Simpson's paradox

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In probability and statistics, Simpson's paradox (or the Yule-Simpson effect) is an apparent paradox in which a correlation (trend) present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics,[1] and it occurs when frequency data are hastily given causal interpretations.[2] Simpson's Paradox disappears when causal relations are brought into consideration (see Implications to Decision Making).

Though it is mostly unknown to laymen, Simpson's Paradox is well-known to statisticians, and it is described in a few introductory statistics books.[3][4] Many statisticians believe that the mainstream public should be informed of the counter-intuitive results in statistics such as Simpson's paradox,[5] in particular to caution people against the inference of causal relationships based on the mere association between two or more variables.[6]

Edward H. Simpson first described this phenomenon in a technical paper in 1951,[7] but the statisticians Karl Pearson, et al., in 1899,[8] and Udny Yule, in 1903, had mentioned similar effects earlier.[9] The name Simpson's paradox was introduced by Colin R. Blyth in 1972.[10] Since Edward Simpson did not actually discover this statistical paradox,[note 1] 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.[11]


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