| 第1行： |
第1行： |
| − | '''Simpson's paradox''' is a paradox from statistics. It is named after Edward H. Simpson, a British statistician who first described it in 1951. The statistician Karl Pearson described a very similar effect in 1899.- Udny Yule's description dates from 1903. Sometimes, it is called the '''Yule–Simpson effect'''. When looking at the statistical scores of groups, these scores may change, depending on whether the groups are looked at one by one, or if they are combined into a larger group. This case often occurs in social sciences and medical statistics. It may confuse people, if frequency data is used to explain a causal relationship. Other names for the paradox include ''reversal paradox'' and ''amalgamation paradox''. | + | {{#seo: |
| | + | |keywords=统计学， |
| | + | |description= |
| | + | }} |
| | + | '''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>. |
| | | | |
| − | 辛普森悖论是一个统计学悖论。它是以 E.H.辛普森的名字命名的，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>.
| |
| | | | |
| | == 样例：肾结石治疗 == | | == 样例：肾结石治疗 == |
| − | This is a real-life example from a medical study comparing the success rates of two treatments for kidney stones.
| + | 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>。 |
| − | | |
| − | The table shows the success rates and numbers of treatments for treatments involving both small and large kidney stones, where Treatment A includes all open procedures and Treatment B is percutaneous nephrolithotomy:
| |
| | | | |
| − | 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>。
| |
| | | | |
| | 下表显示了治疗小肾结石和大肾结石的成功率和治疗次数，其中治疗A包括所有开放手术，治疗B是经皮肾镜取石术: | | 下表显示了治疗小肾结石和大肾结石的成功率和治疗次数，其中治疗A包括所有开放手术，治疗B是经皮肾镜取石术: |
| 第73行： |
第73行： |
| | | | |
| | | | |
| − | The paradoxical conclusion is that treatment A is more effective when used on small stones, and also when used on large stones, yet treatment B is more effective when considering both sizes at the same time. In this example, it was not known that the size of the kidney stone influenced the result. This is called a hidden variable (or lurking variable) in statistics.
| + | 一个自相矛盾的结论是，A疗法对小结石更有效，对大结石也更有效，而B疗法在同时考虑两种大小时更有效。在这个例子中，还不知道肾结石的大小会影响结果。这在统计学中称为隐藏变量(或隐藏变量)。 |
| | | | |
| − | Which treatment is considered better is determined by an inequality between two ratios (successes/total). The reversal of the inequality between the ratios, which creates Simpson's paradox, happens because two effects occur together:
| |
| | | | |
| − | # The sizes of the groups, which are combined when the lurking variable is ignored, are very different. Doctors tend to give the severe cases (large stones) the better treatment (A), and the milder cases (small stones) the inferior treatment (B). Therefore, the totals are dominated by groups three and two, and not by the two much smaller groups one and four.
| + | 哪种治疗方法更好是由两个比率(成功率/总成功率)之间的不平等决定的。造成辛普森悖论的两个比率之间不平等的逆转，是因为两种效应同时发生: |
| − | # The lurking variable has a large effect on the ratios, i.e. the success rate is more strongly influenced by the severity of the case than by the choice of treatment. Therefore, the group of patients with large stones using treatment A (group three) does worse than the group with small stones, even if the latter used the inferior treatment B (group two).
| |
| | | | |
| − | 一个自相矛盾的结论是，A疗法对小结石更有效，对大结石也更有效，而B疗法在同时考虑两种大小时更有效。在这个例子中，还不知道肾结石的大小会影响结果。这在统计学中称为隐藏变量(或隐藏变量)。
| + | :1、当忽略隐藏变量时，组的大小是非常不同的。医生倾向于对严重的病例(大结石)给予较好的治疗(A) ，对较轻的病例(小结石)给予较差的治疗(B)。因此，总数由第三组和第二组支配，而不是由规模小得多的第一组和第四组支配。 |
| | | | |
| − | 哪种治疗方法更好是由两个比率(成功率/总成功率)之间的不平等决定的。造成辛普森悖论的两个比率之间不平等的逆转，是因为两种效应同时发生:
| |
| | | | |
| − | 1、当忽略隐藏变量时，组的大小是非常不同的。医生倾向于对严重的病例(大结石)给予较好的治疗(A) ，对较轻的病例(小结石)给予较差的治疗(B)。因此，总数由第三组和第二组支配，而不是由规模小得多的第一组和第四组支配。
| + | :2、潜伏变量对比率有很大的影响，也就是说成功率更多地受到病情严重程度的影响，而不是治疗方法的选择。因此，治疗 A组(第三组)大结石患者的情况比治疗小结石患者差，即使后者采用劣等治疗 B 组(第二组)。 |
| | | | |
| − | 2、潜伏变量对比率有很大的影响，也就是说成功率更多地受到病情严重程度的影响，而不是治疗方法的选择。因此，治疗 A组(第三组)大结石患者的情况比治疗小结石患者差，即使后者采用劣等治疗 B 组(第二组)。
| |
| | | | |
| | == 参考文献 == | | == 参考文献 == |
| | <references /> | | <references /> |
| | + | |
| | + | |
| | + | ==编者推荐== |
| | + | ===集智课程=== |
| | + | ====[https://campus.swarma.org/course/3527 因果科学读书会第三季：因果+X]==== |
| | + | “因果”并不是一个新概念，而是一个已经在多个学科中使用了数十年的分析技术。通过前两季的分享，我们主要梳理了因果科学在计算机领域的前沿进展。如要融会贯通，我们需要回顾数十年来在社会学、经济学、医学、生物学等多个领域中，都是使用了什么样的因果模型、以什么样的范式、解决了什么样的问题。我们还要尝试进行对比和创新，看能否以现在的眼光，用其他的模型，为这些研究提供新的解决思路。 |
| | + | |
| | + | |
| | + | “因果+X”就是要让因果真正地应用于我们的科学研究中，不管你是来自计算机、数理统计领域，还是社会学、经济学、管理学领域，还是医学、生物学领域，我们希望共同探究出因果研究的范式，真正解决因果的多学科应用问题，乃至解决工业界的问题。 |
| | + | |
| | + | |
| | + | ---- |
| | + | 本中文词条由[[用户:我是猫|我是猫]]翻译，[[用户:薄荷|薄荷]]编辑，如有问题，欢迎在讨论页面留言。 |
| | + | |
| | + | |
| | + | |
| | + | '''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。''' |