# Re: st: Concentration Curve and Index

 From Roger Newson To statalist@hsphsun2.harvard.edu Subject Re: st: Concentration Curve and Index Date Mon, 05 Sep 2005 16:42:14 +0100

```At 15:36 05/09/2005, Tina wrote:
```
```Hello Statalist

I am looking at income inequalities in health and using the
concentration curve and concentration index (based on the Gini and the
Lorenz curve).

I managed to draw a graph and calculated the index number. However I
know there must be a better way then mine since I do not get any
standard deviations or confidence intervals my way... others are
reporting those.

(The way I did it was just by sorting by income, and adding % of total
population health cumulatively, starting from the least advantaged
individual based on family income. Then I drew a curve based on this
information. The index number is supposed to be twice the area between
the line of equality and the concentration curve.  For the Index I
simply calculated the difference between the curve i calculated and
the line of equality and doubled that number.  Basically, I just
worked my way to the answer through the theory behind the curve and
the index.)

I haven't found one paper that describes how this was calculated,
which means it is probably so easy that it should be obvious. I have
looked all over older statalist mails and the Internet and am still in
the dark. Is there a regression involved that I do not know about? Do
any of you know it?

```

The -somersd- package, downloadable from SSC, can calculate confidence intervals for the Gini index, with the option of using the variance-stabilizing z-transformation. In Stata, type

ssc install somersd, replace

to install the latest Stata 9 version of -somersd-, and type

net get somersd

to copy the manuals -somersd.pdf- and -cendif.pdf- to your local folder. The manual -somersd.pdf- contains an example of the calculation of confidence intervals for Gini indices using -somersd-, and an explanation of why the Gini index is a special case of Somers' D.

I hope this helps.

Roger

--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
Division of Asthma, Allergy and Lung Biology
King's College London

5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk
Website: http://phs.kcl.ac.uk/rogernewson/

Opinions expressed are those of the author, not the institution.

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