Technology in Auditing Using Benford?s Law :: essays research papers

Technology in Auditing Using Benford’s Law What started out as a curious observation by an astronomer in 1881 has the potential to have a significant impact on the audit profession 125 years later. In 1881, the astronomer â€Å"Simon Newcomb noticed that the front pages of his logarithmic tables frayed faster than the rest of the pages†¦Ã¢â‚¬ . Newcomb concluded â€Å"the first digit is oftener 1 than any other digit†. Newcomb quantified the probability of the occurrence of the different digits as being the first digit and as well as the second digit. For the most part, Newcomb just considered it a curiosity and left it at that. (Caldwell 2004) In the 1920’s, a physicist at the GE Research Laboratories, Frank Benford, thought it more than a curiosity and conducted extensive testing of naturally occurring data and computed the expected frequencies of the digits. In Table 1, there is a table of these expected frequencies for the first four positions. Benford also determined that the data could not be constrained to only show a restricted range of numbers such as market values of stock nor could it be a set of assigned numbers such as street addresses or social security numbers. (Nigrini 1999) The underlying theory behind why this happens can be illustrated using investments as an example. If you start with an investment of $100 and assume a 5% annual return, it would be the 15th year before the value of the investment would reach $200 and therefore change the first digit value to 2. It would only take an additional 8 years to change the first digit vale to 3, an additional 6 years to change the first digit to 4, etc. Once the value of the investment grew to $1,000 the time it would take to change the first digit (going from $1,000 to $2,000) would revert back to the same pace as it took to change it from $100 to $200. Unconstrained naturally occurring numbers will follow this pattern with remarkable predictability. (Ettredge and Srivastava 1998) In 1961, Roger Pinkham tested and proved that Benford’s law was scale invariant and therefore would apply to any unit of measure and any type currency. In the 1990’s, Dr Mark Nigrini discovered a powerful auditing tool using Benford’s law. He was able to determine that most people assume that the first digit of numbers would be distributed equally amount the digits and that people that make up numbers tend to use numbers starting with digits in the mid range (5, 6, 7).