Mean Absolute Deviation (MAD)
Definition
A practical Benford conformity measure that averages the absolute differences between observed and expected proportions across all leading digits, with Nigrini benchmarks classifying conformity as close, acceptable, marginal, or non-conforming.
- Measures
- Benford's Law digit conformity
- Calculation
- Average absolute difference, observed vs expected proportions
- Framework
- Nigrini benchmark thresholds
- Conformity classes
- Close, acceptable, marginal, non-conforming
Common questions
How does MAD differ from a chi-square test for Benford conformity?+
Chi-square tests statistical significance and is heavily influenced by sample size, flagging large datasets as non-conforming even for trivial deviations, while MAD measures the magnitude of deviation directly and is largely insensitive to how many records are in the dataset.
What does a marginal MAD score mean for an investigator?+
A marginal score sits between acceptable and non-conforming and signals that the digit pattern deviates enough from Benford's Law to warrant closer review of the underlying records, though it is not on its own proof of manipulation.
Related terms
- Benford's Law
- An empirical regularity in naturally occurring numerical datasets: the leading digit follows a logarithmic distribution, with 1 appearing about 30% of the...
- Chi-Square Test
- A goodness-of-fit test comparing the observed digit frequencies in a dataset to the expected Benford frequencies, producing a test statistic that is...
- Second-Digit Test
- Analysis of the second significant digit in isolation, where 0 is expected to appear about 11.97% of the time. A spike in...
- Two-Digit Test
- An extension of Benford's Law to the first two significant digits, producing 90 possible combinations each with a predicted frequency, which is...
- Z-Statistic
- A per-digit test that calculates whether the deviation between an observed frequency and the Benford expected frequency for that single digit is...