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Benford's law (first-digit audit)

Benford's law analysis compares leading-digit frequencies against log₁₀(1 + 1/d), with a chi-square test and Nigrini's MAD conformity bands — a data-auditing screen.

What is Benford's law (first-digit audit)?

Naturally occurring, multi-magnitude data (payments, populations, expenses) tend to have first digit d with probability log₁₀(1 + 1/d): 30.1% ones down to 4.6% nines. Fabricated or constrained numbers rarely respect this.

The chi-square GoF is sample-size sensitive (huge n flags trivial deviations), so Nigrini's mean-absolute-deviation bands are the audit standard: < 0.006 close, < 0.012 acceptable, < 0.015 marginal, above = nonconformity.

Only the first-digit test is implemented (the workhorse); the full audit-sampling workflow is out of scope.

When should I use Benford's law (first-digit audit)?

Screening expenses, invoices, or reported counts for anomalies.
Data-quality checks on collected numeric data spanning several orders of magnitude.

What data does it need?

One numeric column (nonzero values; sign ignored).

What does it report?

Observed vs expected digit distribution (chart + proportions), chi-square + p, MAD + conformity verdict.

What does it assume?

Data span multiple orders of magnitude without artificial bounds (prices clustered at 9.99, assigned IDs, or capped values violate the premise).

How do I interpret the result?

Nonconformity means look closer, not fraud: legitimate constraints (price points, minimum orders) also break Benford.

References

Nigrini (2012). Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection.