![Benford’s Law was discovered in 1881 by the astronomer Simon Newcomb, and then again by Frank Benford, a physicist at General Electric, in 1938. The law is a curious one: it predicts the frequency of the first digits of a collection of numbers. For example, measure the lengths of the world’s rivers, and see how many of the digits begin with “one” (184 miles; 1,543 miles) versus “three” (3,022 miles) or “nine” (985 miles). Newcomb and Benford discovered that the first digit is usually a “one” – fully 30 per cent of the time, over six times more common than an initial “nine”. And the result is true whether one counts the numbers on the front page of The New York Times or leafs through baseball statistics. […] Manipulated data often fail to satisfy Benford’s Law. A manager who must submit receipts for expenses over £20 may end up filing claims for lots of £18 and £19 expenses – and the data will then contain too many ones, eights and nines. A forensic accountant can easily check this, and while not an infallible check (fraudster Bernard Madoff filed Benford-compatible monthly returns), it’s an indicator of possible trouble.
Which brings us back to the data Greece submitted to the European statistics agency. According to Rauch and his colleagues, Greek data are further from the Benford distribution than that of any other European Union member state. Romania, Latvia and Belgium also have abnormally distributed data, while Portugal, Italy and Spain have a clean bill of health.(via Tim Harford — Article — Look out for No. 1)](http://24.media.tumblr.com/tumblr_lroihn0cp41qzggf7o1_500.gif)
Benford’s Law was discovered in 1881 by the astronomer Simon Newcomb, and then again by Frank Benford, a physicist at General Electric, in 1938. The law is a curious one: it predicts the frequency of the first digits of a collection of numbers. For example, measure the lengths of the world’s rivers, and see how many of the digits begin with “one” (184 miles; 1,543 miles) versus “three” (3,022 miles) or “nine” (985 miles). Newcomb and Benford discovered that the first digit is usually a “one” – fully 30 per cent of the time, over six times more common than an initial “nine”. And the result is true whether one counts the numbers on the front page of The New York Times or leafs through baseball statistics. […] Manipulated data often fail to satisfy Benford’s Law. A manager who must submit receipts for expenses over £20 may end up filing claims for lots of £18 and £19 expenses – and the data will then contain too many ones, eights and nines. A forensic accountant can easily check this, and while not an infallible check (fraudster Bernard Madoff filed Benford-compatible monthly returns), it’s an indicator of possible trouble.
Which brings us back to the data Greece submitted to the European statistics agency. According to Rauch and his colleagues, Greek data are further from the Benford distribution than that of any other European Union member state. Romania, Latvia and Belgium also have abnormally distributed data, while Portugal, Italy and Spain have a clean bill of health.(via Tim Harford — Article — Look out for No. 1)
September 17, 2011, 8:10pm
