Chapter 5 reviewed the history of Benford's Law, some possible uses for the results of our tests, and how to run the first-two digits test in Access. The focus of this chapter is on ways to assess the conformity of a data set to Benford's Law. The focus of our attention is Benford's Law, but these methods can be used for conformity to other expected values. We have many statistical methods and the concept of significance so it would seem that assessing the goodness of fit of our data to Benford's Law is a straightforward matter. However, our task is complicated by the fact that we are usually dealing with large data sets where even small deviations from the expected pattern are statistically significant.
Prior to the mid-1990s there was not much of a need to address conformity criteria. Most research papers used relatively small data sets. An exception to this rule was Thomas (1989) who analyzed 69,000 positive earnings numbers and 11,000 negative earnings numbers. In his study the Z-statistic worked well for the test of the first-two digits. The chapter reviews the tests described in most statistics books that would work well for smaller data sets. Thereafter we examine some of the mathematical properties of Benford's Law and the “best” test is suggested based on these properties. The conformity tests are demonstrated using both Access and Excel.
For the first-two digit test there are two ways to look at conformity. The first way is ...