Comments on: Fun (and Fraud Detection) with Benford's Law https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/ The Official Kirix Weblog Tue, 26 Mar 2019 18:52:12 +0000 http://wordpress.org/?v=2.3.3 By: Mark J. Nigrini https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-6342 Mark J. Nigrini Tue, 04 Sep 2012 01:47:03 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-6342 Earlier this year I published a book on the topic ("Benford's Law: Applications for forensic accounting, auditing, and fraud detection, Wiley, 2012). The first few chapters review the maths (the effect of multiplying the numbers by a constant, changing the base, and so on). In the book there are many applications including the census numbers, election results, stream flow numbers, and tax return numbers. The companion site http://www.nigrini.com/benfordslaw.htm has free Excel tempates, data sets, photos, and other interesting items. Enjoy. By: hplc https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-5997 hplc Thu, 15 Mar 2012 05:44:38 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-5997 That is some crazy math. Never even heard of Benford's law before. By: Bill https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-5277 Bill Thu, 02 Jun 2011 11:55:05 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-5277 I wonder how this applies to white noise static? How about to breaking numeric codes? At one point we had an algorithm that required a random number set to simulate background noise so we took random numbers from a calculator to provide the data. Based on Benford's Law, I wonder if the resulting algorithm was accurate or not... By: anonymous https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4695 anonymous Sun, 19 Dec 2010 05:37:15 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4695 Does anyone here recognize the correlation of this principle and the golden ratio? *Gather data sets into separate bins *Analyze mean data of all bins into one "0-9" data points. *Total of all Figures = total 'area' of perfect rectangle. *Divide total by each number; highest to lowest. The result should be a close representation of the ratios of areas of golden triangles descending order. Maybe a derivative of the Fibonacci sequence the same way Pareto's Law is, but interesting just the same. By: Ron https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4648 Ron Wed, 08 Dec 2010 21:59:17 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4648 I've just learned about Benford's law and have decided to apply it to the data from a potentially fraudulent scientific paper. But it's kind of hard to learn all the in's and out's. I decided to use only numbers that are part of the statistical analysis, such values for correlation coefficients, t-tests, and so on. But I excluded things that I wouldn't expect to be fudged, like sample size (and of course not dates and not numbers cited from other people's work). I would like to know what others think about the applicability of Benford's Law in this case. I'm still extracting numbers (by hand, because I have to be able to judge what is a statistic and what isn't). The distribution so far with n = 155 is as follows: 1 16.1% 2 29.0% 3 9.0% 4 17.4% 5 12.3% 6 7.1% 7 5.2% 8 1.9% 9 1.9% Not at all what Benford's law predicts, but there are so many unanswered questions: What is an adequate sample size? Does the fact that some numbers keep recurring in the data mean that I should edit it? For example the power test always comes out around d = 2.xx and the hit rates for different conditions are all in the range of 50-60%. How can I learn a lot more about the forensic use of Bedford's Law, i.e. all the relevant considerations? I've been reading tons so far but nothing to answer the above. ron By: Ken Kaczmarek https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4638 Ken Kaczmarek Tue, 07 Dec 2010 01:23:33 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4638 @Chris -- a vendor number (e.g., 0341993) would be pre-assigned, but any invoice price can vary from one to the next (10 widget A @ \$15; 4 widget B @ \$22, etc.). The "random" nature of the total price would tend to follow benford. By: Chris https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4632 Chris Mon, 06 Dec 2010 04:04:54 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4632 Perhaps I dont understand this aspect of the opener video fully, but aren't the amounts payed to a vendor pre-assigned in every case? Wouldn't they not follow Benford's Law because they instead correlate to a fixed amount of goods/services that this company would be supposedly providing? By: Nudging scientists to share data more « ceptional https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4486 Nudging scientists to share data more « ceptional Sat, 02 Oct 2010 10:04:09 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4486 [...] when humans do this they often leave tell-tale signs that indicate the data were tampered with. See Benford's Law for one example. I know, I know, perhaps only the stupid scientists wouldn't be able to [...] By: Irrational rotations of the circle and Benford's law « Division by Zero https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4443 Irrational rotations of the circle and Benford's law « Division by Zero Wed, 08 Sep 2010 15:27:04 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4443 [...] do not follow Benford's law. For more information you may want to read other accounts of Benford's law on the [...] By: me https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4428 me Wed, 01 Sep 2010 15:35:27 +0000 https://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/#comment-4428 It is seriously cool as it is completely scale invariant. measure it in whatever unit it will always match, though why should nature change its rules depending on how we measure it?