# Benford's Law Cutoffs: Nigrini Mean Absolute Deviation (MAD) 0.0012–0.0022: Flag or Clear?

Hunter Gibson · October 26, 2026

> Compare Nigrini MAD thresholds 0.0012, 0.0018, and 0.0022 for Benford's Law tests, and learn how to verify the live complete option before committing.

This guide compares Nigrini MAD conformity thresholds of 0.0012, 0.0018, and 0.0022 for Benford's Law tests.

It shows how to verify the live, complete option before committing.

![This guide compares Nigrini MAD conformity thresholds of — Benford's Law Cutoffs](https://static.mm-ais.com/article-images-ai/benford-s-law-cutoffs-nigrini-mean-absol-ai-a58b9f2e.jpg)

## How It Works

In continuous audit monitoring, Benford’s Law is applied to a complete numeric population—such as invoice amounts or journal-entry values—by comparing how often each leading digit or digit pair actually appears with the frequency Benford predicts. The mechanism is a frequency comparison, not a single-transaction test: the system counts observed digit frequencies, computes expected frequencies from Benford’s formula, and summarizes the gap with the mean absolute deviation (MAD). A lower MAD means the population’s digit pattern is closer to the expected pattern. Before any threshold is applied, verify that the extract is complete and current; a partial or stale population can make a normal pattern look nonconforming or hide a real anomaly.

For a first-digit test, Benford’s expected proportion for digit d is log10(1 + 1/d), so the nine categories are 1 through 9. For a first-two-digit test, the expected proportion for the two-digit number ab is log10(1 + 1/(10a + b)), giving 90 categories from 10 through 99. MAD is the average of the absolute differences between observed and expected proportions across all categories in the chosen test. Because the number of categories differs, a first-digit MAD and a first-two-digit MAD are not directly comparable; compare only like-for-like tests on like-for-like populations.

The cutoffs 0.0012, 0.0018, and 0.0022 are the MAD conformity thresholds this guide compares. They are read as bands: a MAD at or below 0.0012 indicates close conformity, a MAD above 0.0012 but at or below 0.0018 indicates acceptable conformity, and a MAD above 0.0018 but at or below 0.0022 indicates marginal conformity. A MAD above 0.0022 is treated as nonconformity. These labels are grading conventions, not proof of error; they tell the monitor where to prioritize review. Confirm the band definitions against your own written monitoring terms before applying them.

| MAD cutoff | Common conformity label |
| --- | --- |
| ≤ 0.0012 | Close conformity |
| > 0.0012 to ≤ 0.0018 | Acceptable conformity |
| > 0.0018 to ≤ 0.0022 | Marginal conformity |
| > 0.0022 | Nonconformity |

Key terms: population is the complete set of numeric values in the tested window; window is the fixed period or batch being monitored; digit position is whether the test uses the first digit or first two digits; observed proportion is the actual share of values in a digit category; expected proportion is the Benford-predicted share; MAD is the average absolute gap between those shares; cutoff is the MAD value used to assign a conformity band; flag is a signal that the population exceeded the selected cutoff; false positive is a flag caused by data quality, rounding, or population structure rather than a substantive issue; baseline is the MAD level historically observed for that population under stable conditions.

To use the thresholds correctly, keep the comparison like-for-like: same population definition, same digit position, same window length, and the same completeness standard. A threshold should be committed only after verifying the live, complete option—meaning the full current extract, not a sample, partial file, or prior-period substitute. If any of those elements changes, recompute the MAD and re-evaluate the cutoff rather than carrying forward an old result.

![How It Works — Benford's Law Cutoffs](https://static.mm-ais.com/article-images-ai/benford-s-law-cutoffs-nigrini-mean-absol-ai-c0958e02.jpg)

## Key Factors to Consider

Before committing to any Nigrini MAD conformity cutoff, verify the live, complete option and compare like-for-like totals and terms. The decision should be made on the population that will actually be monitored, not on a convenient extract or a prior-period proxy.

The first criterion is population completeness. Confirm that every in-scope record is included, duplicates are removed or explained, excluded strata are documented, and the date range, entity set, and account population match the monitoring objective. If the population changes, the cutoff decision must be reopened.

The second criterion is like-for-like totals. Compare totals on identical bases: the same currency, rounding convention, tax treatment, credit and debit netting, and adjustment status. A cutoff is only meaningful when the numerator and denominator describe the same complete population.

The third criterion is term consistency. Define the MAD measure, digit-test level, conformity label, and action threshold in writing before results are reviewed, and use those same terms across every run. Changing labels after seeing results turns a threshold into a moving target.

A second mistake is comparing MAD results across populations that are not comparable. For example, comparing a small department’s journal-entry MAD with a company-wide invoice MAD, or comparing a population with many repeated fixed amounts against one with varied amounts, can make one look worse even when both are acceptable. The cutoff is not a universal score; it is a conformity screen for a defined population.

The check is to compare only populations with the same definition, period length, and amount construction, and to review the underlying digit frequencies before escalating. If the population changed, re-baseline rather than reuse an old threshold decision. This prevents a cutoff from being treated as a pass/fail label for unlike data.

![Key Factors to Consider — Benford's Law Cutoffs](https://static.mm-ais.com/article-images-pixabay/benford-s-law-cutoffs-nigrini-mean-absol-b887257b.jpg)

## Insider Tactics

A non-obvious strategy is to run a candidate cutoff in shadow mode against the currently live cutoff on the same complete population, then require the improvement to persist across two consecutive complete populations before committing. A single-period MAD movement can reflect posting timing or a one-time batch, so the shadow run should use the same population definition, digit test, and period boundaries as the live rule.

Timing matters as much as the cutoff value: calculate after the period's posting window is closed and reconciliations are complete, but before the monitoring rule is locked. If late-posted entries arrive, rerun on the updated complete population instead of adjusting or patching the earlier result.

Separate completeness verification from conformity interpretation. Before reading MAD, confirm that the extracted record count and total amount match the live ledger for the same period. If they do not match, treat the MAD result as invalid and stop; do not compare it with a prior period or with another cutoff.

When comparing the 0.0012, 0.0018, and 0.0022 cutoffs, keep the comparison like-for-like: same population, same digit test, same period, and documented live-versus-candidate status. Mixing a candidate cutoff's result with a baseline from a different population or period turns a threshold choice into an apples-to-oranges decision.

Commit during low-change windows, such as after month-end close, and avoid locking a new cutoff during partial-month activity or mid-quarter adjustments. If the business introduces a new invoice series, vendor population, or entry type, reset the baseline and re-establish the comparison before evaluating any cutoff change.

Keep an audit trail of the exact extract timestamp, population filters, and cutoff in force for each run. That record lets a reviewer verify that a committed change was based on a complete population and a like-for-like comparison rather than on a convenient extract.

![Insider Tactics — Benford's Law Cutoffs](https://static.mm-ais.com/article-images-pixabay/benford-s-law-cutoffs-nigrini-mean-absol-18bfe2aa.jpg)

## Comparison

Compared on the same complete population and the same first-two-digit Benford test, the three cutoffs are not interchangeable: 0.0012 demands the tightest conformity, 0.0018 is the middle gate, and 0.0022 is the loosest gate that still counts as marginal conformity.

| Cutoff | Conformity band | Gap from prior cutoff | Wins when |
| --- | --- | --- | --- |
| 0.0012 | Close | — | You can review every exception and want the earliest signal |
| 0.0018 | Acceptable | 0.0006 | You need a reviewable queue and a defensible default |
| 0.0022 | Marginally acceptable | 0.0004 | Volume or noise is high and only large deviations matter |

A MAD of 0.0015 exceeds 0.0012 but falls within 0.0018 and 0.0022; a MAD of 0.0020 exceeds 0.0012 and 0.0018 but falls within 0.0022; a MAD of 0.0024 exceeds all three. Those three outcomes show that the middle cutoff is the hinge: it separates a reviewable exception from a marginal one.

The distance between 0.0012 and 0.0018 is 0.0006, while the distance between 0.0018 and 0.0022 is 0.0004. That asymmetry matters: moving from close to acceptable adds 0.0006 of MAD room, which is 50% of the 0.0012 cutoff, whereas moving from acceptable to marginal adds 0.0004, which is about 22% of the 0.0018 cutoff. The middle cutoff is therefore closer to the strict end than to the loose end.

0.0012 wins in a low-volume, high-risk population where every exception can be cleared and the cost of a missed anomaly exceeds review time. 0.0022 wins in a high-volume population where the MAD is driven by benign rounding, tax, or currency effects and the team can only investigate the largest deviations. 0.0018 wins when the program must set one standing threshold for continuous monitoring and cannot retune it for every population.

For a single standing cutoff, 0.0018 is the recommended default, because it leaves both a stricter (0.0012) and a looser (0.0022) escalation step available. Verify this choice against the live, complete population and like-for-like totals before committing.

Compare the three on identical totals, periods, and digit tests; if the population changes, rerun all three rather than carrying over a prior MAD.

## Frequently Asked Questions

**Which Nigrini MAD conformity thresholds does the guide compare for Benford's Law tests?**

The guide compares Nigrini MAD conformity thresholds of 0.0012, 0.0018, and 0.0022 for Benford's Law tests.

**What must be verified before any threshold is applied?**

Before any threshold is applied, verify that the extract is complete and current.

**What can a partial or stale population do to the apparent pattern?**

A partial or stale population can make a normal pattern look nonconforming or hide a real anomaly.

**What does a lower MAD indicate?**

A lower MAD means the population’s digit pattern is closer to the expected pattern.

**How is MAD defined in the chosen test?**

MAD is the average of the absolute differences between observed and expected proportions across all categories in the chosen test.

**What is Benford's expected proportion for a first-digit test?**

For a first-digit test, Benford’s expected proportion for digit d is log10(1 + 1/d), so the nine categories are 1 through 9.

## Quick answers

| Which Nigrini MAD conformity thresholds does this guide compare? | The guide compares Nigrini MAD conformity thresholds of 0.0012, 0.0018, and 0.0022 for Benford's Law tests. |
| --- | --- |
| What should be verified before any threshold is applied? | Before any threshold is applied, verify that the extract is complete and current. |
| What does a lower MAD indicate? | A lower MAD means the population's digit pattern is closer to the expected pattern. |
| How many categories does a first-digit test have? | For a first-digit test, the nine categories are 1 through 9. |
| How many categories does a first-two-digit test have? | For a first-two-digit test, there are 90 categories from 10 through 99. |

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