benford's law
Noun: A statistical principle stating that in many naturally occurring collections of numbers, the leading digit is likely to be small. Specifically, it predicts the frequency distribution of the first digits (1 through 9) in such datasets, where 1 appears as the first digit about 30.1% of the time, and 9 appears only about 4.6% of the time. It is often used as a tool to detect anomalies in datasets.
Benford's Law is applied to analyze datasets that span several orders of magnitude and are not artificially constrained (like human-set numbers). It is a tool for forensic analysis. - Primary Use: To test the authenticity or naturalness of a dataset. - Typical Contexts: Auditing financial data, checking election results, analyzing scientific data, or detecting tax fraud.
- In Auditing:
- In Data Science:
- General Statement:
- "To follow Benford's Law": Describes a dataset whose first-digit distribution matches the predicted probabilities.
- Genuine accounting data from a large corporation is expected to follow Benford's Law.
- "To violate Benford's Law": Describes a dataset whose first-digit distribution significantly deviates from the predicted pattern, often suggesting human intervention or fabrication.
- The investigator suspected fraud because the submitted expense reports clearly violated Benford's Law.
- First-Digit Law: Another name for Benford's Law.
- Newcomb–Benford Law: A historical variant acknowledging the earlier work of astronomer Simon Newcomb.
- Benford Analysis: The process of applying Benford's Law to a dataset.
- First-digit phenomenon: A descriptive synonym emphasizing the observed pattern.
- Digital analysis: A broader term for techniques analyzing digit patterns, often referencing Benford's Law.
- "To pass the Benford test": An informal phrase meaning a dataset's digit distribution is consistent with the law, implying it appears natural.
- After the audit, the ledger was said to pass the Benford test.
- a law used by auditors to identify fictitious populations of numbers; applies to any population of numbers derived from other numbers
- Benford's law holds that 30% of the time the first non-zero digit of a derived number will be 1 and it will be 9 only 4.6% of the time