Racial Residential Segregation Measurement Project

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Calculation Formula for Segregation Measures

# 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:

bi   = the black population of the ith 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.

wi = the white population of the  ith 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 (bi /B – wi / 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:

wi = the white population of a component part, for example, census tracts, of the larger

geographic entity for which the isolation index is calculate.

ti= the total population of a component part of the larger geographic entity for which the

isolation index  is calculated.

Wi = 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(wi  / W) ´  (wi  / ti)

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:

wi    =  the white population of a component part, e. g. census tract, of the larger

geographic entity for which the exposure index is being calculated.

bi  =  the black population of a component part of the larger geographic entity for white

the exposure index is being calculated.

ti   =  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(wi / W) ´ (bi /ti)  .

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.