Can Benford’s Law Detect Tax Fraud?

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.

The chi-square test has the following steps:

• determine the expected frequency of the first digit;
• determine the observed frequency of the first digit;
• calculate the difference between the observed and expected frequencies;
• square the difference (to eliminate distortion from negative numbers);
• divide the result by the number of expected frequencies.

When the value computed by the chi-square test exceeds a predetermined critical value, it is appropriate to accept the hypothesis of tax fraud.