Abstract:
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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.
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