Chapter 4 begins with a discussion of the types and kinds of data most suitable for an analysis that uses the Benford probability distribution. Next we describe an R computer program – program Benford – designed to evaluate observed data for agreement with the Benford probability distribution; and we give an example of output from the program using a typical dataset. We then move to an overview of our workflow of Benford agreement analyses where we outline our process for assessing the validity of data using Benford agreement analyses. We end the chapter with a discussion of the concept of Benford validity, which we will employ in subsequent chapters.

Chapter 3 describes and illustrates the Benford probability distribution. A brief summary of the origin and evolution of the Benford distribution is drawn and the development and assessment of various measures of goodness of fit between an empirical distribution and the Benford distribution are described and illustrated. These masures are Pearson’s chi-squared, Wilks’ likelihood-ratio, Hardy and Ramanujan’s partition theory, Fisher’s exact test, Kuiper’s measure, Tam Cho and Gaines’ d measure, Cohen’s w measure, and Nigrini’s MAD measure.