School Segregation Index Descriptive Report

Authors

Mateo Frumholtz

Sara Garcia

Published

November 11, 2024

Minnesota School District-Level Indices

How do segregation trends across the Twin Cities 7-county metro compare to each other?

Exposure/Interaction Index

The Exposure/Interaction Index is a measure of segregation. It estimates the probability of members of specific groups interacting with members of another specific group. In the case of school segregation, it measures the probability that students of racial group A will interact with students of racial group B in a specific school within the district. This measure takes into account the proportion of students of each race within a district that attend each school. See the Census Bureau’s brief for more information on this index.

\[Interaction = \sum_{i=1}^n \left( \frac{B_i}{B} \right) \left( \frac{W_i}{T_i} \right)\]

Where:

\(B_i\) is the number of students of a particular racial group in a school \(i\).
\(B\) is the total number of students of the same racial group in the entire district.
\(W_i\) is the number of White students in school \(i\).
\(T_i\) is the total student enrollment of the school district \(i\).
\(n\) is the number of schools in the district.

Exposure Index Limitations

Isolation Index

Isolation index is a measure of…

\[Isolation = \sum_{i=1}^{n} \left(\frac{B_i}{B} \right) \left(\frac{B{_i}}{T_i} \right)\] Where:

\(B_i\) is the number of students of a particular racial group in a school \(i\).
\(B\) is the total number of students of the same racial group in the entire district.
\(T_i\) is the total student enrollment of the district \(i\).
\(n\) is the number of schools in the district.

The isolation index created by Education Opportunity, the source of this data, differs slighlty in the method and interpretation of this index. Rather than the multiplying the race-specific school proportion to the race-specific district total population, they narrow the total district population to specific racial groups. For exmaple, their white-black isolation is the average proportion white of the total white and black students in a school, in the average white student’s school, represented as:

\[Isolation = \sum_{i=1}^{n} \left(\frac{W_i}{W} \right) \left(\frac{W{_i}}{W_i + B_i} \right)\] Where:

\(W_i\) is the number of white students in a school \(i\).
\(W\) is the total number of white students in the entire district.
\(B_i\) is the total number student of Black students in the district \(i\).
\(n\) is the number of schools in the district.

The standard white isolation index is ss_wht_nwh

Isolation Index Metrics

I have not yet understood which are the Isolation Index measures we should use from Stanford’s Administrative dataset. There are many to choose from. We also have to identify what geographies we want to measure across.

Normalized Exposure Index

According to Education Opportunity’s website, the normalized exposure index measures: “the difference between two groups’ exposure to one of the groups. For example, the White-Hispanic normalized exposure index compares the proportions of White (or Hispanic, equivalently) students in the average White and Hispanic students’ schools. A White-Hispanic normalized exposure value of 0.5 indicates that the proportion of White students in the average White student’s school is 50 percentage points higher than in the average Hispanic student’s school (ignoring the presence of other groups aside from the racial dyad of interest).”

Dissimilarity Index

The Dissimilarity index is another measure of segregation. According to the census bureau, the dissimilarity measures the proportion of one group that would have to move to another area to be distributed equally as a comparison group. It can be interpreted in the following way: “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.”

Dissimilarity index is calculated following Wang et al.’s, methods found here.

\[Dissimilarity = \frac{1}{2} \sum_{i=1}^{n} \left|\frac{b_i}{B} - \frac{w{_i}}{W} \right|\] Where:

\(b_i\) is the number of students of a particular racial group in school \(i\).
\(B\) is the total number of students of the same racial group enrolled in the district.
\(w_i\) is the number of white students in school \(i\).
\(W\) is the total number of white students enrolled in the district.
\(n\) is the number of schools in the district.

Information Theory Index Plot

Difference in Exposure to Free Lunch

CBSA-Level Segregation Indices

How do segregation trends in the Twin Cities compare to other cities in the US?

The following analysis compares Twin Cities between-school segregation trends to other US major cities. The first charts highlight city-level trends and the following compares those trends across cities. Only the top 20 CBSA’s by student population were used for these plots. Given the length of the CBSA names, they have been shortened to be legible in these crowded plots. Reference the following table for the abbreviated names:

Twin Cities Metro School Closures, 2001-2022
Full CBSA Name	Short CBSA Name
New York-Newark-Jersey City, NY-NJ	New York, NY
Los Angeles-Long Beach-Anaheim, CA	Los Angeles, CA
Dallas-Fort Worth-Arlington, TX	Dallas, TX
Houston-Pasadena-The Woodlands, TX	Houston, TX
Chicago-Naperville-Elgin, IL-IN	Chicago, IL
Atlanta-Sandy Springs-Roswell, GA	Atlanta, GA
Washington-Arlington-Alexandria, DC-VA-MD-WV	Washington, DC
Philadelphia-Camden-Wilmington, PA-NJ-DE-MD	Philadelphia, PA
Riverside-San Bernardino-Ontario, CA	Riverside, CA
Miami-Fort Lauderdale-West Palm Beach, FL	Miami, FL
Phoenix-Mesa-Chandler, AZ	Phoenix, AZ
Boston-Cambridge-Newton, MA-NH	Boston, MA
Detroit-Warren-Dearborn, MI	Detroit, MI
Minneapolis-St. Paul-Bloomington, MN-WI	Minneapolis, MN
San Francisco-Oakland-Fremont, CA	San Francisco, CA
Seattle-Tacoma-Bellevue, WA	Seattle, WA
San Antonio-New Braunfels, TX	San Antonio, TX
San Diego-Chula Vista-Carlsbad, CA	San Diego, CA
Charlotte-Concord-Gastonia, NC-SC	Charlotte, NC
Denver-Aurora-Centennial, CO	Denver, CO
Data source is the Stanford Segregation Dataset from Education Opportunity.