# Simpson's Paradox

A Simpson's Paradox is a paradox where an observed trend for a system's individual components is reversed when the system is observed as a whole.

**AKA:**Yule–Simpson Effect.**Context:**- It can (typically) occur when comparing two very dissimilarly distributed Populations.

**Example(s):**- Claim: The acceptance rate for women to university U is higher than for men. Evidence: In all 13 of the university's departments, the acceptance rate for women applicants is higher than for men.

Paradox: The acceptance rate for men to university U is higher than for women overall.

Possible Explanation: There are many male-dominated departments who readily accept the handful of women who apply, while the few women-dominated departments were less likely to accept the handful of men who applied.

- Claim: The acceptance rate for women to university U is higher than for men. Evidence: In all 13 of the university's departments, the acceptance rate for women applicants is higher than for men.
**See:**Ecological Fallacy.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Simpson's_paradox Retrieved:2015-3-11.
**Simpson's paradox**, or the Yule–Simpson effect, is a paradox in probability and statistics, in which a trend that appears in different groups of data disappears or reverses when these groups are combined. It is sometimes given the impersonal title**reversal paradox**or amalgamation paradox. This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations.^{[1]}Simpson's paradox disappears when causal relations are brought into consideration. Many statisticians believe that the mainstream public should be informed of the counter-intuitive results in statistics such as Simpson's paradox.^{[2]}^{[3]}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.^{[4]}The name*Simpson's paradox*was introduced by Colin R. Blyth in 1972.^{[5]}

- ↑ Judea Pearl.
*Causality: Models, Reasoning, and Inference*, Cambridge University Press (2000, 2nd edition 2009). ISBN 0-521-77362-8. - ↑ Robert L. Wardrop (February 1995). “Simpson's Paradox and the Hot Hand in Basketball".
*The American Statistician*,**49 (1)**: pp. 24–28. - ↑ Alan Agresti (2002). “Categorical Data Analysis" (Second edition). John Wiley and Sons ISBN 0-471-36093-7
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### 2009

- http://en.wikipedia.org/wiki/Simpson%27s_paradox
- In probability and statistics,
**Simpson's paradox**(or the Yule-Simpson effect) is an apparent paradox in which the successes in different groups seem to be 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.

- In probability and statistics,

### 2008

- (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
**Simpson's paradox**An intriguing paradox illustrating how one may be misled when a relevant *variable is overlooked.