||It has been suggested that Hot-hand fallacy be merged into this article. (Discuss) Proposed since October 2013.|
The clustering illusion is the tendency to erroneously perceive small samples from random distributions to have significant "streaks" or "clusters", caused by a human tendency to underpredict the amount of variability likely to appear in a small sample of random or semi-random data due to chance.
Gilovich, an early author on the subject, argues the effect occurs for different types of random dispersions, including 2-dimensional data such as seeing clusters in the locations of impact of V-1 flying bombs on 2 dimensional maps of London during World War II or seeing streaks in stock market price fluctuations over time. Although Londoners developed specific theories about the pattern of impacts within London, in a statistical analysis by R. D. Clarke originally published in 1946 the impacts of V-2 rockets on London is a close fit to the Poisson distribution, meaning it closely resembles the expected result from a chance dispersion (colloquially known as "random").
The clustering illusion is central to the "hot hand fallacy", the first study of which was reported by Gilovich, Robert Vallone and Amos Tversky. They found that the idea that basketball players shoot successfully in "streaks", sometimes called by sportcasters as having a "hot hand" and widely believed by Gilovich et al.'s subjects, was false. In the data they collected, if anything the success of a previous throw very slightly predicted a subsequent miss rather than another success.
Using this cognitive bias in causal reasoning may result in the Texas sharpshooter fallacy. More general forms of erroneous pattern recognition are pareidolia and apophenia. Related biases are the illusion of control which the clustering illusion could contribute to, and insensitivity to sample size in which people don't expect greater variation in smaller samples. A different cognitive bias involving misunderstanding of chance streams is the gambler's fallacy.
- Gilovich, Thomas (1991). How we know what isn't so: The fallibility of human reason in everyday life. New York: The Free Press. ISBN 0-02-911706-2.
- Kahneman, Daniel; Amos Tversky (1972). "Subjective probability: A judgment of representativeness". Cognitive Psychology 3: 430–454. doi:10.1016/0010-0285(72)90016-3.
- Clarke, R. D. (1946). "An application of the Poisson distribution". Journal of the Institute of Actuaries 72: 481.
- Gilovich, 1991 p. 19
- Mori, Kentaro. "Seeing patterns". Retrieved 3 March 2012.
- "Bombing London". Retrieved 3 March 2012.
- Tierney, John (3 October 2008). "See a pattern on Wall Street?" (October 3, 2008). TierneyLab (New York Times). Retrieved 3 March 2012.
- Gilovich, Thomas; Robert Vallone & Amos Tversky (1985). "The hot hand in basketball: On the misperception of random sequences". Cognitive Psychology 17: 295–314.
- Skeptic's Dictionary: The clustering illusion
- Hot Hand website: Statistical analysis of sports streakiness