Benfords Law

In chatting about Greece and its systematic dishonesty I made reference to this post by Tim Harford. It talks about the intriguing Benfords Law which according to wikipedia is

…….also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.

This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

Basically real data has a regularity or rythm to it that artificial or concocted data does not. Hence, data that has been made up can be spotted using Benfords Law. I came across this neat posting that looks at data reporting data from US companies and its reliability.

Guess what…..the data is dodgy

To quote the blogs author

While these time series don’t prove anything decisively, deviations from Benford’s law are compellingly correlated with known financial crises, bubbles, and fraud waves.  And overall, the picture looks grim. Accounting data seem to be less and less related to the natural data-generating process that governs everything from rivers to molecules to cities.  Since these data form the basis of most of our research in finance, Benford’s law casts serious doubt on the reliability of our results.   And it’s just one more reason for investors to beware.

My emphasis added.