Statistics: Simpson's Paradox

From MathWiki

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," ( 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. (
Airlines on-time data airline on-time or late airport location Moore 2003, p 143. (
Death sentence data race of convicted murderer death sentence: yes or no race of murder victim Witmer 1992, pp 110-112. (
Comparing batting averages person batting hit or out year of that at bat Friedlander 1992, p 845. (
Prenatal care care status infant mortality clinic Bishop, Fienberg and Holland 1975, pp 41-42. (
Type of surgery for kidney stones Open vs percutaneous nephrolithotomy success rate stone diameter Julious & Mullee 1994 (
Diabetes insulin dependence mortality age Julious & Mullee 1994 (
Synthetic microbial system with common-good producers and non-producers time proportion of producers initial proportion in subpopulation Chuang, Rivoire and Leibler, 2009 (