Testing for Benford's Law: A Monte Carlo Comparison of Methods

21 Pages Posted: 6 Jan 2015

See all articles by Dieter Joenssen

Dieter Joenssen

Ilmenau University of Technology - Department of Quantitative Methods for Economics

Date Written: November 25, 2014

Abstract

Testing data for conformity to Benford's law is used not only by auditors exploiting a numerical phenomenon to detect fraudulently reported data. Operationally goodness-of-fit tests are used to conclude if data that should, does indeed comply with Benford's law. Naturally, not all statistical tests share the same sensitivity for detecting departures from the null-hypothesis, and thus the test choice is of central importance.

This study compares seven tests for Benford's law common in literature. These tests are presented together with the critical values required for statistical hypothesis testing. The procedures are compared in terms of their power, at a significance level of 5%, versus 16 alternative distributions covering a wide range of possible deviations. Even though no test consistently dominated all other tests, results show, amongst other findings, that the current method of choice, the Chi^2-test, is consistently outperformed by Watson's-U^2 statistic.

Keywords: Benford's law, Power comparison, Goodness-of-fit tests, Fraud detection, Data manipulation

JEL Classification: M41, C12, C15

Suggested Citation

Joenssen, Dieter, Testing for Benford's Law: A Monte Carlo Comparison of Methods (November 25, 2014). Available at SSRN: https://ssrn.com/abstract=2545243 or http://dx.doi.org/10.2139/ssrn.2545243

Dieter Joenssen (Contact Author)

Ilmenau University of Technology - Department of Quantitative Methods for Economics ( email )

Helmholtzplatz 3
Ilmenau, 98693
Germany

HOME PAGE: http://www.tu-ilmenau.de/qme/mitarbeiter/dieter-w-joenssen/

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