Simpson's Paradox

In probability and statistics, Simpson's paradox (or the Yule–Simpson effect) is a paradox in which a correlation present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations. Simpson's Paradox disappears when causal relations are brought into consideration.

Though it is mostly unknown to laypeople, Simpson's Paradox is well known to statisticians, and it is described in a few introductory statistics books. Many statisticians believe that the mainstream public should be informed of the counter-intuitive results in statistics such as Simpson's paradox.

Edward H. Simpson first described this phenomenon in a technical paper in 1951, but the statisticians Karl Pearson, et al., in 1899, and Udny Yule, in 1903, had mentioned similar effects earlier. The name Simpson's paradox was introduced by Colin R. Blyth in 1972. Since Edward Simpson did not actually discover this statistical paradox (a fact explained by Stigler's law of eponymy), some writers, instead, have used the impersonal names reversal paradox and amalgamation paradox in referring to what is now called Simpson's Paradox and the Yule-Simpson effect.