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Re: st: Zeros and measures of inequality or concentration


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Zeros and measures of inequality or concentration
Date   Mon, 13 Feb 2012 18:13:12 -0500

For exploring and comparing such distributions of counts, it may be
worth looking at Chapter 18 in the 1977 book by John W. Tukey.  I
emphasize that Tukey's techniques are exploratory.  I am not aware of
any systematic theoretical investigation of them.

Tukey, J.W. Exploratory Data Analysis.  Reading, MA: Addison-Wesley, 1977.

David Hoaglin

On Mon, Feb 13, 2012 at 3:44 PM, Troy Payne <paynetc@gmail.com> wrote:
> You're right: data reduction is tougher with such a heavily skewed
> distribution.  Here, the mean crime count is 1.9, the standard
> deviation is 5.7, the median is 0, and 56% of apartment buildings have
> zero crimes.  But even that's not enough information to describe how
> skewed the distribution is: over 72% of the sample is below the mean.
> In other words, most apartments are crime-free or nearly so, while a
> handful are very high-crime.
>
> For purely descriptive purposes, it's usually faster to use a chart,
> which is how much of the criminological literature describes these
> concentrations (e.g., Eck, Clarke and Guerette, 2007).  The
> concentration is usually so dramatic that a graphic conveys it much
> better than any summary measure.
>
> I didn't mention this before, because I tried to keep my question to
> the list quite narrow.  My current research question involves
> comparing the concentration of two different groupings of apartments.
> I was looking for a more formal way to do so than comparing graphs
> visually, and the Gini coefficient (and other measures of
> inequality/concentration) seemed to fit the bill until I ran into the
> question of what each measure does with values of zero.
>
> In general, this issue of heavily skewed distributions is a huge one
> in criminological research... and one that most criminologists (myself
> included) haven't quite figured out how to handle.
>
>
>
> Eck, J.E., Clarke, R.V., and Guerette, R.T. (2007).  Risky facilities:
> Crime concentrations in homogeneous sets of establishments and
> facilities.  Crime Prevention Studies, 21, pp 225-264.  Available:
> http://www.popcenter.org/tools/risky_facilities/PDFs/Eck_etal_press.pdf
>

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