Law of Truly Large Numbers

Law of Truly Large Numbers

The Law of Truly Large Numbers, attributed to Persi Diaconis and Frederick Mosteller, states that with a sample size large enough, any outrageous thing is likely to happen. It seeks to debunk one element of supposed supernatural phenomenology.

Here is a simplified example of the law:

Assume that a given event happens with a likelihood of 0.1% in one occurrence. For it not to happen in a sample of 1000 occurrences would require a probability of 0.999 to the power of 1000, a probability of 36.8%. This means that this individually unlikely event has a probability of 63.2% of happening if 1000 chances are given. In other words, even given a highly unlikely event, the chance that it never happens, given enough time, is even less likely.

Because we never find it notable when the likely thing happens, we highlight unlikely events and notice them more.

In pseudoscience

The law comes up in pseudoscience and is sometimes called the Jeane Dixon effect (see also Postdiction). It holds that the more predictions a psychic makes, the better the odds that one of them will "hit." Thus, if one comes true, the psychic expects us to forget the vast majority which did not happen.

Humans can be susceptible to this fallacy. A similar manifestation can be found in gambling, where gamblers tend to remember their wins and forget their losses and thus hold an inflated view of their real winnings.

ee also

*Coincidence
*Large numbers
*Law of large numbers
*Law of small numbers
*Littlewood's law
*Miracle
*Psychic phenomena

External links

* [http://skepdic.com/lawofnumbers.html skepdic.com on the "Law of Truly Large Numbers"]
* [http://mathworld.wolfram.com/LawofTrulyLargeNumbers.html mathworld.wolfram.com on the "Law of Truly Large Numbers"]
* [http://www.quackwatch.org/04ConsumerEducation/coincidence.html on the "Law of Truly Large Numbers"]


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