23 September, 2010

Benford's law

In 1881 the American astronomer Simon Newcomb noticed that in books of logarithm tables first pages (logarithms of numbers starting with 1) are much more worn than others. This means that  people look up numbers starting with 1 more often than higher ones, which is a pretty weird result.

This effect was rediscovered in 1938 by Frank Benford, who checked it for different real data sets, and it's called Benford's law since then.

The thing is that such a distribution of numbers arises if their logarithms are distributed uniformly, like it's equally probable to find a value between 10 and 100 and between 100 and 1000. This is the case for most of real world statistics, such as distributions of salaries or building heights.

Well, I'm writing about all that because in 1972 the law was proposed to detect fraud in statistics, because people who make up their data tend to distribute numbers pretty much uniformly. For instance, Benford's law was used as an evidence of falsifications in the 2009 Iranian elections.

Be careful if you're making up your experimental data :-)


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