Re: Variance of an index of dispersion

On 14 Dec 2005 09:40:55 -0800, 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
>
> Essentially it looks at all possible dyads (including dyads with
> oneself) in a population, and calculates the proportion of dyads that
> include individuals from differing racial categories.
>
> To do a statistical test, I not only need this index, but also its
> variance, and this raises some issues.

Why do you *think* you need the variance?
You have a set of numbers, which are ordinal scores, and
they can be analyzed by paired t-test, or whatever.

IF you want to say that groups have more females than
their underlying populations, you also have a case
where there is a "variance" associated with each proportion.
That is interesting if you want to test for homogeneity
among one set -- and it might be a nice thing to do.
But most folks would not bother; it does not directly
affect the test that you want.

[snip, rest]

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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