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Benford’s law can uncover fictitious numbers in random data sets because data manipulated for tax evasion purposes will likely deviate from Benford’s law, and in that case it is supposed that there had been a tax fraud act.
The difference between the expected and observed frequencies is determined through use of a chi-square test. A chi-square statistic measures how a model of expectations compares with actual observed data.
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The chi-square test has the following steps:
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In a number set 0 to 99
11% of the numbers start with 1. Likewise, with every other digit from 2 to 9.
In a number set 0 to 199
more than 50% of the numbers start with 1 and less than 6% start with 2 to 9.
In a number set 0 to 299
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Benford’s law is an observation about the distribution of first digits in unmanipulated numerical data sets. Benford’s law states that the first digit in naturally occurring collections of numbers is more likely to be small than large.
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