Conference Program Home
  My Program

All Times EDT

Abstract Details

Activity Number: 199 - Computation Meets Testing for Financial Data
Type: Contributed
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: Business and Economic Statistics Section
Abstract #323301
Title: Severe Testing of Benford’s Law
Author(s): Roy Cerqueti and Claudio Lupi*
Companies: La Sapienza University of Rome and University of Molise
Keywords: Benford’s law; Severity; Goodness of fit
Abstract:

Benford’s law is used in practice to support decisions in different contexts, including assessing the existence of data manipulation or fraud. These decisions must rely on well founded tests of data conformity with Benford’s law. However, many authors have argued against using conventional statistical tests to assess data conformity with Benford’s distribution, because of their “excess power” in the presence of large data sets. Alternative decision criteria, such as the mean absolute deviation (MAD), have been proposed in the literature; however, they seem to lack firm statistical foundations. This paper addresses the excess power controversy in the literature related to Benford’s law testing. We show that the severity principle (Mayo & Spanos, 2006) can and should be used to assess data “Benford-ness”. In order to do so, we also derive the asymptotic distribution of the MAD statistic and propose an asymptotically normal test to which the severity principle can be easily applied. Finally, we carry out severe testing of Benford’s law on six controversial data sets and we show that in three data sets out of six the estimated digit frequencies deviate substantially from Benford’s law.


Authors who are presenting talks have a * after their name.

Back to the full JSM 2022 program