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Re: st: Measure of Variability in a Nominal Variable

From   Ronan Conroy <>
Subject   Re: st: Measure of Variability in a Nominal Variable
Date   Tue, 4 Mar 2008 10:11:26 +0000

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.

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

P Before printing, think about the environment
Ronan Conroy
Royal College of Surgeons in Ireland
Epidemiology Department,
120 St Stephen's Green, Dublin 2, Ireland
+353 (0)1 402 2431
+353 (0)87 799 97 95

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