Simpson's paradox

위키정의:
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, and it occurs when frequency data are hastily given causal interpretations. Simpson's Paradox disappears when any causal relations are derived systematically – i.e. through formal analysis.

예를 보면 쉽다.

1)
데이비드는 1995, 1996년 모두 데릭보다 성적이 좋지만 2년의 결과를 합치면 좋지 않다.

	1995	1996	Combined
Derek Jeter	12/48 .250	183/582 .314	195/630 .310
David Justice	104/411 .253	45/140 .321	149/551 .270

2) 신장결석에 대한 두 가지 치료법에 대한 비교.

	Treatment A	Treatment B
성공률	78% (273/350)	83% (289/350)

전체 성공률만 보면, 치료법 B가 좋아보인다.

하지만 나누어 보면,  결과가 너무 달라진다.

	Treatment A	Treatment B
Small Stones	93% (81/87)	87% (234/270)
Large Stones	73% (192/263)	69% (55/80)
Both	78% (273/350)	83% (289/350)

At best, Simpson's Paradox is used to argue that association is not causation.
At worst, Simpson's Paradox is used to argue that induction is impossible in observational studies.






참고.
http://en.wikipedia.org/wiki/Simpson's_paradox
web.augsburg.edu/~schield/MiloPapers/99ASA.pdf



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