Statistics: Simpson's Paradox

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A collection of examples of Simpson's Paradox now, increasingly known as the Yule-Simpson effect, perhaps next known as the Pearson-Yule-Simpson effect.

The first five examples are cited in Thomas L. Moore (2006) "Paradoxes in Film Ratings," (http://www.amstat.org/publications/jse/v14n1/datasets.moore.html) Journal of Statistics Education 14 (1).

See the references for the complete data and the stories behind the data.


Examples of Simpson's Paradox: Direction of X versus Y association is reversed when controlling for the Z variable
Subject X Y Z Reference
Berkely Admissions Data sex of applicant accept or reject grad program applied to Freedman, et al. 1998, pp 17-20. (http://www.amstat.org/publications/jse/v14n1/datasets.moore.html#Freedman1998)
Airlines on-time data airline on-time or late airport location Moore 2003, p 143. (http://www.amstat.org/publications/jse/v14n1/datasets.moore.html#Moore2003)
Death sentence data race of convicted murderer death sentence: yes or no race of murder victim Witmer 1992, pp 110-112. (http://www.amstat.org/publications/jse/v14n1/datasets.moore.html#Witmer1992)
Comparing batting averages person batting hit or out year of that at bat Friedlander 1992, p 845. (http://www.amstat.org/publications/jse/v14n1/datasets.moore.html#Friedlander1992)
Prenatal care care status infant mortality clinic Bishop, Fienberg and Holland 1975, pp 41-42. (http://www.amstat.org/publications/jse/v14n1/datasets.moore.html#Bishop1975)
Type of surgery for kidney stones Open vs percutaneous nephrolithotomy success rate stone diameter Julious & Mullee 1994 (http://www.bmj.com/cgi/content/full/309/6967/1480)
Diabetes insulin dependence mortality age Julious & Mullee 1994 (http://www.bmj.com/cgi/content/full/309/6967/1480)
Synthetic microbial system with common-good producers and non-producers time proportion of producers initial proportion in subpopulation Chuang, Rivoire and Leibler, 2009 (http://www.sciencemag.org/cgi/content/abstract/323/5911/272)