**Calculation Formula for
Segregation Measures**

*The Index of
Dissimilarity*

* *

*
*This index measures the
evenness with which two mutually exclusive groups are distributed across the
geographic units that make up a larger geographic entity; for example, the
distribution of blacks and whites across the census tracts that make up a
metropolis. Its minimum value is
zero and its maximum value is 100.

Suppose:

b_{i }= the
black population of the i^{th} areal unit, e.g. census
tract

B = the total black
population of the large geographic entity for which the *index of
*

*dissimilarity
* is being
calculated.

w_{i} = the white population of the i^{th} area unit, e. g. census
tract

W = the total white population of the large geographic entity for which
the *index of*

*dissimilarity* is being
calculated

Then the *index of dissimilarity *measuring the segregation
of whites from blacks

(1/2)
SUM (b_{i }/B –
w_{i }/ W |

The summation is over the component areal units such as census
tracts.

With a change in notation, the identical calculation formula will produce
an *index of dissimilarity *measuring the segregation of any one
racial group from any other mutually exclusive racial group. The value of this index is statistical
independent of the relative size of the groups used in its
computation.

*The Isolation Index of
Segregation*

* *

*
*Assume:

w_{i} = the white
population of a component part, for example, census tracts, of the
larger

geographic entity for which
the *isolation index* is calculate.

t_{i}= the total
population of a component part of the larger geographic entity for which
the

*isolation index
*** **is
calculated.

W_{i} = the total
white population of the larger geographic entity for which the *isolation
*

*index *is being
calculate.

Then the *isolation index *for whites
equals:

SUM(w_{i }/
W) ´ (w_{i }/ t_{i})

The summation is over all the component geographic parts of the larger
geographic entity for which the *isolation index* is
calculated.

This will report the percentage of population white in the geographic
unit, e.g., tract, for the typical or average white person. The maximum value of this
*isolation index *is 100.
Even if whites make up only 20 percent of a metropolis’ population, all
of them could live in all-white neighborhoods. The minimum value of the isolation index
is asymptotically close to 0. That
is, if there is only one white person in a metropolis of 100,000, he or she
would live in a geographic unit in which the percent white was close to
zero.

An appropriate change in notation will yield the formula for the
*isolation index* for blacks, Asians or any other racial group. This measure is calculated for one
racial group at a time. It does not
compare the distribution of two groups.
Instead, it measures the concentration or isolation of one
group.

*The Exposure or Interaction
Measure of Segregation*

* *

*
*Assume:

w_{i } = the white population of a component
part, e. g. census tract, of the larger

geographic entity for which
the *exposure index* is being calculated.

b_{i} =
the black population of a component part of the larger geographic entity
for white

the *exposure
index* is being calculated.

t_{i } = the total population of a component part
of the larger geographic entity for which

the *exposure index
* is being
calculated.

W = the total white population of the
larger geographic entity for which the *exposure
*

*index *is being
calculated.

Then the average percent black in the geographic unit of the typical or
average white will be calculated as:

SUM(w_{i} / W) ´ (b_{i}
/t_{i}) .

The
summation is over all the geographic units, e. g. census tracts, comprising the
larger geographic entity for which the *exposure index * is being
calculated.

The maximum value of the *exposure index* is the percent in
the second group. That is, if
blacks make up 30 percent of the population of a metropolis, the maximum value
of the average percent black for white residents of that metropolis will be 30
percent. This will require that the
*index of dissimilarity* measuring the evenness with which blacks
and every other racial group are distributed across the metropolis equals zero.
The minimum value of the *exposure index* is zero. That is, although blacks might make up
30 percent of a metropolis, whites could live in exclusively white
neighborhoods. If the
*exposure index *equals zero, than the *index of
dissimilarity* comparing those two groups will equal zero. The
*exposure index* involves two mutually exclusive racial groups. However, the average percent black in
the census tract of the typical white in a metropolis is almost always different
from the average percent white for the typical black living in the same
metropolis.

The formula for calculating the *exposure index *for any two
races may be obtained by making the appropriate changes in
notation.

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