Benford's Law (2-Digit)
Extend the leading-digit test to the second digit, as supporting analytics against approval thresholds.
- General ledger alone
How the result is read
Structuring amounts just under an approval limit clusters the second digit, but the reverse does not follow — price points, rounded contract values and converted foreign amounts all bend the distribution without anyone structuring anything. So the digit distribution is not the finding. The evidential procedure is the direct comparison against the delegation-of-authority thresholds actually in force.
The worksheet, on the demo engagement
Benford 2nd Digit, as the application draws it for Harrow Precision Engineering Ltd, the fictional demo engagement — one row per second significant digit, 0 to 9.
- Observed
- Benford ±2pp
- Outside band
Band is ±2pp around expectation. The digit-4 excess is where the threshold-avoidance population sits.
- n
- 188,402
- Chi-square (2nd digit)
- 198.4
- MAD
- 0.009
- Key spike
- Digit 4 — 24xx / 49xx pattern
2nd-digit Benford. Digit 4 over-represented: amounts cluster just below 25,000 and 50,000 DOA limits, confirming threshold avoidance.
Result grid6 of 10 rows
| 2nd digit | Observed % | Expected % | Z-score | Key amount cluster | Flag |
|---|---|---|---|---|---|
| 0 | 11.2% | 12.0% | 1.3 | — | |
| 1 | 11.1% | 11.4% | 0.6 | — | |
| 2 | 10.9% | 10.9% | +0.0 | — | |
| 3 | 10.5% | 10.4% | +0.1 | — | |
| 4 | 14.8% | 10.0% | +8.9 | 2,4xx x4,950 · 4,9xx x2,311 | threshold avoidance — 25k & 50k limits |
| 5 | 9.4% | 9.7% | 0.5 | — |
In the application
Benford's Law (2-Digit) is filed under Journal entries, index letter B. "Run all analyses" runs it with every other analysis the ledger can answer. The worksheet states the population it tested on its face — or "Not applicable" with the reason when a column it depends on is empty — and the Excel workbook the engagement exports files it under B, beside an index of the source files with their SHA-256 fingerprints.
Also listed in the application as Benford 2nd Digit
.
Read it with
Run your next audit file test without the Excel crash.
One free engagement to evaluate, valid 60 days. The ledger never leaves the machine.
- 20 minutes
- Runs on a fictional engagement
- No client data required