Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2018 Apr 25;30(2):139-143.
doi: 10.11919/j.issn.1002-0829.218026.

Simpson's Paradox: Examples

Bokai Wang  1 , Pan Wu  2 , Brian Kwan  3 , Xin M Tu  3 , Changyong Feng  1   4
Affiliations

Simpson's Paradox: Examples

Bokai Wang et al. Shanghai Arch Psychiatry. .

Abstract
in English, Chinese

Simpson's paradox is very prevalent in many areas. It characterizes the inconsistency between the conditional and marginal interpretations of the data. In this paper, we illustrate through some examples how the Simpson's paradox can happen in continuous, categorical, and time-to-event data.

辛普森悖论普遍存在于很多领域。它具有数据 的条件性和边缘性解释之间的不一致特征。在本文中， 我们通过一些例子来阐述辛普森悖论是如何在连续性、 分类和时间- 事件数据中产生的。.

Keywords: conditional expectation; odd ratio; time-to-event analysis.

PubMed Disclaimer

Figures

Figure 1.
Figure 1.
Hazard functions in different age categories
Figure 2.
Figure 2.
Marginal hazard functions of two treatment groups
See this image and copyright information in PMC

References

    1. Simpson EH. The Interpretation of Interaction in Contingency Tables. J R Stat Soc Series B. 1951; 13: 238-241
    1. Yule GU. Notes on the Theory of Association of Attributes in Statistics. Biometrika. 1903; 2(2): 121-134. doi: https:://doi.org/10.1093/biomet/2.2.121 - DOI
    1. Heydtmann M. The nature of truth: Simpson’s Paradox and the limits of statistical data. QJM. 2002; 95(4): 247-249. doi: https:://doi.org/10.1093/qjmed/95.4.247 - DOI - PubMed
    1. Lerman K. Computational social scientist beware: Simpson’s paradox in behavioral data. J Comput Soc Sc. 2018; 1: 49-58. doi: https:://doi.org/10.1007/s42001-017-0007-4 - DOI
    1. Malinas G, Bigelow J. Simpson’s Paradox. Edward N. Zalta. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2016 Edition). Available from: https://plato.stanford.edu/archives/fall2016/entries/paradox-simpson

LinkOut - more resources