Clustering illusion

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Random distribution of 10,000 points in which clusters are recognizable, the occurring patterns are created randomly. The recognition of a non-randomly distributed pattern would be a clustering illusion.

The clustering illusion (of English cluster , cluster ' ) describes the human characteristic, random patterns that inevitably occur in sufficiently large amounts of data to attribute meanings. The clustering illusion arises, among other things, due to the human representativeness heuristic and the confirmation error .

Examples

For example, most people consider the sequence “OXXXOXXXOXXOOOXOOXXOO” to be non- random , although in reality it has many properties that one would expect in a real random data stream, such as the same frequency of the two events and the fact that the number of the same symbols directly adjacent is the same for each of the two symbols. Obviously, the viewers of such sequences expect a greater variety than the statistical prediction would suggest. In fact, apparently non-random series are quite likely in short series of experiments . Whether or not a data set contains patterns can often be decided using statistical analysis tools or even computer-aided cryptanalysis . For example, the sequence “XXOXOXOOOXOXOOOXOX” contains a recognizable pattern: the position of the X corresponds to the prime numbers from 2 and that of the O corresponds to the non- prime numbers . Computer programs for data compression are suitable for recognizing patterns in the data and replacing them with alternative references from which the correct algorithm can restore the original data. Large amounts of data that contain non-random clusters can usually be compressed well. On the other hand, data without real accumulations or patterns are rather difficult or impossible to compress.

The clustering illusion is part of a study by Thomas Gilovich , Robert Vallone and Amos Tversky . The hot hand , lucky streaks of the throwers in basketball, was identified as coincidental. However, recent research on a broad database indicates that a hot-hand effect can actually be demonstrated with an increased hit probability in the range of 1.2 to 2.4 percent. Although theories about the patterns of the impacted V2 rockets were developed in London after World War II , RD Clarke was able to show that the distribution fits a random distribution.

The so-called leukemia cluster Elbmarsch , in which individual cases of leukemia in the Elbmarsch nuclear power plants were assigned, is also an example of a correspondingly incorrect attribution of meaning for a pattern that is not perceived as random. The possible randomness is not an exclusion criterion for possibly underestimated concrete causes. A well-known example is the appearance of military passwords such as Dieppe , Omaha , Utah and Mulberry prior to related military operations in crossword puzzles in the British Daily Telegraph during World War II. The author of the crossword puzzles, headmaster in his main profession, was therefore initially suspected and questioned by the secret service, but the synchronicity of the puzzle term and military operation was considered a coincidence. In fact, as it turned out later, he had had his puzzle templates filled out by students who had picked up passwords from soldiers.

Another example is the questions from the SAT (an important multiple-choice entry test for American students). They are deliberately chosen by the test developers in such a way that no longer series of identical answers occur, because experience has shown that the students consider such series to be unlikely. Candidates may feel compelled to give wrong answers just to avoid a series. Further variants of the clustering illusion are e.g. B. the pareidolia in the recognition of faces on objects or the apophenia in schizophrenia .

Individual evidence

  1. ^ David Aronson: Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals. In: Volume 274 by Wiley Trading. John Wiley & Sons, 2011. ISBN 978-1-118-16058-9 . Chapter 2: The intuitive judgment and the role of heuristics.
  2. ^ T. Gilovich: How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life. The Free Press, New York 1993, ISBN 0-02-911706-2 .
  3. ↑ T. Gilovich, R. Vallone, A. Tversky: The hot hand in basketball: On the misperception of random sequences. In: Cognitive Psychology. Volume 17, 1985, pp. 295-314.
  4. ↑ A. Bocskocsky, J. Ezekowitz, C. Stein: The hot hand: A new approach to an old 'fallacy' . 8th Annual With Sloan Sports Analytics Conference. 2014.
  5. ^ RD Clarke: An application of the Poisson distribution. In: Journal of the Institute of Actuaries (1946), Volume 72, p. 481. (PDF)
  6. ^ A b Hans-Hermann Dubben, Hans-Peter Beck-Bornholdt: The dog that lays eggs: Recognizing misinformation through lateral thinking . Rowohlt E-Book, 2011, ISBN 978-3-644-44011-1 ( google.com [accessed October 15, 2015]).
  7. ↑ a b Who put secret D-Day clues in the 'Telegraph' crossword? In: Telegraph.co.uk. Retrieved October 16, 2015 .

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