Polarizability: Difference between revisions

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→‎Electric polarizability: Polarizability volume can be defined also in SI, and reference for notation.
→‎Definition: The definition was mathematically inconsistent: you can't "divide" two vectors to yield a scalar. Fixed
 
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The '''index of dissimilarity''' is a [[demographic]] measure of the evenness with which two groups are distributed across the component geographic areas that make up a larger area.  The index score can also be interpreted as the [[percent]]age of one of the two groups included in the calculation that would have to move to different geographic areas in order to produce a distribution that matches that of the larger area. The index of dissimilarity can also be used as a measure of inequality.
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The basic formula for the index of dissimilarity is:
:<math>\frac{1}{2} \sum_{i=1}^N  \left| \frac{b_i}{B} - \frac{w_i}{W} \right| </math>
 
where (comparing a black and white population, for example):
:''b<sub>i</sub>'' = the black population of the ''i''<sup>th</sup> area, e.g. census tract
:''B''  = the total black population of the large geographic entity for which the index of dissimilarity  is being calculated.
:''w<sub>i</sub>'' = the white population of the ''i''<sup>th</sup> area
:''W'' = the total white population of the large geographic entity for which the index of dissimilarity is being calculated.
 
The ID is applicable to any [[categorical variable]] (whether demographic or not) and because of its simple properties is useful for input into multidimensional scaling and clustering programs. It has been used extensively in the study of [[social mobility]] to compare distributions of origin (or destination) occupational categories.
 
==See also==
*[[Kullback-Leibler distance]]
*[[Isolation index]]
 
==External links==
*http://enceladus.isr.umich.edu/race/calculate.html
 
[[Category:Index numbers]]

Latest revision as of 10:09, 22 October 2014

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