09 Feb 2017
by James Alty
Rob Downs, founding director at Apteco, explores Benford’s Law
which can be used to detect accounting fraud.
We know our numbers
Apteco was first established in 1987 as a database consultancy.
We soon started working on massive databases and our FastStats
range of data analysis and campaign automation software was born.
We’ve a dedicated team of developers, support consultants and
project managers - all of which are highly talented individuals,
and all of which are really rather good with numbers and data.
Perhaps none more so than Rob Downs.
As one of our founding directors and director of technology, Rob
leads the R&D of the data analysis server at the heart of our
FastStats software and is team leader of the R&D group. When
he isn’t deep diving into big data he enjoys running long
distances over mountains.
In this blog Rob shows his love of math and introduces us to
“naturally occurring” numbers and how these can be used within
FastStats as a method of highlighting made-up or fraudulent
Testing for dodgy numbers using FastStats and Benford’s Law.
"Naturally occurring" numbers usually have a non-uniform
distribution of the first digit with the lower digits being
relatively more common i.e. more 1's than 2's, more 2's than 3's
When first heard that seems a strange idea. But it is sort of
obvious when you think of prices in the supermarket or house
numbers on streets. Trying running that one through your head as
you're walking home.
This observation is known as Benford’s Law see here for an
Obviously it doesn't apply to random numbers or structured
numbers like SIC codes or telephone numbers which have their own
It is easy enough to test the numbers in any FastStats variable.
I’ve used an expression to pick out the first digit. The first
digit frequencies are then analysed in a cube and the
distribution is dragged onto a Charting window to visualise.
Benford’s Law is used as a method of detecting accounting
fraud.If you're just making up the numbers then you won't easily
get this distribution. The effect was even used as "evidence"
against the Greek government's suspect accounts by the EU
Further reading suggests that it is quite possible (although
relatively rare) to have naturally occurring sets of numbers that
don't follow Benford's Law. So in fact it isn’t a “law” at all.
However, used carefully it is a useful fraud flag: a quick test
for dodgy numbers.
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