Forensic Analytics, 2nd Edition

CHAPTER 4Benford's Law: Advanced Topics

CHAPTER 3 REVIEWED THE HISTORY of Benford's Law, explained the bases for expecting conformity to Benford, showed some accounting-related results, and showed how to run the tests in Excel and Access. This chapter discusses how to quantify the level of conformity to Benford, reviews some cases that resulted in valuable findings from the tests, and introduces the relatively new second-order test. The chapter also stresses that conformity to Benford is not a guarantee that there are no anomalies or material misstatements. It seems that assessing the goodness-of-fit (the conformity) of our data to Benford should be a straightforward matter. That task is complicated by the fact that we are usually dealing with large data sets, and in those circumstances even small deviations from Benford are statistically significant.

There are two ways to look at conformity. We can test whether a specific first-two digit combination deviates significantly from Benford. We can also test whether the digit combinations (10, 11, 12, …, 99) taken together conform to Benford. This chapter starts with the caveat that compliant data does not mean that there are no errors and we then move on to a series of advanced Benford-related topics.

CONFORMITY AND THE LIKELIHOOD OF MATERIAL ERRORS

Conformity to Benford is not a guarantee that our data is free of anomalies or material errors. This section is an adaptation of the chapter by Cleary and Thibodeau in Miller (2015). ...