Segregation Report
Katie Goulding
October 20, 2018
Overview
The following report investigates levels of segregation in 14 United States cities. The first three metrics of segregation (correlation ratio, dissimilatiy index, interaction index) are from the U.S. Census Bureau and can be found here. The data used in the computation of these metrics are from the American Community Survey. It is to be noted that this data breaks racial composition into a binary of white (majority) and non-white (minority). It is recognized that this is not an effective nor accurate measure of socially constructed racial compositions and is done so only for computational simplicity.
Metric Definition
Correlation Ratio:
The correlation ratio measures the potential contact between minority and majority group members utilizing the isolation index. This metric is an adjusted version of the isolation index. The isolation index measures the probability a minority person shares an area with another minority person. The correlation ratio corrects for the possibility of more than one minority group producing a value from 0 to 1. The closer the ratio is to 0, the more integrated the city is. Oppositely, the closer the ratio is to 1, the more segregated the city is.
The correlation ratio is advantageous as it adjusts for proportion of the population. Since this metric standardizes the evenness index by eliminating asymmetry, it becomes useful when measuring segregation between multiple groups at the same time. Footnote #3 in the pdf describing each metric mentions that the interaction and isolation indices sum to unity for each group. One disadvantage of the correlation ratio is that it will no longer sum to unity with the interaction index. However more concerning, a ratio closer to 1 represents more segregation. That same ratio would also represent that minorities live closer among other minorities. Given how segregation is perceived, I can infer that the creation of this metric was through a white perspective and the validity of can be questioned.
\[\frac{\left( I - P \right)}{\left( 1 - P \right)}\] where:
I = isolation index (computed as the minority weighted average of the minority proportion in each area)
P = the ratio of the total minority popluation to the total population
| correlation_ratio | |
|---|---|
| Denver | 0.1317017 |
| Ok_city | 0.1444560 |
| Wichita | 0.1889306 |
| Charleston | 0.2292909 |
| Columbus | 0.2485485 |
| Kc | 0.2689151 |
| Pittsburgh | 0.2942981 |
| Syracuse | 0.2967734 |
| Dayton | 0.3676721 |
| Chicago | 0.3783064 |
| Memphis | 0.3920073 |
| Baltimore | 0.4408417 |
| St_louis | 0.4462921 |
| Milwaukee | 0.4498372 |
According to the correlation ratio, Milwaukee is the most segregated based on the highest value of 0.450. This ratio states that there is a 45% probability that a not white person shares a geographic living area with another not white person in Milwaukee.
Dissimilarity Index:
The dissimilarity index is used to measure evenness, the differential distribution of a specific population. It measures the percentage of a group’s population that would have to change residence for every neighborhood to have the same percentage of that group as the metropolitan area. It can further be interpreted as the minimum percentage of minorities who would have to change their residence for an unsegregated distribution to be produced. This metric ranges from 0.0 to 1.0 where 0.0 indicates complete integration and 1.0 indicates complete segregation.
The dissimilarity index provides insight into historic discriminatory practices of housing segregation. While it lends insight into the spread of minorities, one fault with this metric is that only measures the percentage of minorities who would have to move residence to become more integrated. I think this metric further perpetuates racial hierarchies and should include the percent of white people who would have to change residence so not to put all the actual action on that of the minorities.
The formula to compute the dissimilarity index is as follows: \[\frac{\sum_{i=1}^{n}\left[ t_i\left\lvert(p_i - P)\right\rvert \right]}{\left[ 2TP(1 - P) \right]}\] where:
n = number of areas (census tracts) in the metropolitan area, ranked smallest to largest
\(t_i\) = total population of area i
\(p_i\) = ratio of \(x_i\) to \(t_i\) (proportion of area i’s population that is minority)
P = the ratio of the total minority popluation to the total population
T = the total population
| dissimilarity_index | |
|---|---|
| Ok_city | 0.3217329 |
| Denver | 0.3562831 |
| Wichita | 0.4122590 |
| Charleston | 0.4161646 |
| Columbus | 0.4292138 |
| Kc | 0.4498272 |
| Chicago | 0.5173891 |
| Dayton | 0.5212164 |
| Pittsburgh | 0.5228730 |
| Syracuse | 0.5381421 |
| Memphis | 0.5716063 |
| St_louis | 0.6044759 |
| Baltimore | 0.6111194 |
| Milwaukee | 0.6187397 |
The dissimilarity index reveals that Milwaukee is again most segregated with an index value of 0.619. This value represents 61.9% of minorities would have to move residence to achieve an unsegregated distribution.
Interaction Index:
The interaction index reflect the probability that a minority person shares a unit area with a majority person. It measures the exposure of minority group members to majority group members as the minority-weighted average. The index ranges from 0 to 1, where a value closer to 0 represents higher segregation.
The interaction index is attempting to measure how much white and not white people interact in a given area based on how racially mixed the area is. This does not actually measure interaction, but rather assumes that if large populations of white and not white people live in the same area, then they must interact. It does not measure whether those interactions are positive, negative, or overall neutral suggesting more of a “tolerance” than an interaction.
\[\sum_{i=1}^{n}\left[ \left( \frac{x_i}{X} \right) \left( \frac{y_i}{t_i} \right) \right]\] where:
n = number of areas (census tracts) in the metropolitan area, ranked smallest to largest
\(x_i\) = the minority population of area i
X = the total minority population
\(y_i\) = the majority population of area i
\(t_i\) = total population of area i
| interaction_index | |
|---|---|
| Baltimore | 0.2170937 |
| Chicago | 0.3362153 |
| Milwaukee | 0.4042414 |
| St_louis | 0.4204528 |
| Memphis | 0.4811954 |
| Dayton | 0.5072700 |
| Charleston | 0.5181057 |
| Columbus | 0.5370268 |
| Kc | 0.5806695 |
| Pittsburgh | 0.6029657 |
| Syracuse | 0.6061708 |
| Ok_city | 0.6134721 |
| Wichita | 0.6395624 |
| Denver | 0.6852802 |
The interaction index suggests Baltimore to be the most segregated with an index value of 0.217. This value represents a 21.7% probability that a minority person shares a geographic unit area with a majority person.
Metric Comparison
These three metrics are all used to measure segregation. The closer the value of the correlation ratio and the dissimilarity index is to 1, represents greater segregation in each specified city. For the interaction index the closer the value is to 1 represents less segregation. It is important to note that these values do not have the same relational value. This is to say that a 0.5 value of the correlation ratio is not equivalent to a 0.5 value of the dissimilarity index.
| correlation_ratio | dissimilarity_index | interaction_index | city |
|---|---|---|---|
| 0.4408417 | 0.6111194 | 0.2170937 | Baltimore |
| 0.2292909 | 0.4161646 | 0.5181057 | Charleston |
| 0.3783064 | 0.5173891 | 0.3362153 | Chicago |
| 0.2485485 | 0.4292138 | 0.5370268 | Columbus |
| 0.3676721 | 0.5212164 | 0.5072700 | Dayton |
| 0.1317017 | 0.3562831 | 0.6852802 | Denver |
| 0.2689151 | 0.4498272 | 0.5806695 | Kc |
| 0.3920073 | 0.5716063 | 0.4811954 | Memphis |
| 0.4498372 | 0.6187397 | 0.4042414 | Milwaukee |
| 0.1444560 | 0.3217329 | 0.6134721 | Ok_city |
| 0.2942981 | 0.5228730 | 0.6029657 | Pittsburgh |
| 0.4462921 | 0.6044759 | 0.4204528 | St_louis |
| 0.2967734 | 0.5381421 | 0.6061708 | Syracuse |
| 0.1889306 | 0.4122590 | 0.6395624 | Wichita |
Most Segregated Cities
Taking in account all three metrics, the top three most segragated cities are: Baltimore, Milwaukee, and St. Louis.
| correlation_ratio | |
|---|---|
| Baltimore | 0.4408417 |
| St_louis | 0.4462921 |
| Milwaukee | 0.4498372 |
| dissimilarity_index | |
|---|---|
| St_louis | 0.6044759 |
| Baltimore | 0.6111194 |
| Milwaukee | 0.6187397 |
| interaction_index | |
|---|---|
| Baltimore | 0.2170937 |
| Chicago | 0.3362153 |
| Milwaukee | 0.4042414 |
Metric Proposal
My proposed metric explores how much (by percentage) the nonwhite population for each city needs to grow to reach the projected national population average in 2045.
The United States Census Bureau (the same source as the city data throughout this report) projects that the nation will become “minority white” in 2045. It is projected that white people will comprise 49.7% of the population. It is also cited that 24.6% of the population will be hispanic, 13.1% black, 7.9% asian, and 3.8% multiracial. To continue with consistency of the data and calculations above, I minimized the racial categories to a binary of white and not white. The source of this information and where to find out more about these projections can be found here.
My equation is as follows:
\[ toGrow \approx (1 - 0.497) - \mu_{pct.nw} \] where:
$ _{pct.nw} $ = mean of the percent of population that is not white
In other words:
\[ percentOfNotWhitePopulationToGrow \approx projectedNationalNotWhitePop_{2045} - avgNotWhitePop \] It finds the difference of the national projected nonwhite population percentage to the average nonwhite population percentage per city. It is acknowledged that this metric is not perfectly accurate with numerous issues including but not limited to population density, population growth, and geographical diversity. However, if working under the assumption that racial diversity becomes evenly dispersed across the nation, then this metric provides an estimate of how much the population of each city will need change to meet the projected national average in 2045.
| city | percent to reach 2045 projection | percent not white |
|---|---|---|
| Denver | 0.3004616 | 0.2025384 |
| Pittsburgh | 0.3196335 | 0.1833665 |
| Syracuse | 0.3270481 | 0.1759519 |
| Note: | ||
| This table compares the evaluated metric for the cities that need the greatest increase in minority populations to the current percent of the population that is not white. This is to display the cities that need greater diversity. |
In exploring this metric, it was discovered that Syracruse, Pittsburgh, and Denver will need to see the greatest increase in a not white population. Additionally, the data displays that Baltimore will need to see an increase in a white population in order to be at the projected national average. I find this most intersting becuase the metrics above suggest Baltimore to be one of the most segragated cities. Its population is currently greater not white than white, yet it was calculated to be the most segragated. This further leads me to believe these metrics were created with a white perspective. I looked into this further and found a report, Time for justice: Tackling race inequalities in health and housing, which uses the same segregation data and historical context to explore racial inequity in health and housing.