Simpson's Paradox

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.
See: Ecological Fallacy.

References

(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. The name Simpson's paradox was introduced by Colin R. Blyth in 1972.

↑ 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

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.

(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.