The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed.[1] Because we never find it notable when likely events occur, we highlight unlikely events and notice them more. The law is often used to falsify different pseudo-scientific claims; as such, it is sometimes criticized by fringe scientists.[2][3]
The law is meant to make a statement about probabilities and statistical significance: in large enough masses of statistical data, even minuscule fluctuations attain statistical significance. Thus in truly large numbers of observations, it is paradoxically easy to find significant correlations, in large numbers, which still do not lead to causal theories (see: spurious correlation), and which by their collective number,[4] might lead to obfuscation as well.
The law can be rephrased as "large numbers also deceive", something which is counter-intuitive to a descriptive statistician. More concretely, skeptic Penn Jillette has said, "Million-to-one odds happen eight times a day in New York" (population about 8,000,000).[5]
^Everitt 2002
^Beitman, Bernard D., (15 Apr 2018), Intrigued by the Low Probability of Synchronicities? Coincidence theorists and statisticians dispute the meaning of rare events. at PsychologyToday
^Sharon Hewitt Rawlette, (2019), Coincidence or Psi? The Epistemic Import of Spontaneous Cases of Purported Psi Identified Post-Verification, Journal of Scientific Exploration, Vol. 33, No. 1, pp. 9–42[unreliable source?]
^Tyler Vigen, 2015, Spurious Correlations Correlation does not equal causation, book website with examples
^Kida, Thomas E. (Thomas Edward) (2006). Don't believe everything you think : the 6 basic mistakes we make in thinking. Amherst, N.Y.: Prometheus Books. p. 97. ISBN 1615920056. OCLC 1019454221.
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