Second-Digit Test
Definition
Analysis of the second significant digit in isolation, where 0 is expected to appear about 11.97% of the time. A spike in 0 or 5 as second digits often signals rounding to pleasing numbers.
- Basis
- Benford's Law expected frequency of the second digit
- Expected frequency of 0
- About 11.97 percent
- Red flag pattern
- Spike in 0 or 5 as second digits
- Interpretation
- Suggests rounding to pleasing or approximate numbers
Common questions
Why does a spike in second-digit 0 or 5 suggest manipulation rather than genuine data?+
Numbers that occur naturally, such as transaction amounts drawn from real business activity, rarely cluster around round figures, but a person fabricating or estimating figures tends unconsciously to pick numbers ending near 0 or 5, so an unusual concentration there is a marker of human-generated rather than organically occurring data.
How does the second-digit test complement the more commonly used first-digit test?+
The first-digit test catches gross distortions in overall magnitude, but skilled manipulators sometimes anticipate first-digit scrutiny and adjust only the trailing digits, so the second-digit test catches a different and subtler form of tampering that the first-digit analysis alone would miss.
Does a deviation from the expected second-digit frequency prove fraud on its own?+
No, deviations can also arise from legitimate business patterns, such as prices set at round numbers by policy, so a second-digit anomaly is a prompt for further investigation and sampling, not standalone proof that fraud occurred.
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...
- Mean Absolute Deviation (MAD)
- A practical Benford conformity measure that averages the absolute differences between observed and expected proportions across all leading digits, with Nigrini benchmarks...
- 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...