Using Enron to explain Bedford’s law of forensics statistics

Some frauds are sometimes easier to uncover. For example, in a recent Iranian presidential election, the governing candidate led by 2 to 1 votes all night. Next to no variation despite returns coming in from the more liberal cities and the rather conservative country ballot boxes.

Bedford’s law is used to uncover fraud through peculiarity in the occurrence of numbers. The law states that in many naturally occurring collections of numbers, the small digits occur disproportionately often as leading significant digits such as the number one.

In the finest traditions of Stephen Stigler’s law of scientific epiphany, Benford was the second person to discover it  and he got credit for it rather than the first (Simon Newcomb) by undertaking a proper analysis:

Newcomb didn’t provide any sort of explanation for his finding. He noted it as a curiosity, and in the face of a general lack of interest it was quickly forgotten.

That was until 1938, when Frank Benford, a physicist at the general electric company, noticed the same pattern. Fascinated by this discovery, Benford set out to see exactly how well numbers from the real world corresponded to the law. He collected an enormous set of data including baseball statistics, areas of river catchments, and the addresses of the first 342 people listed in the book American Men of Science.

Benford observed that even using such a menagerie of data, the numbers were a good approximation to the law that Newcomb had discovered half a century before.

About 30% began with 1, 18% with 2 and so on. His analysis was evidence for the existence of the law, but Benford, also, was unable to explain quite why this should be so.

If someone tries to falsify  numbers, they will have to invent some data. They use too many numbers starting with digits in the mid range, 5,6,7 and not enough numbers starting with 1. This violation of Bedford’s Law, suggesting the possibility such as at Enron.

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