Monday, May 26, 2014

FIRST DIGIT LAW - BENFORD'S LAW


The First Digit Law is an old theory which states that the number of times that 1 will be the first digit number in any random selection of numbers will be the highest.  The chances of the first digit being 1 is 30%.  Number 2 would occur on 17% of the cases.  The number of times that 9 will occur as the first digit is said to be only 4.6%.  The most interesting feature of this theory is that the chances of the first digit keeps decreasing from 1 right upto 9. 


Frank Benford stated this in 1938 and thus came to be known as the Benford Law since then.  He tested the theory on 20 different sets of data and came up with the finding that the first digit occurs more with smaller numbers.  However this has been previously propounded by Simon Newcomb in 1881.  Simon Newcomb said the earlier pages of a logarithm table were more worn than the later pages.

The Benford's law can be applied in real life situation for forensic accounting and auditing.  In the USA it is accepted by the Federal Courts when evidence is based on the Benford's Law.  Scrutiny of election results with the Benford's law has helped to find frauds in some countries.  When data is presented to us we can apply the Benford's Law to test if the data is reliable.

This theory can be applied to a wide variety of data like electricity bills; stock prices; national data on births/deaths, etc.  In the present world we are over loaded with data all the time and on many occasions I have wondered if there is a way of quickly checking the authenticity of the data.  The answer lies in the Benford's Law.

Regards,
T.P.Anand
Dubai, U.A.E.
26th May 2014

1 comment:

  1. Dear Anand atimber
    This is a very efficient statistical tool one uses to analyze large data. I use it to identify manual intervention in data patterns derived from automated processes. An example can be analysis of list of purchase order values taken from sap. One limitation of this law is that it cannot be used when the data is controlled. For example we can use this on invoice values but not on invoice numbers primarily because invoice numbers are serial controlled and patters are preset. Good stuff but unfortunately not many in our profession know about such tools.

    Thanks and regards
    Aditya am

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