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. For instance, it strikes many as unexpected if, in a series of 20 coin flips, 4 heads come up in a row, but in reality the odds of that happening are almost 50%.[1][a]46.2% using the binomial probability formula. The illusion is caused by the human tendency to underestimate the amount of variability likely to appear in a small sample of random or pseudorandom data; the law of averages only ensures that there will be the expected 50-50 split after a large number of coin tosses.[2]
Some might perceive patterns in stock market price fluctuations over time,[3] or clusters in two-dimensional data such as the impact locations of the Second World War V-1 flying bombs and V-2 rockets on maps of London. But despite the theories of many Londoners, a post-war statistical analysis of the data showed that the impacts of those weapons on London were a close fit to a random distribution.[2]
The clustering illusion has much in common with the fallacy of division, the assumption that the characteristics of a large population will be replicated in all of its subsets.[1]
See also
- Sample size fallacyFailure to consider sample size when estimating the probability of obtaining a particular value drawn from a known population.
