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In probability and statistics, Simpson's paradox (or the YuleSimpson 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 socialscience and medicalscience 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 wellknown 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 counterintuitive 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 YuleSimpson effect.^{[11]}
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