Which is more segregated: San Francisco or its schools?
Which schools are the most integrated?
Every resident of San Francisco knows that it has neighborhoods where the population is predominantly one racial group or another. Pacific Heights is White, the Sunset is Asian, the Mission is Latino, Bayview is African American etc. Many of its schools, both public and private, also have majorities from one group or another. Which is more integrated, the city or its schools? Of all the schools, which are most integrated?
Defining Segregation and Integration
“Segregation” and “integration” are loaded terms that are used widely but which lack standard definition. For my purposes, school A is more integrated than school B (and school B is more segregated than school A) if the racial/ethnic mix of its student body more closely matches the city average. A perfectly integrated school would be one where the student body exactly matches the city average.
Two questions naturally arise:
what average do you compare to?
how do you measure closeness to that average?
What is the city average?
Detailed enrollment information for public schools is available on Dataquest. Data for the private schools comes from the Private School Universe Survey conducted of all private schools in the country by the National Center for Education Statistics. The most recent data is from 2017-18 so it’s not as timely as the similar private school survey conducted by the California Department of Education (CDE) but, unlike the CDE report, it does include the enrollment by race/ethnicity. The Private School Universe Survey doesn’t include data about socioeconomic status or language fluency or special education status so the analysis will be restricted to race and ethnicity.
This gives us data for 181 schools:
103 SFUSD
11 Charter
30 Nonsectarian
24 Catholic
13 Other Religious
I considered simply combining the enrollment data for these 181 schools and using that as the benchmark but decided against it because:
the private school data is incomplete because a bunch of schools (Lycee Francais, French American, several Catholic k-8 schools etc.) did not file their reports
many private schools, particularly at the high school level, attract students from outside the city
some schools made obvious errors in their reports. For example, several reported zero children of Two or more races even though those same schools report on their websites that more than 10% of their kids fall into this category.
Instead, I chose as the benchmark San Francisco’s Under 18 population as recorded in the 2020 census. I’ll use this benchmark for looking at both residential and school segregation. This choice is not perfect either because the school-age population (say those aged 5-17) may have a slightly different profile than the Under 18 population but the Census Bureau hasn’t yet published a more detailed breakdown for 2020.
As this chart shows, the under 18 population is much less White and Asian than the adult population1. 39% of all San Franciscans are White but only 29% of all San Franciscans under 18 are White. Similarly, 34% of all San Franciscans are Asian but only 30% of San Franciscans under 18 are Asian. That’s partly because many White and Asian parents have kids of Two or More Races and partly because there is a far higher percentage of kids in the Latino population.
The population mix also varies significantly at the various types of school in the city.
SFUSD has more Asian and Latino kids than the city average2. Charter schools are majority Latino. Catholic schools have White pluralities (meaning they are the largest group but not a majority) while nonsectarian private schools are majority White. These averages obviously hide huge variation from school to school. Within SFUSD, there are schools that are majority Black and schools that are majority White.
How to Measure Integration
If you study the chart above, you’d quickly conclude that the students attending Catholic schools and the students attending SFUSD are both much closer to the San Francisco Under 18 distribution than the students attending Other Religious, Nonsectarian, or Charter schools. But you might find it harder to determine whether the Catholic school distribution (with its excess of White students) or the SFUSD distribution (with its excess of Asian students) was closer to the average.
Fortunately, demographers, sociologists, and education researchers have been measuring segregation in housing and schooling for generations. Unfortunately, they’ve proposed many different formulae down the years. This Census Bureau overview gives an introduction to the subtly different concepts demographers try to measure.
From that vast arsenal of tools, I’ve chosen to use a divergence index because it produces exactly what I need: a number that represents how much the observed racial mix at a school differs from the benchmark, the San Francisco Under 18 population. Divergence scores are a standard tool for measuring school and residential segregation. A group at U.C. Berkeley used them to analyze residential segregation in the Bay Area. I used them to show that San Francisco is becoming more integrated residentially.
Understanding Divergence Scores
Divergence scores depend on two factors:
the size of a group as a proportion of its expected size (so being 10% instead an expected 5% is more significant than being 20% instead of an expected 15%)
the actual size of the group (so the change in a group that’s 20% of the population is more significant than the change in a group that’s 10% of the population).
A school whose racial/ethnic mix exactly matches the city’s will have a divergence score of 0. Divergence scores typically range from 0 to 1 with a higher score indicating greater divergence from the benchmark.
To get a sense of scale, here are the divergence scores for the different school types in Figure 2 above. These scores represent how much racial mix at that school type diverges from the San Francisco Under 18 racial mix.
Catholic: 0.015
SFUSD: 0.040
Other Religious: 0.064
Nonsectarian: 0.137
Charter: 0.229
The order probably matches what you would come up with just by eyeballing the chart. The divergence becomes more useful when the distributions look very different. Consider these three schools. Starr King is a public elementary school on the south side of Potrero Hill with both a Mandarin Immersion and a General Education program. In comparison with the city average, it has nearly three times as many African Americans (15% vs 5.4%) and twice as many Two or More Race kids (25% vs 12.3%) but only one-third the percentage of White kids (9% vs 29%). Galileo is a majority (60% vs 30% city-wide) Asian public high school near North Beach that is underweight in White and Two or more race kids. University is a majority (58% vs 29% city-wide) White private high school in Pacific Heights that is underweight in Latino and Asian kids.
These three very different schools have identical divergence scores of 0.132, which is lower (i.e. more integrated) than two-thirds of all schools in the city.
School Divergence Scores
The 181 schools in the sample had a median divergence score of 0.193 and a mean of 0.238 with a range of 0.017 to 0.962. The scores for all schools are available here.
I expected larger schools would have lower divergence scores than smaller schools because, in most situations, the larger the sample the closer the sample is to the overall population. It turns out not to make any difference here. A student chosen at random will on average be in a school with a divergence score of 0.193, exactly the same as the median school.
Which Schools Are Most Integrated?
Seven of the ten schools with the lowest divergence scores and six of the ten with the largest divergence scores are SFUSD elementary schools. Most integrated of all is Sherman Elementary in Cow Hollow at 0.017 but it is close: Redding Elementary in Polk Gulch at 0.020 would have taken the top spot if it had two American Indian students instead of three. Notice that Sherman’s score is still higher than the universe of Catholic schools (0.015). The individual Catholic schools all have higher divergence scores (some are more Latino, some are more White) but their aggregate student population comes closer to the city Under 18 mix than the most integrated individual school.
In third and fourth spot, at 0.020 and 0.021, are two high schools, Ruth Asawa School of the Arts (SOTA) at the top of Glen Canyon and Archbishop Riordan, which is near City College. SOTA is frequently attacked by commentators for being too White in comparison with the rest of SFUSD and Riordan is typically seen as less prestigious than some of other Catholic high schools but they do the best job of capturing the city’s racial diversity.
The middle school that comes closest to the city-wide population mix is Presidio Middle School in Outer Richmond with a divergence score of 0.032. It cracks the top ten of all schools even though it is 45% Asian. Not far behind it at 0.039 is Stratford School, most integrated of the private K-8 schools.
The median school, with a divergence score of 0.193, is St. Stephen, a Catholic K-8 school that is 62% White and 20% Two or More races.
The schools with the highest divergence scores are either in the Mission and > 85% Latino; in the Bayview and > 50% African American; or they serve very targeted communities. Examples include:
the Jewish and Armenian schools which, unsurprisingly, are nearly entirely White
the schools associated with the Cornerstone Evangelical Baptist Church which are > 90% Asian
Mission Education Center and Ed Lee, the newcomer schools operated by SFUSD for new immigrants from Latin America and Asia respectively.
De Marillac Academy, a Catholic school that offers 100% scholarships to all students and targets the Tenderloin. Its student population is more than 25% Pacific Islander even though they are only 0.5% of the city’s U18 population.
The single highest divergence score (0.962) belongs to Carver Elementary in Bayview which is 63% Black and 13% Pacific Islander. It might be surprising (at least it was to me) that this is higher than the score of, for example, the Ed Lee newcomer school which is 100% Asian. The intuitive explanation is that having 10x the percentage of Black kids and 26x the percentage of Pacific Islander kids is more ‘surprising’ to the formula than having 3.1x the percentage of Asian kids.
You can explore the composition of all schools and their associated divergence scores here or by clicking on the map below.
Comparing Residential and School Segregation
Are the schools more or less integrated than the city?
It is standard practice to measure residential segregation by census tract. The Census Bureau divides the country into census tracts, each of which is supposed to represent a neighborhood of around 4000 people. The 2020 census divides San Francisco into about 240 tracts and gives the population by race and ethnicity for each. We can calculate divergence scores for those tracts and see if they are higher or lower on average than the divergence scores of the schools.
When demographers measure residential segregation, they measure it in terms of all residents no matter the age. That’s, for example, what the Urban Institute did when they examined segregation in neighborhoods and schools across the country. But if we’re trying to figure out whether schools are more or less integrated than the city, a better comparison group is probably with the distribution of the city’s under 18 population i.e. its child residents. It’s a mistake to assume that these are the same. Children are not evenly distributed among the census tracts. Some parts of the city appeal to new graduates without kids. Some parts of the city have older populations whose kids are now adults. Other districts appeal to families with kids. In addition, the proportion of children varies significantly by race: tracts with a high percentage of Latino residents will tend to have more children than tracts with a high percentage of White residents. At the extremes, one census tract is more than 27% children; another is only 2% children.
I therefore computed two divergence scores for each tract. One measured the divergence of the tract’s population mix from the city’s population mix i.e. an all residents divergence. The other measured the divergence of the tract’s Under 18 population mix from the city’s Under 18 population mix i.e. a Child Resident divergence.
Schools are more segregated than Child residents who are in turn more segregated than all residents. A randomly selected person lives in a census tract with a divergence score of 0.083 (compared to the distribution of all the city’s residents). A randomly selected child lives in a census tract with a divergence score of 0.126 (compared to the distribution of the city’s child residents) but attends a school with a divergence score of 0.193.
Here is a histogram showing the distribution of divergence scores for each category.
What is Going On?
Another concept used by demographers, isolation, helps to explain what’s going on. Suppose a group is 20% of the population. If the group were spread evenly through the city the average member of that group would live in a census tract where 20% of population were other members of the group. If the group members tend to cluster together and live in the same neighborhoods, this percentage will rise. The more it rises, the more isolated the group members become because they live primarily among other members of the group. This clustering can happen by choice or by law or by economics.
All groups show a tendency to cluster residentially.
39% of the population is White but the average White resident lives in a census tract that is 49% White.
34% of the population is Asian but the average Asian lives in a census tract that is 43% Asian.
16% of the population is Latino but the average Latino lives in a census tract that is 22% Latino.
5% of the population is Black but the average Black resident lives in a census tract that is 14% Black.
Children are, if anything, even more clustered (isolated), particularly at school.
30% of the children in San Francisco are Asian but the average Asian child in San Francisco lives in a census tract where 41% of the children are Asian and attends a school where 51% are Asian.
29% of the children in San Francisco are White but the average White child in San Francisco lives in a census tract where 42% of the children are White and attends a school where 45% are White.
23% of the children in San Francisco are Latino but the average Latino child in San Francisco lives in a census tract where 33% of the children are Latino and attends a school where 48% are Latino.
5% of the children in San Francisco are Black but the average Black child in San Francisco lives in a census tract where 21% of the children are Black and attends a school where 14% are Black.
The last number is not a typo. Black kids are the only ones to break the pattern of increasing concentration. Asian, Latino, and White kids all attend schools that are more Asian/Latino/White than the census tracts where they live but Black kids attend schools that are less Black than the ones where they live.
We can speculate about why that might be. Possible explanations include:
Black parents don’t want their kids to have Black peers in school. I’d need to see some evidence before believing this.
Even if Black parents would prefer, other things being equal, to have their children near other Black kids, other things are not equal and they prefer to send their kids to better schools that are further away. There is evidence for this. There may be three majority Black schools but they suffer from low enrollment. Meanwhile, there are substantial numbers of Black students at some charter schools, particularly the KIPP schools. Go to the enrollment tab of SFUSD’s data dashboard and try to find any school anywhere in the city that doesn’t have students from the zip codes in the southeast (94124 and 94134). Those kids could attend nearby public schools where they would have more Black peers but their parents have chosen to send them across the city in search of better schools.
Asian and Latino parents can send their kids to schools that offer Chinese or Spanish language programs where their classmates will be primarily Asian or Latino. White parents are more likely to be able to afford to send their kids to private schools where their kids’ classmates will therefore be predominantly White. Black parents don’t have the option of isolating their kids using language or money.
Few Black parents may be able to afford the $30k-$50k per year it costs to send a child to a nonsectarian private school (or the half that it costs to attend a Catholic school) but Black kids still make up 4% of the students at those schools, not far below the 5% which would match their share of the city’s under 18 population. In comparison, 23% of the city’s kids but only 6% of the students at nonsectarian private schools are Latino. Either Black parents are more likely than Latino parents to apply to these schools or the schools find Black kids to be more attractive recipients of their financial aid budgets. In any case, it means that Black kids are not confined to public schools to the extent that their lack of money would suggest.
Next Steps
Most analysis of SFUSD treats the district’s schools in isolation. So SOTA and Lowell are compared only with other SFUSD schools, not with the city’s population as I’ve done here. The same is true for the elementary and middle schools. In the next installment, I’ll do just that and analyze segregation within SFUSD assuming it is its own hermetically sealed world.
Methodology Notes
The number of school-age children in San Francisco should be about the same as the number of kids actually attending school in San Francisco. School dropouts would push the number actually attending school down. Students commuting from outside the city would push it up. But they should be roughly in balance.
The racial mix of the school-age kids and the students should also be about the same. To the extent that school dropouts are more likely to be Black and Latino, the actual students might be slightly more White and Asian.
The ideal benchmark would be the city’s school age population rather than its Under 18 population but that’s not directly available. The 2020 Census shows San Francisco as having 113,227 people under 18 but doesn’t break it down any further by age. The 2019 American Community Survey does provide a breakdown. It estimates that those aged 5-17 (i.e. the school-age population) were 66.9% of the Under 18s. If we accept that percentage (and ignore the fact that the ACS overestimated the size of the U18 population by 5000), we get an estimate of 75,800 school-age children.
If we then add up the enrollment of all the schools for which we have data, we get 77,600 i.e. more school kids than kids of school age. And we know that some schools are missing from the school data. That would seem to indicate that a lot more kids are commuting in than are dropping it.
Where it gets weird is the racial mix. The census shows that 29.2% of the city’s U18 population is non-Hispanic White. But the schools (public and private combined) are only 24.4% White. The census also shows higher numbers of children of Two or More Races (12.3% vs 8.9%) and fewer numbers of Asians (29.6% vs 32.9%), Latinos (22.9% vs 26.6%), and African Americans (5.4% vs 6.2%). It’s hard to explain such a big difference. Some of the factors that might be involved are:
it may be that the U-5 population contains a higher proportion of children who are White and of Two or more races than the 5-17 population. It is certainly true that those groups form a much bigger part of the elementary school population in SFUSD than the high school population, indicating that they are growing in size.
private schools do not capture race and ethnicity in any standard way and certainly not in the same way that they are asked to report on it for the Private School Survey. This can lead to errors (for example, International, Lick-Wilmerding, Sacred Heart, and San Francisco School all reported 0% Two or More Races). The largest private school in the city, St. Ignatius, is commendably open and publishes detailed numbers about its racial/ethnic makeup but they use a non-standard classification system that I found impossible to reconcile with the numbers they reported on the survey.
How much difference would it have made if I had used the aggregate school enrollment data as my benchmark instead of the census count of child residents? I computed the divergence scores with this new benchmark (fewer White and Two or more students and more Asian, Latino, and African American students) and found that it didn’t have as much effect as I’d expected. The median divergence index went up slightly (0.193 to 0.208) but the size-weighted mean went down slightly (0.193 to 0.184). Of the ten schools with the lowest divergence scores, seven remained in the top ten when the benchmark was changed. Redding Elementary School moved up 1 spot to #1 and Aptos Middle School moved up from #17 to #2 while Riordan and SOTA remained3 the top high schools at 8th and 9th.
The census treats race and ethnicity as independent attributes but I’ve followed the model of all education reports and combined them. So “White” means “White and not Hispanic or Latino”, “Asian” means “Asian and Not Hispanic or Latino” etc. I’ve also excluded the “Other Race and Not Hispanic or Latino” category (1% of total) which has no equivalent in education reports.
These percentages were calculated after adjusting for the number whose ethnicity is Not Reported.
Actually, the now closed Mercy High School was ranked #4.
SF Chronicle used your approach for its data analysis published yesterday ...
"Is Lowell segregated? Here’s how every S.F. school scores on a racial ‘divergence’ index"
by Nami Sumida | Aug. 24, 2022 | Updated: Aug. 25, 2022 2:58 p.m.
https://www.sfchronicle.com/bayarea/article/san-francisco-schools-17393471.php