Benford's Law Forensic Accounting Calculator
Test a dataset's first-digit distribution against Benford's law using a chi-square statistic, a classic forensic-accounting red-flag test.
How to Use the Benford's Law Forensic Accounting Calculator
- Count how often digits 1 through 9 appear as the first digit in your dataset.
- Enter them as 9 comma-separated numbers.
- Click Calculate to see the chi-square and whether it departs from Benford's law.
Casos de Uso
- •Forensic audit of expense reports.
- •Early detection of invoice fabrication.
- •Academic dataset quality checks.
Fórmula
Expected P(d) = log₁₀(1 + 1/d) for d=1..9. χ² = Σ (observed − expected)² / expected. χ² > 15.51 (8 d.f.) ⇒ p < 0.05.
Preguntas Frecuentes
What is Benford's law?
In many naturally-occurring datasets (revenues, populations, expense lines), the leading digit d appears with probability log₁₀(1 + 1/d). Values above ~15.51 on an 8 d.f. chi-square test flag a statistically significant departure from this distribution.
When does Benford apply?
Best results on datasets spanning several orders of magnitude, with no imposed minimums or maximums. It does not apply to lottery numbers, assigned IDs or bounded measurements.
Disclaimer
A Benford flag is only a red-flag indicator, not proof of fraud. Combine with other forensic tests (Z-test on digits, number duplication analysis, interview).