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

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.