一个真实的例子,来自一项医学研究<ref>C. R. Charig; D. R. Webb; S. R. Payne; O. E. Wickham (29 March 1986). "Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy". ''Br Med J (Clin Res Ed)''. '''292''' (6524): 879–882. doi:10.1136/bmj.292.6524.879. PMC 1339981. <nowiki>PMID 3083922</nowiki>.</ref>,比较两种治疗肾结石的成功率<ref>Steven A. Julious and Mark A. Mullee (1994-12-03). "Confounding and Simpson's paradox". BMJ. 309 (6967): 1480–1481. doi:10.1136/bmj.309.6967.1480. PMC 2541623. <nowiki>PMID 7804052</nowiki></ref>。 | | 这是一个真实的例子,来自一项医学研究<ref>C. R. Charig; D. R. Webb; S. R. Payne; O. E. Wickham (29 March 1986). "Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy". ''Br Med J (Clin Res Ed)''. '''292''' (6524): 879–882. doi:10.1136/bmj.292.6524.879. PMC 1339981. <nowiki>PMID 3083922</nowiki>.</ref>,比较两种治疗肾结石的成功率<ref>Steven A. Julious and Mark A. Mullee (1994-12-03). "Confounding and Simpson's paradox". BMJ. 309 (6967): 1480–1481. doi:10.1136/bmj.309.6967.1480. PMC 2541623. <nowiki>PMID 7804052</nowiki></ref>。 |