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# Re: [Phys-L] Fwd: Benford

Unfortunately it can't be used to detect fraud when the return is fairly
simple so it has low statistics. And now with the computer number matching,
most people can not submit as many faked numbers. If you are like me with
low medical expenses and no mortgage, there is little possibility of
cheating. But the very wealthy have lots of opportunity, and presumably
good accountants know about this little statistical device that the IRS may
use. So only the amateurs are likely to get caught.

But there is an even stranger piece of disparate evidence. Apparently you
have an innate sense of logarithmic scales. Small children when asked what
is half way between 1 and 9 will answer 3 instead of 5. Actually I suspect
that many students will also come up with 3. Most students do not seem to
know that the average is the half way point.

John M. Clement
Houston, TX

Oldie but oldie! Used for detecting tax return irregularities:
people dream up way to many 5's too few ones.
[From an ECN on line piece....]

Brian W

Dr. Benford discovered, in a huge assortment of number
sequences -- random samples from a day's stock quotations, a
tournament's tennis scores, the numbers on the front page of
The New York Times, the populations of towns, electricity
bills in the Solomon Islands, the molecular weights of
compounds the half-lives of radioactive atoms and much more
-- [something unexpected.]

Given a string of at least four numbers sampled from one or
more of these sets of data, the chance that the first digit
will be 1 is not one in nine, as many people would imagine;
according to Benford's Law, it is
30.1 percent, or nearly one in three. The chance that the
first number in the string will be 2 is only 17.6 percent,
and the probabilities that successive numbers will be the
first digit decline smoothly up to 9, which has only a 4.6
percent chance.

A strange feature of these probabilities is that they are
"scale invariant" and "base invariant."