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The ubiquity of the Simpson’s Paradox
Journal of Statistical Distributions and Applications Pub Date : 2017-03-28 , DOI: 10.1186/s40488-017-0056-5
Alessandro Selvitella

The Simpson’s Paradox is the phenomenon that appears in some datasets, where subgroups with a common trend (say, all negative trend) show the reverse trend when they are aggregated (say, positive trend). Even if this issue has an elementary mathematical explanation, it has a deep statistical significance. In this paper, we discuss basic examples in arithmetic, geometry, linear algebra, statistics, game theory, gender bias in university admission and election polls, where we describe the appearance or absence of the Simpson’s Paradox. In the final part, we present our results concerning the occurrence of the Simpson’s Paradox in Quantum Mechanics with focus on the Quantum Harmonic Oscillator and the Nonlinear Schrödinger Equation. We discuss how likely it is to incur in the Simpson’s Paradox and give some concrete numerical examples. We conclude with some final comments and possible future directions.

中文翻译:

辛普森悖论无处不在

辛普森悖论是某些数据集中出现的现象,其中具有共同趋势(例如,所有负趋势)的子组在汇总时(例如,正趋势)显示出反向趋势。即使此问题具有基本的数学解释,它也具有深远的统计意义。在本文中,我们讨论了算术,几何,线性代数,统计,博弈论,大学入学和选举民意测验中的性别偏见的基本示例,其中我们描述了辛普森悖论的出现或​​不存在。在最后一部分中,我们将介绍有关量子力学中辛普森悖论的发生的结果,重点是量子谐振子和非线性薛定ding方程。我们讨论了辛普森悖论发生的可能性,并给出了一些具体的数值示例。
更新日期:2017-03-28
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