Simpson's Paradox

Simpson's paradox, also known as the amalgamation paradox, reversal paradox, or Yule-Simpson effect, is a paradox in which a statistical trend appears to be present when data are segmented into separate groups of data but disappears (or reverses) when the data is considered as a whole. Simpson's paradox can arise when causal relations are ignored, but disappears when they are properly accounted for.

REFERENCES

Blyth, C. R. "On Simpson's Paradox and the Sure-Thing Principle." J. Amer. Stat. Assoc. 67, 364-366, 1972.

Good, I. J. and Mittal, Y. "The Amalgamation and Geometry of Two-by-Two Contingency Tables." Ann. Stat. 15, 694-711, 1987.

Paulos, J. A. A Mathematician Reads the Newspaper. New York: BasicBooks, p. 135, 1995.

Pearson, K.; Lee, A.; and Bramley-Moore, L. "Genetic (Reproductive) Selection: Inheritance of Fertility in Man, and of Fecundity in Thoroughbred Racehorses." Philos. Trans. Roy. Soc. A 192, 257-330, 1899.

Simpson, E. H. "The Interpretation of Interaction in Contingency Tables." J. Roy. Stat. Soc. 13, 238-241, 1951.Yule, G. U. ""Notes on the Theory of Association of Attributes in Statistics." Biometrika 2, 121-134, 1903.