help for ^benford^ (Nikos Askitas)
Apply Benford's Law to a variable
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^benford^ varname [if] [in]
Description
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^benford^ reads in the values of a variable and returns a 4 column table:
Column 1 contains the digits 1 through 9, column 2 contains the total number
of values in the variable starting with that digit, Column 3 contains the
percentage Column 2 represents and Column 4 is what benfords law expects.
So the closer Columns 3 and 4 are the more your numbers conform to Benfords
law.
Remarks
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^benford^ just presents the measurements in a form which makes it easy to inspect.
Both knowing whether your variable should conform to Benford's law or not and whether
the results suggest your dataset is authentic or rigged is up to you. The author is happy
to point the user to N. J. Cox's ^firstdigit^ module for a more comprehensive treatment
as well as acknowledge a masterful rewrite of the first - a more pedestrian - version.
Examples
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While developing I played with auto.dta which is both too small and contains no
variables which should conform to Benford's law. So to just see it work you can do:
. ^sysuse auto.dta^
. ^benford price^
The dataset http://www.stata-press.com/data/r9/census6.dta contains variables which
are suitable for Benford's Law. Although it is too small to get any reliable
distribution it still shows a relative conformity.
. ^ use http://www.stata-press.com/data/r9/census6.dta^
. ^ benford pop^
will return:
Digit Count Frequency Benford
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1 10 20.00 30.10
2 8 16.00 17.60
3 5 10.00 12.50
4 10 20.00 9.70
5 7 14.00 7.90
6 2 4.00 6.70
7 2 4.00 5.80
8 1 2.00 5.10
9 6 12.00 4.60
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Author
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Dr Nikos Askitas, IZA, Bonn, Germany.
Email: ^nikos@@iza.org^