Minimum sample size requirements for applying Benford’s law

Dept. of Electrical Power Engineering, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Košice, Slovakia

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Published online: 11 June 2026

Abstract

Benford’s law explains the characteristic probability distribution of leading digits observed in many naturally occurring datasets. When data are artificially modified or manipulated, this distribution typically diverges from the theoretical expectation. Consequently, Benford-based techniques are valuable for detecting irregularities that suggest non-natural data alterations. This study provides a concise explanation of the theoretical background of Benford’s law and summarizes its essential features. It then examines statistical conformity tests employed to identify discrepancies between altered and original datasets. The analyzed data originate from electricity consumption meters. The findings illustrate how artificially modified datasets align or fail to align with Benford’s distribution through simulations involving exceptionally small sample sizes. These limited samples intentionally challenge standard assumptions of conformity, offering insight into the law’s robustness under constrained data conditions.