Re: Variance of an index of dispersion
- From: Michael.Lacy.junk@xxxxxxxxxxxxx
- Date: 14 Dec 2005 11:06:51 -0700
weare@xxxxxxx wrote:
> I wish to test a hypothesis that neighborhood organizations are more
> racially homogeneous than the neighborhoods that they represent.
> Because race is a categorical variable I am measuring homogeneity with
> an index of dispersion called the Lieberson Index. The formula sums
> the squared proportion of each racial group and substracts that figure
> from one:
> L = 1 - summation[(n(i)/N)^2]
> Where n(i) is number of members in group i
> N = total number of all members
...... snip, snip
> To do a statistical test, I not only need this index, but also its
> variance, and this raises some issues.
> 1. First there is a conceptual issue. Does it make sense to have a
> variance of a measure of dispersion, since dispersion is already a type
> of measure of variance?
Yes.
> 2. If this is not an issue, this is how I would calculate a variance,
> but I am not sure that I am correct.
The canonical article here is:
Agresti, A. and B. F. Agresti. 1977. "Statistical Analysis of
Qualitatitve Variation." Pp. 204-237 in _Sociological Methodology_
(ed. K. F. Schuessler).
The measure you describe appears in many different forms
and under different names (Simpson's index, IQV, etc.),
but they're all basically the same. The Agresti and Agresti
has several examples, IIRC, of calculating the variance
for such a measure.
--
=-=-=-=-=-=-=-=-=-==-=-=-=
Mike Lacy, Ft Collins CO 80523
Clean out the 'junk' to email me.
.
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