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Re: st: Measure of Variability in a Nominal Variable


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Measure of Variability in a Nominal Variable
Date   Mon, 3 Mar 2008 21:30:47 +0000 (GMT)

--- Kevin Daley <kevin.daley@mail.mcgill.ca> wrote:
>    I would like to ask if anyone can identify and/or tell me how to
> run a certain descriptive statistic in Stata.  I am working with a
> nominal variable and would like to provide some indication of the
> variability within the sample along this variable.  I would like to
> use a statistic discussed by Agresti in his categorical data analysis
> book that gives the probability that two randomly selected
> independent observations in a given dataset will end up in different
> categories of the given variable.  The statistic has a minimum value
> of 0 and a maximum value of J-1.  Can anyone tell me what this
> descriptive statistic is called?  More importantly, can anyone tell
> me the order needed to run it in Stata? Thank you very much, Kevin. 

If it is a probability than the maximum is 1. In that case you could
compute it as follows:

*---------- begin example -------------
sysuse auto, clear
preserve
contract rep78 , percent(p) nomiss
gen double psq = (p/100)^2
sum psq, meanonly
di 1-r(sum)
restore
*--------- end example -----------------
(For more on how to use examples I sent to the Statalist, see
http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )

Given your description of the maximum I suspect this is not what you
are after. Maybe you are looking for the entropy?

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


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