Dataset used on this page: sf21
Segregation here refers to the spatial separation of people in where they reside. There are other types of segregation -- separation of people into different jobs in workplaces, separation of students into different tracks in schooling, and so on. But residential segregation seems to have particular importance in things that effect the life chances of individuals.
Dissimilarity
One way to conceptualize segregation is to think about the neighborhoods of an urban area and how different groups of people are spread out among those neighborhoods. San Francisco, for example, has 244 neighborhoods (Census tracts). In the entire area, the ethnoracial identities of people break down like this:
If these eight populations were evenly spread among all neighborhoods, every neighborhood in San Francisco would be about 39% White, about 34% Asian, about 15% Latinx, and so forth. To the extent we find neighborhoods that are way more White or Asian or Latinx than these percentages, we have spatial dissimilarity.
The simplest and most common measure of dissimilarity is called the Index of Dissimilarity (D). It's a formula that looks at how two groups are distributed across neighborhoods. If they have the same proportional representation everywhere, then the two groups are not separated at all and the D is 0. If the two groups live in completely different neighborhoods with no overlap, then the D is 1. You can interpret the D as the proportion of one group that would have to change neighborhoods in order to balance out the city. The formula for D is:
The two populations are represented by the A and B. Capital A and B refer to the number of people in each group living in the city. The lower case a and b refer to the number of people in each group living in the particular neighborhood. This function is exactly what is written above. It gives us a new R command called "dissimilarity" with which we can quickly calculate D scores. To use the function, we simply type in: dissimilarity(ethnoracial$white, ethnoracial$asian). If we run this function for each of the eight groups shown in the table above, we get these figures:
As you can see, segregation, as measured by D, is moderate in San Francisco among the three big groups -- Whites, Asians, and Latinx. The first figure, 0.40, between Whites and Asians tells us that 40% of either Whites or Asians would have to move Census tracts in order for them to be completely integrated.
As you can also see, all three of the large groups are slightly more segregated from African Americans. This is consistent with American racism, where African Americans have represented the pariah group; the part of urban areas where African Americans are concentrated tend to be avoided by other groups. However, even these segregation numbers in San Francisco are still in what is generally considered the "moderate" range (0.3 to 0.6).
High segregation is witnessed exclusively with the NHPI and AIAN groups. This might be do to the fact that the size of these groups is so much smaller; just a few large families here and there would lead to very high D scores even if there were no active forces of individual or institutional discrimination.
Isolation
A different way to think about segregation is to consider how isolated members of a group are to just themselves. If members of a group live entirely in neighborhoods where they are the only residents, then they are completely isolated (and the isolation index score would be 1.00). If they are always just five percent of the population in a neighborhood, then they would be completely mixed in with other groups (and the isolation index score would be 0.05). The formula for the Isolation Index is:
This formula can be thought of as an average. The first fraction represents the proportion of group A that lives in a given tract. The second fraction represents the proportion of the tract's population comprised of group A people. Let's take a simple example using a four tract city with only two groups -- A and B.
There are 100 members of group A, with 25% living in each neighborhood. In the first neighborhood (upper left), group A represents 25% of the neighborhood population. In the other three neighborhoods, A's represent 12.5% of the neighborhood population. Using the formula above, we get:
I = (.25*.25) + (.25*.125) + (.25*.125) + (.25*.125) = 0.15625
We can interpret this I score this way: the typical A resident of this city lives in a neighborhood that 15.625% A residents.
Isolation scores range from whatever the group's proportion of the city is all the way up to 1.0. In other words, if group A represents 17% of a city's population, the I score can go from 0.17 if group members are 17% of every neighborhood's population to 100% if group A members only live in neighborhoods where they are the only residents.