Editing Clustering illusion

{{short description|Erroneously seeing patterns in randomness}}
[[File:Plot of random points.gif|right|thumb|upright=1.5|1,000 points randomly distributed inside a square, showing apparent clusters and empty spaces]]
The '''clustering illusion''' is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of [[Statistical dispersion|variability]] likely to appear in a small sample of random or [[pseudorandom]] data.<ref name="gilovich">{{cite book|last=Gilovich|first=Thomas|title=How we know what isn't so: The fallibility of human reason in everyday life|url=https://archive.org/details/howweknowwhatisn00gilorich|url-access=registration|year=1991|publisher=The Free Press|location=New York|isbn=978-0-02-911706-4}}</ref>

[[File:Air Raid Damage Map - East Marylebone.jpg|thumb|upright|Map of air raid damage in [[Marylebone]], London]]
[[Thomas Gilovich]], an early author on the subject, argued that the effect occurs for different types of random dispersions. Some might perceive patterns in [[stock market]] price fluctuations over time, or clusters in two-dimensional data such as the locations of impact of [[World War II]] [[V-1 flying bomb]]s on maps of London.<ref name="gilovich" /><ref name="kv">{{cite journal|last=Kahneman|first=Daniel|author2=Amos Tversky|title=Subjective probability: A judgment of representativeness|journal=Cognitive Psychology|year=1972|volume=3|issue=3|pages=430–454|doi=10.1016/0010-0285(72)90016-3}}</ref> Although Londoners developed specific theories about the pattern of impacts within London, a statistical analysis by R. D. Clarke originally published in 1946 showed that the impacts of [[V-2 rocket]]s on London were a close fit to a random distribution.<ref>{{cite journal|last=Clarke|first=R. D.|title=An application of the Poisson distribution|journal=Journal of the Institute of Actuaries|year=1946|volume=72|issue=3|page=481|url=https://www.actuaries.org.uk/documents/application-poisson-distribution|doi=10.1017/S0020268100035435|url-access=subscription}}</ref><ref>Gilovich, 1991 p. 19</ref><ref>{{cite web|last=Mori|first=Kentaro|title=Seeing patterns|url=http://forgetomori.com/2009/skepticism/seeing-patterns/|access-date=3 March 2012}}</ref><ref>{{cite web|title=Bombing London|url=http://www.dur.ac.uk/stat.web/bomb.htm|access-date=3 March 2012|archive-url=https://web.archive.org/web/20120221221013/http://www.dur.ac.uk/stat.web/bomb.htm|archive-date=2012-02-21|url-status=dead}}</ref><ref name="tierney">{{cite news|last=Tierney|first=John|title=See a pattern on Wall Street?|url=http://tierneylab.blogs.nytimes.com/2008/10/03/see-a-pattern-here/|publisher=New York Times|work=TierneyLab|access-date=3 March 2012|format=October 3, 2008|authorlink=John Tierney (journalist)|date=3 October 2008}}</ref>

==Similar biases==
Using this [[cognitive bias]] in causal reasoning may result in the [[Texas sharpshooter fallacy]], in which differences in data are ignored and similarities are overemphasized. 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]].

==Possible causes==
[[Daniel Kahneman]] and [[Amos Tversky]] explained this kind of misprediction as being caused by the [[representativeness heuristic]]<ref name="kv"/> (which itself they also first proposed).

==See also==
* [[Apophenia]]
* [[Alignments of random points]]
* [[Complete spatial randomness]]
* [[Confirmation bias]]
* [[List of cognitive biases]]
* [[Numeracy bias]]
* [[Poisson clumping]]
* [[Poisson distribution]]
* [[Statistical randomness]]

==References==
<references />

==External links==
{{Commonscat}}
* [http://skepdic.com/clustering.html Skeptic's Dictionary: The clustering illusion]
* [http://thehothand.blogspot.com/ Hot Hand website:  Statistical analysis of sports streakiness]

{{Biases}}
{{Hidden messages}}

[[Category:Cognitive biases]]
[[Category:Statistical randomness]]
[[Category:Illusions]]
[[Category:Cluster analysis]]