Re: st: Measure of Variability in a Nominal Variable

[Ronan Conroy <rconroy@rcsi.ie>]

On 3 Mar 2008, at 19:54, Kevin Daley 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.
It occurs to me that the delta coefficient, originally introduced by  
Ferguson in 1949 and developed by Hankins 2007, which Jean-Benoit  
Hardouin has made available on ssc (findit delta). Although both  
Hankins and Ferguson called it a measure of discrimination, this  
usage is misleading. It is better thought of as a measure of dispersion.

Th delta coefficient measures the degree to which observations follow  
a uniform distribution across the categories of a variable. Though  
intended to be used with ordinal scale measures, it also applies to  
categorical scales, since it is got by summing across the categories  
of the variable, without taking order into account.

Delta is 1 for a uniform distribution and about 0.9 for a normal  
distribution. Jean-Benoit's ado can be applied either to a number of  
items forming a scale or to a single variable which represents the  
frequency of each scale score.

See
 Hankins M. (2007) Questionnaire discrimination: (re)- introducting  
coefficient delta. BMC Medical Research Methodology, 7:19.



P    Before printing, think about the environment
=================================
Ronan Conroy
rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
120 St Stephen's Green, Dublin 2, Ireland
+353 (0)1 402 2431
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