ABOUT DISSIMILARITY INDICES
The dissimilarity index is the most commonly used measure of segregation
between two groups, reflecting their relative distributions across neighborhoods within the same
city (or metropolitan area). In this study displayed on CensusScope.org, neighborhood areas are
defined as block groups (link) (with average populations of 1000) based on data from the 2000
Census. Unlike the exposure index (link), which measures a single group's average exposure to
all other groups, the dissimilarity index is always a comparison between two groups, and
measures their relative separation (high dissimilarity) or integration (low dissimilarity) across all
neighborhoods in the city or metropolitan area.
The dissimilarity index varies between 0 and 100, and measures the percentage
of one group that would have to move across neighborhoods to be distributed the same way as the
second group. (It is a symmetrical measure so that this interpretation can apply to either
group). A dissimilarity index of 0 indicates conditions of total integration under which both
groups are distributed in the same proportions across all neighborhoods. A dissimilarity index
of 100 indicates conditions of total segregation such that the members of one group are located
in completely different neighborhoods than the second group. Neither extreme value is generally
seen in most cities and metropolitan areas. Rather the value typically lies somewhere
in-between 0 and 100.
In a simple example, lets assume there are only three neighborhoods in a
metropolitan area with 1200 whites and 600 blacks. If one dot represents 100 people and yellow
and red dots represent white and black people, respectively, the following situation depicts
complete segregation, or a dissimilarity index of 100:
This represents a scenario of complete segregation because all 1200 whites reside in Blocks A
and B, and all 600 blacks reside in Block C. Here, the dissimilarity index is 100 because 100% of the 600 blacks
would have to move to be distributed like the 1200 whites. In this case, 300 blacks would move to block A and 300
blacks would move to block B. As a result, both blacks and whites would be distributed the same way: half of all
blacks would be located in each Blocks A and B; and half of all whites would be located in
Blocks A and B.
(Alternatively, the blacks could stay where they were, and all whites could move to Block C so
that there would
again be a similar distribution of both races).
A scenario of complete integration would be:
In this case, the 600 blacks are equally distributed across the three blocks,
with a third (200 blacks) located in each. Similarly the 1200 whites are equally distributed
with a third (400 whites) located in each. No black or white would need to relocate to make the
distribution any more equal. Here the segregation index is 0.
However, the more usual situation lies somewhere in-between complete segregation and complete
integration. The following represents such an example:
In this case, the segregation index is 50. That is because it would be
necessary for either half the blacks or half the whites to change neighborhoods to be
distributed like the other group. In the case of blacks, 300 (50% of all blacks) would have to
move out of Block A with 100 going to Block B and 200 going to Block C. As a result, both
Blacks and Whites would have one-sixth of their populatons in Block A, two-sixth of their
populations in Block B, and three sixth of their populations in Block C.
Alternatively, similar black-white distributions could be achieved by the movement of whites.
In this case, the 600 whites in Block C (50% of all whites) would have to move to Block A. As a
result, both blacks and whites would have two thirds of their populations in Block A and one
third of their populations in
Block B, again achieving the same distributions.
It should be noted that the dissimilarity index can range from 0 to 100 irrespective of the
relative sizes of each group. In the above example there were 1200 whites and 600 blacks. However, these sizes
could be reversed (or even take on completely different values) and it would still be possible to achieve
dissimilarity values ranging from 0 to 100. This is because the dissimilarity index only measures the relative
distribution of each group across neighborhoods, (ie. are they distributed similarly or differently?). The
measure does not reflect the relative sizes of each group in a given neighborhood, or in an average neighborhood.
The latter is measured by the Exposure Index (link).
Dissimilarity Index formula:
The formula used to calculate the dissimilarity index for two race and ethnic groups within the
same city (or metropolitan area) is as follows:
where P1 = city -wide population of Group 1
P2 = city -wide population of Group 2
P1i = neighborhood i population of Group 1
P2i = neighborhood i population of Group 2
n = number of neighborhoods in city