Testing for Benford's Law in very small samples: Simulation study and a new test proposal

Area of Science:

• Statistics
• Data Analysis
• Fraud Detection

Background:

• Benford's Law describes expected digit distributions in natural datasets.
• Deviations from Benford's Law can indicate data manipulation or fraud.
• Reliability of conformity tests is questionable with small sample sizes.

Purpose of the Study:

• To analyze and compare Benford conformity tests on small datasets using Monte Carlo simulations.
• To develop a novel, robust testing procedure for small samples.
• To demonstrate the practical utility of Benford testing in anti-fraud efforts.

Main Methods:

• Extensive Monte Carlo simulations were performed.
• Various conformity tests and alternative distributions were analyzed.
• A new testing procedure was developed by combining three existing tests.

Main Results:

• The study assessed the performance of different Benford conformity tests under small sample conditions.
• Simulation results informed the design of a new, more powerful testing procedure.
• The proposed method demonstrated effectiveness across diverse alternative scenarios.

Conclusions:

• Benford conformity testing is vital for identifying anomalies in small datasets.
• The new combined testing procedure offers improved power and reliability.
• This approach is valuable for anti-fraud investigations requiring robust data validation.