| Digit | Count | Actual | Expected | Difference |
|---|---|---|---|---|
| 1 | 11 | 55.0% | 30.1% | 24.9 pts |
| 2 | 3 | 15.0% | 17.6% | -2.6 pts |
| 3 | 2 | 10.0% | 12.5% | -2.5 pts |
| 4 | 1 | 5.0% | 9.7% | -4.7 pts |
| 5 | 1 | 5.0% | 7.9% | -2.9 pts |
| 6 | 1 | 5.0% | 6.7% | -1.7 pts |
| 7 | 0 | 0.0% | 5.8% | -5.8 pts |
| 8 | 0 | 0.0% | 5.1% | -5.1 pts |
| 9 | 1 | 5.0% | 4.6% | 0.4 pts |
Background reading: what is a forensic audit and the forensic audit guide.
Benford's law says that in many naturally occurring sets of numbers, the first digit is not spread evenly. The digit 1 leads about 30.1% of the time, 2 about 17.6%, and 9 only about 4.6%. The expected share of digit d is log10(1 + 1/d).
The checker counts the first digit of each amount you paste, compares the actual share of each digit with the expected share, and reports two measures. Chi-squared adds up the squared gaps between the actual and expected counts, scaled by the expected counts. With eight degrees of freedom, a value above 15.507 rejects conformity at the 5% level and above 20.090 at the 1% level. The mean absolute deviation averages the gaps between the actual and expected percentages, and is read against bands from the forensic accounting literature: up to 0.006 is close conformity, up to 0.012 acceptable, up to 0.015 marginal, and above that is non-conformity.
A departure is a prompt to look closer. It is not proof of error or fraud, and a conforming result does not prove the figures are right. The test suits large populations of amounts that span several orders of magnitude, such as invoices, payments or journal entries.
An auditor pastes twenty invoice amounts. Eleven start with 1, four with 2, two with 3, and one each with 4, 5 and 6. Is the pattern in line with Benford?
