RE: Benford's Law

[Steven_S_Prevette@rl.gov]

>Any thoughts about the use of Benford's law to ferret out faked data. (<A 
>HREF="http://www.newscientist.com/ns/19990710/thepowerof.html">The Power of

>One</A> is a quick and dirty summary of its use.)

I don't think it is valid.  In the sales example given, perhaps sales were
stable with a lower control limit of $85 and an upper control limit of $109.
That could give the pattern of sales figures first digits seen.

At Hanford, we write an average of 17 occurrence reports per month, and it
follows a c-chart (Poisson) control limits since August 1999.  The monthly
data are:  18  18  25  18  9  16  17  24  19  11  19  13  21  14  19.  Is
this falsified data?

About the only basis I can think of for such a "law" would be when data
cross over orders of magnitude.  For example, if I had data uniformly
distributed between 40 and 500, then 100/460 would start with 1, 2, or 3,
and 110/460 would start with 4, but only 10/460 would start with 5 through
9.  

If I conceive of randomly picking low ends and randomly picking high ends
for these ranges, it is conceivable that I would skew towards 1 as I
consolidate thousands of distributions together.  Perhaps someone good at
computer modeling could perform this.

Steve Prevette
QA Engineer, ESH Radiological Compliance
Fluor Hanford, A Fluor Global Services Company
ASQ Certified Quality Engineer
steven_s_prevette@rl.gov
509-373-9371