# Test scores, class and race: report

Chapter 3.1 of ZIP Code Destiny, by Vishal Singh (NYU Stern). Generated from the chapter's data files; the reading version is at https://vishalsingh.org/zipcode/test-scores-class-and-race. Table n of this report is figure n of the chapter.

## Identification

- Title: Test scores, class and race
- Label: The classroom staircase
- Chapter: 3.1 (Part III, School; An American life)
- Question: How far apart are average test scores across counties and districts, and how much of the gap between groups follows family income rather than race?
- Dek: Average achievement in third through eighth grade, 2009 to 2019, differs by 2.54 grade levels between the 5th and 95th percentile of counties and rises with county income in 45 of 45 states.
- Grain: counties
- Status: published
- Published: 2026-10-09
- Updated: not revised
- Data sources:
  - Stanford Education Data Archive. Stanford Education Data Archive 6.0, pooled math and reading achievement for counties and geographic school districts, grades 3 to 8, school years 2009 to 2019, for all students and by group, with gaps between groups; years: 2009-2019 (version 6.0); weights: tests counted; each analysis names its weight
  - County Health Rankings. County Health Rankings 2024: median household income (Census SAIPE, 2022), school segregation (Theil's index, NCES Common Core of Data, school year 2022 to 2023), Black-white residential segregation (ACS 2018 to 2022), non-Hispanic Black share of residents; years: 2024 release; weights: none (published county measures); analyses weight counties by SEDA tests counted
- Canonical URL: https://vishalsingh.org/zipcode/test-scores-class-and-race
- Report: https://vishalsingh.org/zipcode/test-scores-class-and-race/report
- Markdown: https://vishalsingh.org/zipcode/test-scores-class-and-race/report.md
- BibTeX key: singh2026testscoresclassandrace

```bibtex
@misc{singh2026testscoresclassandrace,
  author = {Singh, Vishal},
  title = {Test scores, class and race},
  year = {2026},
  url = {https://vishalsingh.org/zipcode/test-scores-class-and-race},
  note = {In ZIP Code Destiny. Published 9 October 2026.}
}
```

## Principal estimates

The facts the dek and the opening prose cite, in order of appearance.

| Estimand | Population | Period | Value | Interval | n | Weights | Source | Fact id |
| --- | --- | --- | ---: | --- | ---: | --- | --- | --- |
| 95th minus 5th percentile of the county average of math and reading, counties weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled | 2.54 |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | ach_spread |
| count of states where the county slope of average achievement on log income is positive | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 45 |   |   | none (each state counts once) | Stanford Education Data Archive | slope_pos |
| count of states fitted | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 45 |   |   | none (full count) | Stanford Education Data Archive | slope_states |
| count of counties | counties and county equivalents in the SEDA county file with a math and a reading estimate for all students (Virginia, DC and a few small counties have none) | test results for third through eighth grade, school years 2009 to 2019 pooled | 3,000 |   |   | none (full count) | Stanford Education Data Archive | n_counties_ach |
| 5th percentile of the county average of math and reading, counties weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled | −1.27 |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | ach_p5 |
| 95th percentile of the county average of math and reading, counties weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled | +1.27 |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | ach_p95 |
| count of counties in the income comparison | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 2,999 |   |   | none (full count) | Stanford Education Data Archive | n_counties_income |
| weighted slope of the county average on the log (base 2) of median household income, bootstrap interval over states | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 1.28 | 95% CI 0.94 to 1.72 | 2,999 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | income_slope |
| weighted mean of the district gap in math, bootstrap interval over states (districts in a state resemble one another) | geographic school districts with a math estimate for both groups (white minus Black) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 0.64 | 95% CI 0.61 to 0.67 | 5,729 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | wbg_mean |
| weighted mean of the district gap in math, bootstrap interval over states (districts in a state resemble one another) | geographic school districts with a math estimate for both groups (not economically disadvantaged minus economically disadvantaged) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 0.58 | 95% CI 0.55 to 0.61 | 11,815 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | neg_mean |

## Findings

Average achievement in third through eighth grade differs by 2.54 grade levels between the county at the 5th percentile and the county at the 95th, among 3,000 counties whose math and reading results cover the school years 2009 to 2019. Counties are weighted by the tests counted. The 5th-percentile county averages −1.27 grade levels from the national average and the 95th-percentile county +1.27.

Average achievement moves with county income. Across 2,999 counties, each doubling of median household income goes with 1.28 (95% CI 0.94 to 1.72) more grade levels.

Inside the same school districts, white students score 0.64 (95% CI 0.61 to 0.67) standard deviations above Black students in math, and students who are not economically disadvantaged score 0.58 (95% CI 0.55 to 0.61) standard deviations above those who are. Each gap is averaged over the districts that report it. Every figure describes counties or districts, not individual students.

### One scale for every state's tests

Each state gives its own tests, so raw scores cannot be compared across state lines. The Stanford Education Data Archive (SEDA) links each state's results to the National Assessment of Educational Progress, which puts them on a common scale. It publishes averages for counties and school districts, for all students and for groups of students. The averages here pool third through eighth grade and the school years 2009 to 2019. They are empirical-Bayes estimates, which pull the figure for a place with few tests toward the average of similar places. They rest on 404.9 million math and reading tests in the county files, where a test is one student's result in one subject, grade and year.

The archive reports its scale in two ways. A standard-deviation score says how many standard deviations a group's average lies from the national average for the same grade. A grade-level score restates the same quantity so that one unit is the national average gain between adjacent grades. One standard deviation equals 3.3 grade levels in the county averages and 3.2 in the math gaps, so on the grade-level scale the white–Black math gap inside districts is about 2.0 (95% CI 1.9 to 2.1) grade levels and the income gap about 1.8 (95% CI 1.7 to 1.9). County averages below are in grade levels from the national average, so a county at zero matches the nation. Group levels, gaps and their spreads are in standard deviations, which the archive recommends for research, and the two scales never share an axis.

### Where county averages are highest and lowest

Counties with the lowest averages are concentrated in the South. Of the lowest tenth of counties, 74% are there, against 43% of all counties (Table 1, with regions as the Census Bureau defines them). The highest tenth sits mostly in the Northeast and the Midwest, which hold 67% of that tenth and 42% of all counties.

The five lowest county averages are in Kusilvak and Bethel Census Areas in Alaska, Todd and Oglala Lakota Counties in South Dakota, and Sioux County in North Dakota, led by Kusilvak at −4.3 grade levels. Forsyth County, Georgia, has the highest average, +2.3. Counting each county once instead of weighting by tests puts the 5th and 95th percentiles at −1.57 and +1.01, a spread of 2.58. Both ends move down, since the lowest-scoring counties tend to have few tests and the highest-scoring ones many.

Table 1. 74% of the counties in the lowest tenth for average achievement are in the South, which holds 43% of counties

The map leaves 142 places gray. Virginia has no math estimates in the archive's sixth version, so none of its 133 counties and independent cities has an average of math and reading. The District of Columbia has no county rows, and 8 small counties are missing an estimate for math or reading. Each gray place carries its reason in the tooltip.

### Average achievement rises with county income

County averages are higher where median household income is higher (Table 2). Across counties, average achievement has a correlation of +0.59 (95% CI 0.43 to 0.76) with the log of median household income, and income accounts for 34% (95% CI 19% to 59%) of the variance in county averages, which leaves the rest to everything else that differs between counties. The lowest tenth of counties by income averages −1.12 (95% CI −1.44 to −0.75) grade levels from the national average and the highest tenth +0.41 (95% CI 0.02 to 0.87). Counties at any income level still scatter widely around the line, with a standard deviation of 0.63 (95% CI 0.49 to 0.72) grade levels, so income alone does not place a county. The income measure is the Census Bureau's modeled estimate for 2022 as County Health Rankings reports it. The test results are for 2009 to 2019, so it stands in for income during the test years.

Table 2. Average achievement is higher in counties with higher median household income, a correlation of +0.59 with log income across 2,999 counties

Counties in one state resemble each other, so the intervals here come from a bootstrap that resamples whole states, and they are wider than intervals that treat counties as independent. Counting each county once instead of weighting by tests gives a similar correlation and a slope within the interval.

### County income and achievement inside each state

A national slope could come from comparing rich states with poor ones, with no link inside any state. Table 3 fits the slope one state at a time, for the 45 states with 10 or more counties. The estimated slope is positive in 45 of 45. Its 95% interval, from robust standard errors with t intervals, lies above zero in 40. The intervals that include zero are those for Kentucky, Wyoming, Utah, New Hampshire and North Dakota.

In the median state a doubling of county income goes with 1.57 more grade levels. The slope is steepest in Alaska (3.27 (95% CI 1.66 to 4.87)) and shallowest in Kentucky (0.33 (95% CI −0.08 to 0.74)).

Table 3. The slope of county average achievement on county median income is positive in 45 of 45 states, with a 95% interval above zero in 40

The count of intervals above zero depends on how they are built. With heteroskedasticity-consistent (HC3) standard errors and normal intervals it is 36 of 45.

It also depends on the minimum number of counties. At a minimum of 8 counties, 46 states are fitted (Connecticut joins) and 41 have an interval above zero. At a minimum of 15 counties, 42 are fitted and 38 do.

New Hampshire has exactly 10 counties and is among the states whose interval includes zero. The estimated slope stays positive in every fitted state at every minimum up to 30 counties, but not at every income year. Wyoming's slope is close to zero, and with the Census Bureau's 2019 estimate of median household income in place of the 2022 one it is slightly negative.

A slope across counties compares places, not students, and a county average reflects everything that happens to children in and out of school, so a steep slope does not show that schools in poorer counties do worse. How much students learn from one grade to the next, as distinct from where they start, is the subject of Chapter 3.3, Learning growth and starting level (https://vishalsingh.org/zipcode/learning-growth; planned).

### Gaps between groups inside the same districts

SEDA reports an average for each group and the gap between two groups in the same geographic school district. Table 4 shows the distribution of those gaps in math. Each gap is averaged over the districts that report it, weighted by the tests of the two groups, so the rows cover different districts. White students score 0.64 (95% CI 0.61 to 0.67) standard deviations above Black students, about 2.0 (95% CI 1.9 to 2.1) grade levels on the archive's own grade-level gap. White students score above Black students in 99.8% of the 5,729 districts that report both.

Students who are not economically disadvantaged score 0.58 (95% CI 0.55 to 0.61) above those who are, about 1.8 (95% CI 1.7 to 1.9) grade levels. The white–Hispanic gap is 0.43 (95% CI 0.40 to 0.46) standard deviations. The white–Asian gap is −0.31 (95% CI −0.35 to −0.26), negative because Asian students score higher, as they do in 87% of the 4,353 districts that report both groups.

Table 4. Within the same districts, white students score 0.64 standard deviations above Black students in math, and the other gaps shown are smaller or negative

The income gap is reported by more districts than the white–Black gap (11,815 against 5,729). The 6,157 districts that report only the income gap have a smaller mean income gap, 0.40 (95% CI 0.38 to 0.41).

The two headline gaps are therefore compared on the 5,658 districts that report both. There the white–Black gap averages 0.64 (95% CI 0.61 to 0.67) and the income gap 0.60 (95% CI 0.57 to 0.63), a difference of 0.04 (95% CI 0.02 to 0.06) standard deviations.

The gaps vary widely between districts. Among districts weighted by tests, the white–Black gap is 0.28 standard deviations at the 5th percentile and 1.08 at the 95th, and the second view of the figure shows the same spread for the other gaps. Weighting districts by tests gives larger gaps than counting each district once, which gives 0.52 for the white–Black gap and 0.43 for the income gap, since districts with more tests tend to have larger gaps. States define economic disadvantage in their own ways, so the income gap compares groups that are defined differently from state to state.

### Where each group stands

A gap is a difference between two levels, and Table 5 shows the levels. Relative to the national average of all students, which is zero, math scores of Asian students average +0.66 standard deviations, white students +0.24, Hispanic students −0.30, Native American students −0.38 and Black students −0.53. SEDA takes its groups from state reports under federal race and ethnicity categories that are mutually exclusive, so Hispanic students of any race form their own group and the Asian, Black, white and Native American groups exclude them.

Students who are not economically disadvantaged average +0.39 and students who are −0.35. Each mean covers the counties that report the group, so the groups are measured in different places, and the figure carries the number of counties for each.

Table 5. In math, Asian students average +0.66 standard deviations from the national average and Black students −0.53

Counting each county once instead of weighting by the group's tests pulls every level toward zero. It gives +0.44 for Asian students, +0.08 for white students, −0.25 for Hispanic students, −0.23 for Native American students and −0.47 for Black students. For students who are not economically disadvantaged it gives +0.23, and for students who are, −0.28. Native American students then rank above Hispanic students, so the order of those two groups depends on the weighting. Black students have the lowest level either way.

### School segregation and the white–Black gap

Reardon, Kalogrides and Shores found, across districts and metropolitan areas, that racial gaps in test scores are larger where schools are more segregated and where racial groups differ more in family income and education.[1] County Health Rankings' 2024 release publishes a school segregation index for the 2022 to 2023 school year. It is Theil's index of how unevenly students of every racial and ethnic group are spread across a county's schools relative to the county as a whole, lowest when every school mirrors the county and highest under complete segregation. The index has a standard deviation of 0.07 across counties. Across 2,101 counties the white–Black math gap has a correlation of +0.59 (95% CI 0.51 to 0.66) with it (Table 6). Within states, a county one standard deviation higher on the index has a gap wider by 0.11 (95% CI 0.09 to 0.14) standard deviations, a regression with state fixed effects.

Table 6. The white–Black math gap is wider in counties with more school segregation, a correlation of +0.59 across 2,101 counties

Card and Rothstein studied SAT scores across metropolitan areas and found that residential segregation was consistently associated with a larger Black–white gap while school segregation had no independent association, though they could not reject that the two were equal.[2] Here, residential segregation alone moves with the gap, with a correlation of +0.25 (95% CI 0.12 to 0.37) and a within-state coefficient of 0.07 (95% CI 0.02 to 0.12). The two indices correlate at +0.46 (95% CI 0.31 to 0.56) across counties, so they are different measures.

A county regression with state fixed effects puts four measures in at once. They are school segregation, the Black–white residential index of dissimilarity for 2018 to 2022, the non-Hispanic Black share of residents and the log of median income. Across 1,849 counties, in standard deviations of the gap per standard deviation of the measure, it gives 0.11 (95% CI 0.08 to 0.13) for school segregation and −0.01 (95% CI −0.04 to 0.02) for residential segregation. In this regression school segregation keeps its association while the residential index loses its. The Black share of residents has a coefficient of 0.03 (95% CI 0.00 to 0.07) and the log of median income 0.09 (95% CI 0.06 to 0.11).

That pattern differs from Card and Rothstein's, but the studies differ in outcome (SAT takers against every tested student in third through eighth grade), in unit (metropolitan areas against counties), in the segregation measure (a Black–white index against one that covers every group) and in period. This is therefore not a test of their result. Neither study isolates segregation from the other differences between places.

### The income gap and the white–Black gap

Counties with a wide gap between students who are not and are economically disadvantaged tend to have a wide white–Black gap (Table 7). Across 2,092 counties the two correlate at +0.80 (95% CI 0.75 to 0.84), and a line through them has slope 0.99 (95% CI 0.91 to 1.08). The income gap accounts for 64% (95% CI 57% to 71%) of the variance in the race gap. That share is partly mechanical, because the two gaps are measured on overlapping groups of students and their estimation errors are correlated.

The mean income gap across these counties is 0.69 standard deviations and the mean white–Black gap 0.74. Around the line the white–Black gap still varies from county to county, with a residual spread of 0.14 (95% CI 0.13 to 0.15) standard deviations.

Table 7. Counties with a wider income gap have a wider white–Black gap, a correlation of +0.80 across 2,092 counties, and the two gaps are of similar size

SEDA does not cross race with economic disadvantage, so these data cannot say how large a white–Black gap would be among students in the same economic circumstances. A strong correlation across counties does not make either gap a version of the other. Chapter 4.3, Race, income and mobility (https://vishalsingh.org/zipcode/race-income-and-mobility) compares Black and white children from families with the same income who grew up in the same neighborhood, with adult income as the outcome.

### How much each gap varies across counties

A gap between two groups differs from one county to the next (Table 8). Across the 2,020 counties that report all four gaps, the white–Black math gap has a standard deviation of 0.24 (95% CI 0.22 to 0.26) standard deviations, the white–Hispanic gap 0.23 (95% CI 0.21 to 0.25) and the income gap 0.19 (95% CI 0.17 to 0.20).

The gap between boys and girls in reading, a yardstick whose own size is the subject of Chapter 3.2, Gender gaps in reading and math (https://vishalsingh.org/zipcode/gender-gaps-in-reading-and-math), has a spread of 0.06 (95% CI 0.05 to 0.07). The white–Black spread is 4.1 (95% CI 3.3 to 5.2) times that (3.0 (95% CI 2.5 to 3.8) counting each county once).

Table 8. Relative to its average size, the white–Black math gap varies 1.34 times as much across counties as the boys minus girls reading gap

A larger gap has more room to vary, so the comparison that matters is the spread relative to the average gap. The white–Black gap averages 3.0 (95% CI 2.8 to 3.3) times the reading gap. Relative to its average, its spread is 0.33 (95% CI 0.30 to 0.35) against 0.24 (95% CI 0.19 to 0.29) for the reading gap, a ratio of 1.34 (95% CI 1.08 to 1.76), or 1.26 (95% CI 1.04 to 1.63) counting each county once.

The white–Hispanic gap varies most relative to its average (0.43 (95% CI 0.39 to 0.48)), and the income gap (0.27 (95% CI 0.26 to 0.29)) about as much as the reading gap. In standard deviations the race and income gaps vary several times as much as the reading gap, but relative to their size the difference is modest, so these data do not show that race and class gaps depend on place much more than the gender gap does. Standard errors are smaller than the spreads, with a median of 0.03 for a county's white–Black gap and 0.01 for its boys-minus-girls reading gap.

### Two studies of Head Start and school spending

Everything above is description. Two studies use designs that can speak to whether early education and school funding change what children achieve. Each is reported under its own design, and neither estimates what it would take to close the gaps in this chapter.

> Causal evidence: Head Start funding and children's later outcomes (Regression discontinuity)
>
> In 1965 the federal Office of Economic Opportunity gave help with writing Head Start proposals to the poorest counties, those above a cutoff in the 1960 county poverty rate. Head Start funding was sharply higher above the cutoff, a difference that lasted, while other federal social spending did not jump there. Ludwig and Miller compared counties on either side of the cutoff, which should be alike in other respects.[3] Young school-age children in counties above the cutoff had lower mortality from causes that Head Start could affect, and the study found suggestive evidence of more schooling among cohorts old enough to have been exposed. Its outcomes are mortality and educational attainment, not test scores in third through eighth grade.

> Causal evidence: School finance reforms and adult outcomes (Event study with instrumental variables)
>
> Jackson, Johnson and Persico followed children born between 1955 and 1985 through 2011. They used the timing of court-ordered school finance reforms, and the type of funding formula each reform changed, as a source of variation in per-pupil spending, and compared cohorts exposed to a reform for more of their school years with cohorts exposed for fewer.[4] Higher spending over the school years raised educational attainment and adult wages and lowered adult poverty, with much larger effects for children from low-income families.

Both studies are about the policies and years they cover. Neither measures what a change in a county's income or segregation would do for its students.

### What these data cannot show

The figures describe counties and districts, and a county average blends every child in it (ecological inference). A pattern across counties need not hold for the students inside them. An average level is not a school's contribution, since it reflects families, neighborhoods, health and schools together. Reardon found that the income gap in achievement is already large when children enter kindergarten and does not widen much during the school years.[5] That fits a gap that is mostly in place at school entry, though county averages for third through eighth grade cannot show when each gap arises.

The achievement estimates are state tests placed on a national scale, pooled over a decade of cohorts. They are empirical-Bayes estimates, so small places are pulled toward the mean and the spreads here understate the spread of the true values, most for places with few tests. Virginia has no math estimates and DC no county rows. The groups come from state reports, states define economic disadvantage differently, and the data do not cross race with income.

The covariates come from other years than the tests. Median income is for 2022, the school segregation index for the 2022 to 2023 school year and the residential index for 2018 to 2022, while the tests are for 2009 to 2019, so the comparisons assume that a county's position changed little in the years between. The school segregation index covers every racial and ethnic group, not only Black and white students. The correlations and slopes are associations across places. The state fixed effects remove differences between states but not differences between counties, so none of them says what would happen to a county's students if its income or segregation changed. How schools discipline students, and what follows, is the subject of Chapter 3.4, School discipline and incarceration (https://vishalsingh.org/zipcode/school-discipline-and-incarceration).

## Tables

### Table 1. 74% of the counties in the lowest tenth for average achievement are in the South, which holds 43% of counties

Average of math and reading achievement in third through eighth grade, in grade levels above or below the national average, by county, 2009 to 2019 pooled

No inline rows: the values of Table 1 are in https://vishalsingh.org/zipcode/data/test-scores-class-and-race/scores_map.json.

Note: Virginia has no math estimates in the archive's sixth version, so its 133 counties and independent cities have no average of math and reading. The District of Columbia has no county rows, and 8 small counties have no average because the archive lists no estimate for them or no reading estimate. Puerto Rico is not drawn.

Note: Connecticut is drawn as its eight legacy counties, the codes SEDA uses. Valdez-Cordova Census Area in Alaska (split in 2019) is drawn on its two successors, Chugach and Copper River, with the one value SEDA reports.

Note: The archive reports empirical-Bayes estimates, which pull the figure for a place with few tests toward the average of similar places. Pooled results cover third through eighth grade and the school years 2009 to 2019.

Source: Stanford Education Data Archive 6.0, 2009-2019 (county averages for all students); modeled estimates, each county drawn once (unweighted)

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/scores_map.json

### Table 2. Average achievement is higher in counties with higher median household income, a correlation of +0.59 with log income across 2,999 counties

Average of math and reading achievement (grade levels from the national average) against median household income (dollars, log scale), one dot per county; dot area is the tests counted

No inline rows: the values of Table 2 are in https://vishalsingh.org/zipcode/data/test-scores-class-and-race/scores_vs_income.json.

Note: Income is the Census Bureau's modeled estimate of county median household income for 2022 as County Health Rankings reports it. Test results are for 2009 to 2019, so a county's income stands in for its income during the test years. One county, Valdez-Cordova in Alaska, has no income in that file and is left out.

Note: Intervals resample whole states, because counties in a state resemble one another and share state tests and school funding rules. Counting each county once instead of weighting by tests gives a slope within the interval.

Note: Forsyth County, Georgia, and Kusilvak Census Area, Alaska, are labeled as the counties with the highest and lowest averages.

Source: Stanford Education Data Archive 6.0, 2009-2019, and County Health Rankings 2024 (Census SAIPE median household income for 2022); weighted by tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/scores_vs_income.json

### Table 3. The slope of county average achievement on county median income is positive in 45 of 45 states, with a 95% interval above zero in 40

Within-state slope of the county average of math and reading on county median household income (grade levels per doubling of income), states with 10 or more counties

| conf_high | conf_low | n | slope | state |
| ---: | ---: | ---: | ---: | --- |
| 0.739 | −0.083 | 120 | 0.328 | Kentucky |
| 1.01 | 0.015 | 92 | 0.514 | Nebraska |
| 1.53 | −0.472 | 23 | 0.527 | Wyoming |
| 1.63 | −0.230 | 29 | 0.699 | Utah |
| 1.83 | −0.048 | 10 | 0.891 | New Hampshire |
| 1.44 | 0.372 | 77 | 0.907 | Oklahoma |
| 1.68 | 0.215 | 33 | 0.948 | New Mexico |
| 2.70 | −0.705 | 53 | 0.996 | North Dakota |
| 1.47 | 0.535 | 55 | 1.00 | West Virginia |
| 1.50 | 0.800 | 15 | 1.15 | Arizona |
| 1.72 | 0.669 | 115 | 1.20 | Missouri |
| 1.86 | 0.541 | 44 | 1.20 | Idaho |
| 1.59 | 1.02 | 62 | 1.30 | New York |
| 2.63 | 0.082 | 17 | 1.36 | Nevada |
| 1.81 | 0.912 | 87 | 1.36 | Minnesota |
| 1.90 | 0.834 | 64 | 1.37 | Colorado |
| 1.78 | 1.02 | 252 | 1.40 | Texas |
| 1.86 | 0.955 | 16 | 1.41 | Maine |
| 2.29 | 0.546 | 95 | 1.42 | Tennessee |
| 1.89 | 0.987 | 64 | 1.44 | Louisiana |
| 1.90 | 1.21 | 99 | 1.55 | Iowa |
| 1.93 | 1.19 | 67 | 1.56 | Alabama |
| 1.93 | 1.22 | 100 | 1.57 | North Carolina |
| 2.11 | 1.16 | 67 | 1.63 | Florida |
| 2.42 | 0.856 | 14 | 1.64 | Vermont |
| 2.23 | 1.14 | 102 | 1.69 | Illinois |
| 2.19 | 1.22 | 36 | 1.71 | Oregon |
| 2.13 | 1.36 | 88 | 1.75 | Ohio |
| 2.01 | 1.49 | 58 | 1.75 | California |
| 2.18 | 1.33 | 159 | 1.76 | Georgia |
| 2.17 | 1.35 | 46 | 1.76 | South Carolina |
| 2.17 | 1.45 | 75 | 1.81 | Arkansas |
| 2.28 | 1.47 | 92 | 1.87 | Indiana |
| 3.28 | 0.578 | 56 | 1.93 | Montana |
| 2.51 | 1.36 | 39 | 1.93 | Washington |
| 2.69 | 1.32 | 105 | 2.00 | Kansas |
| 2.41 | 1.65 | 81 | 2.03 | Mississippi |
| 3.28 | 1.07 | 67 | 2.18 | Pennsylvania |
| 2.73 | 1.64 | 14 | 2.18 | Massachusetts |
| 2.92 | 1.52 | 24 | 2.22 | Maryland |
| 2.93 | 1.63 | 82 | 2.28 | Michigan |
| 3.02 | 1.96 | 21 | 2.49 | New Jersey |
| 3.71 | 1.99 | 72 | 2.85 | Wisconsin |
| 4.33 | 1.57 | 65 | 2.95 | South Dakota |
| 4.88 | 1.66 | 27 | 3.27 | Alaska |

Note: Each state is fitted on its own counties, weighted by the tests counted. Standard errors are robust to unequal variances, with t intervals. States with fewer counties than the minimum (Delaware, Hawaii, Rhode Island, Connecticut) are not fitted, and Virginia and DC have no average.

Note: With heteroskedasticity-consistent standard errors and normal intervals the interval clears zero in 36 states. Using the Census Bureau's 2019 income estimate in place of the 2022 one gives the same pattern, except that Wyoming's slope, close to zero in both, turns slightly negative.

Note: A slope across counties describes places. It does not say what a change in a county's income would do to its students.

Source: Stanford Education Data Archive 6.0, 2009-2019, and County Health Rankings 2024 (Census SAIPE median household income for 2022); weighted by tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/income_slopes_by_state.json

### Table 4. Within the same districts, white students score 0.64 standard deviations above Black students in math, and the other gaps shown are smaller or negative

Mean gap in math achievement between two groups of students in the same geographic school district, in standard deviations of the national cohort, averaged over the districts that report each gap, with the spread of district gaps as a bar

| conf_high | conf_low | gap | grade_levels_high | grade_levels_low | mean | mean_in_grade_levels | mean_unweighted | n | p25 | p5 | p50 | p75 | p95 |
| ---: | ---: | --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| 0.667 | 0.607 | White minus Black students | 2.12 | 1.93 | 0.636 | 2.02 | 0.525 | 5,729 | 0.475 | 0.279 | 0.617 | 0.777 | 1.07 |
| 0.605 | 0.546 | Not disadvantaged minus disadvantaged students | 1.92 | 1.73 | 0.575 | 1.83 | 0.431 | 11,815 | 0.434 | 0.252 | 0.555 | 0.717 | 0.939 |
| 0.464 | 0.401 | White minus Hispanic students | 1.47 | 1.27 | 0.432 | 1.37 | 0.328 | 8,561 | 0.272 | 0.105 | 0.403 | 0.569 | 0.833 |
| −0.258 | −0.351 | White minus Asian students | −0.820 | −1.11 | −0.312 | −0.990 | −0.288 | 4,353 | −0.489 | −0.749 | −0.333 | −0.154 | 0.199 |

Views: Interquartile range of districts (every row); 5th to 95th percentile of districts (every row).

Note: Each gap is the first group's average minus the second group's. A positive gap means the first group scores higher. Gaps use the standard-deviation scale the archive recommends for research.

Note: Counting each district once gives a smaller mean gap for the white–Black and income gaps (0.52 and 0.43) because districts with more tests have larger gaps. The archive shrinks districts with few tests toward the mean, so the spread of district gaps understates the spread of the true gaps.

Note: States define economic disadvantage in their own ways, so the income gap compares groups that are defined differently from state to state. Virginia (no math), DC and Hawaii (no districts) are absent.

Source: Stanford Education Data Archive 6.0, 2009-2019 (geographic school districts, math, standard-deviation scale); weighted by tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/gap_distribution.json

### Table 5. In math, Asian students average +0.66 standard deviations from the national average and Black students −0.53

Mean math achievement of each group of students relative to the national average of all students, in standard deviations of the national cohort, over counties that report the group

| conf_high | conf_high_unweighted | conf_low | conf_low_unweighted | group | kind | level | level_unweighted | n |
| ---: | ---: | ---: | ---: | --- | --- | ---: | ---: | ---: |
| 0.803 | 0.497 | 0.498 | 0.388 | Asian | Race and ethnicity | 0.662 | 0.445 | 1,563 |
| 0.282 | 0.121 | 0.191 | 0.032 | White | Race and ethnicity | 0.237 | 0.078 | 2,975 |
| −0.179 | −0.218 | −0.422 | −0.285 | Hispanic | Race and ethnicity | −0.301 | −0.249 | 2,640 |
| −0.296 | −0.180 | −0.472 | −0.289 | Native American | Race and ethnicity | −0.380 | −0.231 | 1,349 |
| −0.478 | −0.434 | −0.594 | −0.510 | Black | Race and ethnicity | −0.532 | −0.471 | 2,133 |
| 0.428 | 0.265 | 0.355 | 0.184 | Not economically disadvantaged | Economic status | 0.393 | 0.225 | 2,966 |
| −0.292 | −0.237 | −0.413 | −0.320 | Economically disadvantaged | Economic status | −0.352 | −0.277 | 2,994 |

Note: Each group's mean covers only the counties that report the group, and the number of counties differs by group (it is in each row's tooltip), so the groups are not measured in the same places. SEDA takes the groups from state reports. Race and ethnicity follow the federal categories, which are mutually exclusive, so Hispanic students of any race form their own group and the Asian, Black, white and Native American groups exclude them. States define economic disadvantage themselves.

Source: Stanford Education Data Archive 6.0, 2009-2019 (county averages by group, math, standard-deviation scale); weighted by each group's tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/group_levels.json

### Table 6. The white–Black math gap is wider in counties with more school segregation, a correlation of +0.59 across 2,101 counties

White minus Black math gap (standard deviations of the national cohort) against the school segregation index (Theil's index across racial and ethnic groups), one dot per county; dot area is the tests counted

No inline rows: the values of Table 6 are in https://vishalsingh.org/zipcode/data/test-scores-class-and-race/gap_vs_segregation.json.

Note: The index measures how unevenly students of every racial and ethnic group are spread across a county's schools relative to the county's composition. It is not a Black–white index, and it is for the 2022 to 2023 school year in County Health Rankings' 2024 release of NCES school data, after the test years.

Note: The gap is white minus Black, so a positive value means white students score higher.

Source: Stanford Education Data Archive 6.0, 2009-2019 (county gaps, math), and County Health Rankings 2024 (school segregation, school year 2022 to 2023, NCES Common Core of Data); weighted by tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/gap_vs_segregation.json

### Table 7. Counties with a wider income gap have a wider white–Black gap, a correlation of +0.80 across 2,092 counties, and the two gaps are of similar size

White minus Black math gap against the gap between students who are not and are economically disadvantaged, standard deviations of the national cohort, one dot per county; dot area is the tests counted

No inline rows: the values of Table 7 are in https://vishalsingh.org/zipcode/data/test-scores-class-and-race/class_gap_vs_race_gap.json.

Note: SEDA does not cross race with economic disadvantage, so the two gaps are measured on overlapping but different groups of students, and their estimation errors are correlated. The comparison describes counties and does not isolate a racial gap among students in the same economic circumstances.

Note: Counties are weighted by all-student tests counted. The standard deviation of the race gap around the line is 0.14 standard deviations.

Source: Stanford Education Data Archive 6.0, 2009-2019 (county gaps, math); weighted by tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/class_gap_vs_race_gap.json

### Table 8. Relative to its average size, the white–Black math gap varies 1.34 times as much across counties as the boys minus girls reading gap

Standard deviation across counties of each gap divided by the average gap, counties with all four gaps, weighted by the tests of the two groups in each gap

| cv | cv_high | cv_low | cv_unweighted | gap | median_se | n | sd | sd_high | sd_low | sd_unweighted |
| ---: | ---: | ---: | ---: | --- | ---: | ---: | ---: | ---: | ---: | ---: |
| 0.326 | 0.353 | 0.300 | 0.375 | White minus Black, math | 0.028 | 2,020 | 0.238 | 0.256 | 0.218 | 0.209 |
| 0.433 | 0.484 | 0.388 | 0.606 | White minus Hispanic, math | 0.025 | 2,020 | 0.229 | 0.249 | 0.207 | 0.209 |
| 0.274 | 0.291 | 0.255 | 0.288 | Not disadvantaged minus disadvantaged, math | 0.011 | 2,020 | 0.189 | 0.201 | 0.174 | 0.157 |
| 0.244 | 0.293 | 0.187 | 0.299 | Boys minus girls, reading | 0.010 | 2,020 | 0.059 | 0.069 | 0.047 | 0.069 |

Views: Relative to the average gap (every row); Standard deviation (every row).

Note: Relative spread is the weighted standard deviation across counties divided by the weighted average gap, so a larger gap has no more room to vary. Counting each county once gives a ratio of 3.0 for the standard deviations and 1.26 for the relative spreads. The median standard error of a county's white–Black gap is 0.03 standard deviations and of its boys minus girls reading gap 0.01.

Note: The archive shrinks small counties toward the mean, which lowers every spread, most for the gaps measured least precisely. The boys minus girls gap appears only as a yardstick.

Source: Stanford Education Data Archive 6.0, 2009-2019 (county gaps, math and reading, standard-deviation scale); weighted by tests counted, modeled estimates

Data: https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/place_made_gaps.json

## All estimates

Every fact in facts.json (115), sorted by id.

| Fact id | Value | Unit | Estimand | Population | Period | Interval | n | Weights | Source | Note |
| --- | ---: | --- | --- | --- | --- | --- | ---: | --- | --- | --- |
| ach_bottom | −4.3 | grade levels from the national average (positive is above) | county average of math and reading (grade-level scale, minus the grade the pooled estimate is centered on) | the county with the lowest average of math and reading, Kusilvak Census Area, AK | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 15,890 tests | none (one county) | Stanford Education Data Archive |   |
| ach_inc_d1 | −1.12 | grade levels from the national average (positive is above) | weighted mean of the county average of math and reading within the tenth (equal numbers of counties), bootstrap interval over states | counties in the lowest tenth by median household income, among counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI −1.44 to −0.75 | 299 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| ach_inc_d10 | +0.41 | grade levels from the national average (positive is above) | weighted mean of the county average of math and reading within the tenth (equal numbers of counties), bootstrap interval over states | counties in the highest tenth by median household income, among counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI 0.02 to 0.87 | 300 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| ach_p5 | −1.27 | grade levels from the national average (positive is above) | 5th percentile of the county average of math and reading, counties weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | A spread of the county averages, not an interval. |
| ach_p5_unw | −1.57 | grade levels from the national average (positive is above) | 5th percentile of the county average of math and reading, each county counted once | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | none (each county counts once) | Stanford Education Data Archive |   |
| ach_p95 | +1.27 | grade levels from the national average (positive is above) | 95th percentile of the county average of math and reading, counties weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | A spread of the county averages, not an interval. |
| ach_p95_unw | +1.01 | grade levels from the national average (positive is above) | 95th percentile of the county average of math and reading, each county counted once | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | none (each county counts once) | Stanford Education Data Archive |   |
| ach_spread | 2.54 | grade levels | 95th minus 5th percentile of the county average of math and reading, counties weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | A spread of the county averages, not an interval. The first edition's span from the lowest to the highest county rested on two counties. |
| ach_spread_unw | 2.58 | grade levels | 95th minus 5th percentile of the county average of math and reading, each county counted once | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | none (each county counts once) | Stanford Education Data Archive |   |
| ach_top | +2.3 | grade levels from the national average (positive is above) | county average of math and reading (grade-level scale, minus the grade the pooled estimate is centered on) | the county with the highest average of math and reading, Forsyth County, GA | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 433,229 tests | none (one county) | Stanford Education Data Archive |   |
| asn_level | +0.66 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | Asian students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.50 to 0.80 | 1,563 counties | the group's math tests counted in each county | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| asn_level_unw | +0.44 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | Asian students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.39 to 0.50 | 1,563 counties | none (each county counts once) | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| b_black | 0.03 | standard deviations of the national cohort of the white minus Black gap per standard deviation of the measure | coefficient on the Black share of residents (standardized) in one weighted regression with state fixed effects, errors clustered on state | counties with a white minus Black math gap and a school segregation index, a residential segregation index, the Black share of residents and median household income | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.00 to 0.07 | 1,849 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| b_inc | 0.09 | standard deviations of the national cohort of the white minus Black gap per standard deviation of the measure | coefficient on the log of median household income (standardized) in one weighted regression with state fixed effects, errors clustered on state | counties with a white minus Black math gap and a school segregation index, a residential segregation index, the Black share of residents and median household income | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.06 to 0.11 | 1,849 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| b_resid | −0.01 | standard deviations of the national cohort of the white minus Black gap per standard deviation of the measure | coefficient on the Black-white residential segregation index (standardized) in one weighted regression with state fixed effects, errors clustered on state | counties with a white minus Black math gap and a school segregation index, a residential segregation index, the Black share of residents and median household income | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI −0.04 to 0.02 | 1,849 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| b_resseg | 0.07 | standard deviations of the national cohort of the white minus Black gap per standard deviation of the residential index | slope of the gap on the standardized residential index in a weighted regression with state fixed effects (no other measure), errors clustered on state | counties with a white minus Black math gap and a Black-white residential segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.02 to 0.12 | 1,859 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| b_school | 0.11 | standard deviations of the national cohort of the white minus Black gap per standard deviation of the measure | coefficient on the school segregation index (standardized) in one weighted regression with state fixed effects, errors clustered on state | counties with a white minus Black math gap and a school segregation index, a residential segregation index, the Black share of residents and median household income | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.08 to 0.13 | 1,849 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| b_seg | 0.11 | standard deviations of the national cohort of the white minus Black gap per standard deviation of the index | slope of the gap on the standardized school segregation index in a weighted regression with state fixed effects, errors clustered on state | counties with a white minus Black math gap and a school segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.09 to 0.14 | 2,101 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| blk_level | −0.53 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | Black students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.59 to −0.48 | 2,133 counties | the group's math tests counted in each county | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| blk_level_unw | −0.47 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | Black students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.51 to −0.43 | 2,133 counties | none (each county counts once) | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| both_diff | 0.04 | standard deviations of the national cohort, white minus Black gap minus income gap | difference between the weighted mean white minus Black gap and the weighted mean income gap over the same districts, bootstrap interval over states | geographic school districts with a math estimate for both the white minus Black gap and the income gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.02 to 0.06 | 5,658 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| both_n | 5,658 | districts | count of districts that report both gaps | geographic school districts with a math estimate for both the white minus Black gap and the income gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   |   | none (full count) | Stanford Education Data Archive |   |
| class_var | 64% | percent of the variance of the county white minus Black gap | square of the weighted correlation (the share of weighted variance in the county race gap that the income gap accounts for) | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 57% to 71% | 2,092 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| cty_neg_mean | 0.69 | standard deviations of the national cohort | weighted mean of the county income gap in math | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 2,092 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| cty_wbg_mean | 0.74 | standard deviations of the national cohort | weighted mean of the county white minus Black gap in math | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 2,092 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| cv_mfg_rla | 0.24 | ratio of the spread to the average gap | weighted standard deviation across counties of the boys minus girls reading gap divided by the absolute value of its weighted mean, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.19 to 0.29 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| cv_neg | 0.27 | ratio of the spread to the average gap | weighted standard deviation across counties of the income math gap divided by the absolute value of its weighted mean, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.26 to 0.29 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| cv_wbg | 0.33 | ratio of the spread to the average gap | weighted standard deviation across counties of the white minus Black math gap divided by the absolute value of its weighted mean, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.30 to 0.35 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| cv_whg | 0.43 | ratio of the spread to the average gap | weighted standard deviation across counties of the white minus Hispanic math gap divided by the absolute value of its weighted mean, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.39 to 0.48 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| ecd_level | −0.35 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | economically disadvantaged students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.41 to −0.29 | 2,994 counties | the group's math tests counted in each county | Stanford Education Data Archive |   |
| ecd_level_unw | −0.28 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | economically disadvantaged students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.32 to −0.24 | 2,994 counties | none (each county counts once) | Stanford Education Data Archive |   |
| gap_seg_d1 | 0.47 | standard deviations of the national cohort, white minus Black | weighted mean white minus Black math gap within the tenth (equal numbers of counties), bootstrap interval over states | counties in the least segregated tenth by school segregation index, among counties with a white minus Black math gap and a school segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.44 to 0.50 | 210 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| gap_seg_d10 | 0.90 | standard deviations of the national cohort, white minus Black | weighted mean white minus Black math gap within the tenth (equal numbers of counties), bootstrap interval over states | counties in the most segregated tenth by school segregation index, among counties with a white minus Black math gap and a school segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.86 to 0.95 | 211 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| gl_per_sd | 3.3 | grade levels per standard deviation | slope of the county average on the grade-level scale against the county average on the standard-deviation scale (math and reading averaged), weighted by tests counted | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| gl_per_sd_gap | 3.2 | grade levels per standard deviation | slope of the archive's grade-level gap on its standard-deviation gap across the four math gaps, bootstrap over states | geographic school districts with a math estimate for the white minus Black, white minus Hispanic, white minus Asian or income gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 30,458 district gap estimates | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| hsp_level | −0.30 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | Hispanic students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.42 to −0.18 | 2,640 counties | the group's math tests counted in each county | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| hsp_level_unw | −0.25 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | Hispanic students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.29 to −0.22 | 2,640 counties | none (each county counts once) | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| income_corr | +0.59 | correlation coefficient | weighted correlation of the county average of math and reading with the log of county median household income, bootstrap interval over states (counties in a state resemble one another) | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI 0.43 to 0.76 | 2,999 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | Counting each county once gives a similar correlation. |
| income_r2 | 34% | percent of the variance of county average achievement | square of the weighted correlation with log income (the share of weighted variance in county averages that income accounts for) | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI 19% to 59% | 2,999 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| income_resid_sd | 0.63 | grade levels | weighted standard deviation of the county average around the income line, bootstrap interval over states | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI 0.49 to 0.72 | 2,999 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | The archive shrinks small counties toward the mean, which lowers this spread. |
| income_slope | 1.28 | grade levels of county average achievement per doubling of median household income | weighted slope of the county average on the log (base 2) of median household income, bootstrap interval over states | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI 0.94 to 1.72 | 2,999 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | Counting each county once gives a slope within the interval. |
| min_alt_hi | 15 | counties | a higher minimum number of counties a state needs for its own slope (a sensitivity check) | states fitted one at a time | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (inclusion rule) | Stanford Education Data Archive |   |
| min_alt_lo | 8 | counties | a lower minimum number of counties a state needs for its own slope (a sensitivity check) | states fitted one at a time | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (inclusion rule) | Stanford Education Data Archive |   |
| min_alt_max | 30 | counties | highest minimum number of counties tried in the sensitivity check | states fitted one at a time | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (inclusion rule) | Stanford Education Data Archive |   |
| min_counties_state | 10 | counties | minimum number of counties a state needs for its own slope | states fitted one at a time | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (inclusion rule) | Stanford Education Data Archive |   |
| n_classrace | 2,092 | counties | count of counties in the comparison | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   |   | none (full count) | Stanford Education Data Archive |   |
| n_common | 2,020 | counties | count of counties with all four gaps | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) |   |   | none (full count) | Stanford Education Data Archive |   |
| n_counties_ach | 3,000 | counties | count of counties | counties and county equivalents in the SEDA county file with a math and a reading estimate for all students (Virginia, DC and a few small counties have none) | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (full count) | Stanford Education Data Archive |   |
| n_counties_income | 2,999 | counties | count of counties in the income comparison | counties with a SEDA average for both math and reading and a median household income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (full count) | Stanford Education Data Archive |   |
| n_joint | 1,849 | counties | count of counties in the joint regression | counties with a white minus Black math gap and a school segregation index, a residential segregation index, the Black share of residents and median household income | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) |   |   | none (full count) | Stanford Education Data Archive |   |
| n_map_nodata | 142 | counties | count of drawn counties with no average of math and reading | counties and county equivalents on the map (Puerto Rico not drawn) | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (full count) | Stanford Education Data Archive |   |
| n_map_other | 8 | counties | count of counties missing from the SEDA county file or missing a math or a reading estimate | counties on the map outside Virginia and DC with no average | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (full count) | Stanford Education Data Archive |   |
| n_off_scale | 73 | counties | count of counties whose average lies farther from the national average than the end of the key | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (full count) | Stanford Education Data Archive |   |
| n_seg | 2,101 | counties | count of counties in the segregation comparison | counties with a white minus Black math gap and a school segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) |   |   | none (full count) | Stanford Education Data Archive |   |
| n_va | 133 | counties | count of Virginia places with no average of math and reading because SEDA has no Virginia math estimates | Virginia counties and independent cities on the map | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (full count) | Stanford Education Data Archive |   |
| nam_level | −0.38 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | Native American students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.47 to −0.30 | 1,349 counties | the group's math tests counted in each county | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| nam_level_unw | −0.23 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | Native American students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.29 to −0.18 | 1,349 counties | none (each county counts once) | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| nec_level | +0.39 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | students who are not economically disadvantaged in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.35 to 0.43 | 2,966 counties | the group's math tests counted in each county | Stanford Education Data Archive |   |
| nec_level_unw | +0.23 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | students who are not economically disadvantaged in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.18 to 0.26 | 2,966 counties | none (each county counts once) | Stanford Education Data Archive |   |
| neg_gl | 1.8 | grade levels, not disadvantaged minus disadvantaged | weighted mean district gap in math on the archive's grade-level scale (its own grade-level gap rows), bootstrap interval over states | geographic school districts with a math estimate for both groups | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 1.7 to 1.9 | 11,815 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| neg_mean | 0.58 | standard deviations of the national cohort, not economically disadvantaged minus economically disadvantaged | weighted mean of the district gap in math, bootstrap interval over states (districts in a state resemble one another) | geographic school districts with a math estimate for both groups (not economically disadvantaged minus economically disadvantaged) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.55 to 0.61 | 11,815 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | Each gap is averaged over the districts that report it, so the gaps cover different sets of districts. |
| neg_mean_both | 0.60 | standard deviations of the national cohort, not economically disadvantaged minus economically disadvantaged | weighted mean of the district gap in math over the districts that report both gaps, bootstrap interval over states | geographic school districts with a math estimate for both the white minus Black gap and the income gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.57 to 0.63 | 5,658 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| neg_mean_unw | 0.43 | standard deviations of the national cohort, not disadvantaged minus disadvantaged | unweighted mean of the district gap in math (each district counts once) | geographic school districts with a math estimate for both groups | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 11,815 districts | none (each district counts once) | Stanford Education Data Archive |   |
| neg_n | 11,815 | districts | count of districts with a gap estimate | geographic school districts with a math estimate for both groups (not economically disadvantaged minus economically disadvantaged) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   |   | none (full count) | Stanford Education Data Archive |   |
| neg_only_mean | 0.40 | standard deviations of the national cohort, not economically disadvantaged minus economically disadvantaged | weighted mean of the district income gap in math, bootstrap interval over states | geographic school districts with an income gap but no white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.38 to 0.41 | 6,157 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| neg_only_n | 6,157 | districts | count of districts that report the income gap only | geographic school districts with an income gap but no white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   |   | none (full count) | Stanford Education Data Archive |   |
| nm_all_share | 42% | percent of counties in the Northeast or Midwest | share of all counties with an average that are in the Northeast or the Midwest | counties with a SEDA average for both math and reading, grouped by U.S. Census Bureau region | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | none (each county counts once) | Stanford Education Data Archive |   |
| nm_high_share | 67% | percent of counties in the highest tenth by average achievement that are in the Northeast or Midwest | share of the highest tenth of counties in the Northeast or the Midwest | counties with a SEDA average for both math and reading, grouped by U.S. Census Bureau region | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 300 counties | none (each county counts once) | Stanford Education Data Archive |   |
| r_classrace | +0.80 | correlation coefficient | weighted correlation of the county income gap with the county white minus Black gap in math, bootstrap interval over states | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.75 to 0.84 | 2,092 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| r_resseg | +0.25 | correlation coefficient | weighted correlation of the county gap with the residential index of dissimilarity (0 to 100, ACS 2018 to 2022), bootstrap interval over states | counties with a white minus Black math gap and a Black-white residential segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.12 to 0.37 | 1,859 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| r_seg | +0.59 | correlation coefficient | weighted correlation of the county white minus Black math gap with the school segregation index (Theil's index across racial and ethnic groups, 0 to 1), bootstrap interval over states | counties with a white minus Black math gap and a school segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.51 to 0.66 | 2,101 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| r_sseg_rseg | +0.46 | correlation coefficient | weighted correlation of the school segregation index with the residential index, bootstrap interval over states | counties with both segregation indices and a white minus Black math gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) | 95% CI 0.31 to 0.56 | 1,849 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| ratio_cv | 1.34 | ratio | relative spread of the white minus Black math gap divided by the relative spread of the boys minus girls reading gap, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 1.08 to 1.76 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| ratio_cv_unw | 1.26 | ratio | the same ratio with each county counted once, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 1.04 to 1.63 | 2,020 counties | none (each county counts once) | Stanford Education Data Archive |   |
| ratio_mean | 3.0 | ratio | average white minus Black math gap divided by the average boys minus girls reading gap (absolute values), bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 2.8 to 3.3 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| ratio_sd | 4.1 | ratio | spread of the white minus Black math gap divided by the spread of the boys minus girls reading gap, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 3.3 to 5.2 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| ratio_sd_unw | 3.0 | ratio | the same ratio with each county counted once, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 2.5 to 3.8 | 2,020 counties | none (each county counts once) | Stanford Education Data Archive |   |
| resid_sd | 0.14 | standard deviations of the national cohort | weighted standard deviation of the county white minus Black gap around its line on the income gap, bootstrap interval over states | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.13 to 0.15 | 2,092 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive | The archive shrinks small counties toward the mean, which lowers this spread. |
| scale_cap | 2 | grade levels | distance from the national average at which the key ends (a display choice) | the key of the county map | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (display rule) | Stanford Education Data Archive |   |
| sd_mfg_rla | 0.06 | standard deviations of the national cohort | weighted standard deviation across counties of the boys minus girls reading gap estimate, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.05 to 0.07 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive | The archive shrinks small counties toward the mean, which lowers this spread. |
| sd_neg | 0.19 | standard deviations of the national cohort | weighted standard deviation across counties of the income math gap estimate, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.17 to 0.20 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive | The archive shrinks small counties toward the mean, which lowers this spread. |
| sd_sseg | 0.07 | Theil's index (0 to 1) | standard deviation of the school segregation index across counties (each county once) | counties with a white minus Black math gap and a school segregation index | test results for third through eighth grade, school years 2009 to 2019 pooled (math); school segregation for the 2022 to 2023 school year, residential segregation for 2018 to 2022 (County Health Rankings 2024) |   | 2,101 counties | none (each county counts once) | Stanford Education Data Archive |   |
| sd_wbg | 0.24 | standard deviations of the national cohort | weighted standard deviation across counties of the white minus Black math gap estimate, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.22 to 0.26 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive | The archive shrinks small counties toward the mean, which lowers this spread. |
| sd_whg | 0.23 | standard deviations of the national cohort | weighted standard deviation across counties of the white minus Hispanic math gap estimate, bootstrap interval over states | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) | 95% CI 0.21 to 0.25 | 2,020 counties | math tests counted for the two groups in the gap | Stanford Education Data Archive | The archive shrinks small counties toward the mean, which lowers this spread. |
| se_mfg_rla_med | 0.01 | standard deviations of the national cohort | median standard error of the county gap estimate (boys minus girls reading) | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) |   | 2,020 counties | none (median over counties) | Stanford Education Data Archive |   |
| se_wbg_med | 0.03 | standard deviations of the national cohort | median standard error of the county gap estimate (white minus Black math) | counties with an estimate of all four gaps (white minus Black, white minus Hispanic and income gaps in math, boys minus girls gap in reading) | test results for third through eighth grade, school years 2009 to 2019 pooled (math, and reading for the boys minus girls gap) |   | 2,020 counties | none (median over counties) | Stanford Education Data Archive |   |
| sig_alt_hi | 38 | states | count of those states where the 95% interval for the slope lies above zero | states with 15 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (each state counts once) | Stanford Education Data Archive |   |
| sig_alt_lo | 41 | states | count of those states where the 95% interval for the slope lies above zero | states with 8 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (each state counts once) | Stanford Education Data Archive |   |
| slope_classrace | 0.99 | standard deviations of the white minus Black gap per standard deviation of the income gap | weighted slope of the county white minus Black gap on the county income gap, bootstrap interval over states | counties with a math estimate for both the income gap and the white minus Black gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.91 to 1.08 | 2,092 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| slope_hi | 3.27 | grade levels of county average achievement per doubling of median household income | tests-weighted slope of the county average on log (base 2) income within the state, robust errors with t intervals (each county its own cluster) | counties in Alaska, the state with the steepest slope | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI 1.66 to 4.87 | 27 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| slope_lo | 0.33 | grade levels of county average achievement per doubling of median household income | tests-weighted slope of the county average on log (base 2) income within the state, robust errors with t intervals (each county its own cluster) | counties in Kentucky, the state with the shallowest slope | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 | 95% CI −0.08 to 0.74 | 120 counties | math and reading tests counted for all students in the county | Stanford Education Data Archive |   |
| slope_med | 1.57 | grade levels of county average achievement per doubling of median household income | median across states of the within-state slope (tests-weighted regression of the county average on log (base 2) income) | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   | 45 states | none (each state counts once) | Stanford Education Data Archive |   |
| slope_pos | 45 | states | count of states where the county slope of average achievement on log income is positive | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (each state counts once) | Stanford Education Data Archive |   |
| slope_sig | 40 | states | count of states where the 95% interval for the slope lies above zero | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (each state counts once) | Stanford Education Data Archive |   |
| slope_sig_hc3 | 36 | states | count of states where the 95% interval from heteroskedasticity-consistent (HC3) errors with a normal approximation lies above zero | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (each state counts once) | Stanford Education Data Archive |   |
| slope_states | 45 | states | count of states fitted | states with 10 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (full count) | Stanford Education Data Archive |   |
| south_all_share | 43% | percent of counties in the South | share of all counties with an average that are in the South | counties with a SEDA average for both math and reading, grouped by U.S. Census Bureau region | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 3,000 counties | none (each county counts once) | Stanford Education Data Archive |   |
| south_low_share | 74% | percent of counties in the lowest tenth by average achievement that are in the South | share of the lowest tenth of counties (equal numbers of counties, ranked by the county average) in the South | counties with a SEDA average for both math and reading, grouped by U.S. Census Bureau region | test results for third through eighth grade, school years 2009 to 2019 pooled |   | 300 counties | none (each county counts once) | Stanford Education Data Archive |   |
| states_alt_hi | 42 | states | count of states fitted at that minimum | states with 15 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (full count) | Stanford Education Data Archive |   |
| states_alt_lo | 46 | states | count of states fitted at that minimum | states with 8 or more counties that have an average and an income | test results for third through eighth grade, school years 2009 to 2019 pooled; median household income for 2022 |   |   | none (full count) | Stanford Education Data Archive |   |
| tests_m | 404.9 million | math and reading tests | sum of the math and the reading tests counted behind the county averages (one test is one student's result in one subject, grade and year) | counties with a SEDA average for both math and reading | test results for third through eighth grade, school years 2009 to 2019 pooled |   |   | none (full count) | Stanford Education Data Archive |   |
| wag_asian_share | 87% | percent of districts where Asian students score higher than white students | share of districts with a negative white minus Asian gap in math (each district counts once) | geographic school districts with a math estimate for both white and Asian students | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 4,353 districts | none (each district counts once) | Stanford Education Data Archive |   |
| wag_mean | −0.31 | standard deviations of the national cohort, white minus Asian | weighted mean of the district gap in math, bootstrap interval over states (districts in a state resemble one another) | geographic school districts with a math estimate for both groups (white minus Asian) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI −0.35 to −0.26 | 4,353 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | Each gap is averaged over the districts that report it, so the gaps cover different sets of districts. |
| wag_n | 4,353 | districts | count of districts with a gap estimate | geographic school districts with a math estimate for both groups (white minus Asian) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   |   | none (full count) | Stanford Education Data Archive |   |
| wbg_gl | 2.0 | grade levels, white minus black | weighted mean district gap in math on the archive's grade-level scale (its own grade-level gap rows), bootstrap interval over states | geographic school districts with a math estimate for both groups | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 1.9 to 2.1 | 5,729 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| wbg_mean | 0.64 | standard deviations of the national cohort, white minus Black | weighted mean of the district gap in math, bootstrap interval over states (districts in a state resemble one another) | geographic school districts with a math estimate for both groups (white minus Black) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.61 to 0.67 | 5,729 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | Each gap is averaged over the districts that report it, so the gaps cover different sets of districts. |
| wbg_mean_both | 0.64 | standard deviations of the national cohort, white minus Black | weighted mean of the district gap in math over the districts that report both gaps, bootstrap interval over states | geographic school districts with a math estimate for both the white minus Black gap and the income gap | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.61 to 0.67 | 5,658 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive |   |
| wbg_mean_unw | 0.52 | standard deviations of the national cohort, white minus black | unweighted mean of the district gap in math (each district counts once) | geographic school districts with a math estimate for both groups | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 5,729 districts | none (each district counts once) | Stanford Education Data Archive |   |
| wbg_n | 5,729 | districts | count of districts with a gap estimate | geographic school districts with a math estimate for both groups (white minus Black) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   |   | none (full count) | Stanford Education Data Archive |   |
| wbg_p5 | 0.28 | standard deviations of the national cohort, white minus Black | 5th percentile of the district gap in math, districts weighted by tests counted | geographic school districts with a math estimate for both white and Black students | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 5,729 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | A spread of district gaps, not an interval. |
| wbg_p95 | 1.08 | standard deviations of the national cohort, white minus Black | 95th percentile of the district gap in math, districts weighted by tests counted | geographic school districts with a math estimate for both white and Black students | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 5,729 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | A spread of district gaps, not an interval. |
| wbg_pos_share | 99.8% | percent of districts where white students score higher than Black students | share of districts with a positive white minus Black gap in math (each district counts once) | geographic school districts with a math estimate for both white and Black students | test results for third through eighth grade, school years 2009 to 2019 pooled (math) |   | 5,729 districts | none (each district counts once) | Stanford Education Data Archive |   |
| whg_mean | 0.43 | standard deviations of the national cohort, white minus Hispanic | weighted mean of the district gap in math, bootstrap interval over states (districts in a state resemble one another) | geographic school districts with a math estimate for both groups (white minus Hispanic) | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.40 to 0.46 | 8,561 districts | math tests counted for the two groups in the gap | Stanford Education Data Archive | Each gap is averaged over the districts that report it, so the gaps cover different sets of districts. |
| wht_level | +0.24 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, over counties that report the group, bootstrap interval over states | white students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.19 to 0.28 | 2,975 counties | the group's math tests counted in each county | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |
| wht_level_unw | +0.08 | standard deviations of the national cohort | mean math achievement of the group relative to the national average of all students, each county counted once, bootstrap interval over states | white students in counties that report the group | test results for third through eighth grade, school years 2009 to 2019 pooled (math) | 95% CI 0.03 to 0.12 | 2,975 counties | none (each county counts once) | Stanford Education Data Archive | Race and ethnicity groups follow the federal categories that states report: they are mutually exclusive, and Hispanic students of any race form their own group. |

## Definitions

- SD units (SEDA): Test scores stated in units of the typical spread of scores around the national average, so that a score reads as the number of such spreads above or below the national average. SEDA also reports scores in grade levels, which are a separate scale.
- Bootstrap interval: A range for an estimate found by recomputing it on many random resamples of the data and reading the range from the results. It shows how much the estimate would vary from sample to sample.
- Fixed effects: A regression adjustment that gives each group, such as each county, its own baseline. The estimate then rests on differences within groups.
- Ecological inference: Drawing conclusions about individuals from data about places or groups. A pattern across counties need not hold for the people inside them.

## Methods

This chapter compares county average achievement in grades 3 to 8, pooled over the school years 2009 to 2019 from the Stanford Education Data Archive 6.0, with county income and school and residential segregation, and compares achievement gaps between groups of students. The county income and segregation measures come from County Health Rankings and refer to other years than the test scores. The archive's estimates are empirical-Bayes, which shrink small places toward the mean and lower every spread, and counties lacking either math or reading, including all of Virginia, have no average.

### Which students, grades and years the scores cover

Achievement is the Stanford Education Data Archive 6.0 pooled estimate for grades 3 to 8 over the school years 2009 to 2019, read for counties and for geographic school districts through the book's loader.

Race and ethnicity groups follow the federal categories that states report (mutually exclusive, with Hispanic students of any race in their own group); economic disadvantage is as each state defines it.

### How grade levels, standard deviations and gaps are defined

County averages in grade levels are the archive's grade-level estimate minus the grade it is centered on (5.5), averaged over math and reading, so zero is the national average; counties lacking either subject (all of Virginia, which has no math estimates, and two others) have no average, and DC has no rows.

Group levels, gaps and spreads use the standard-deviation scale, which the archive recommends for research; the two scales are never mixed on one axis. Gaps are the archive's own gap rows (first group minus second group). Estimates are empirical-Bayes, which shrink small places toward the mean.

Explains Table 5, Table 4 and Table 8.

### Where the income and segregation measures come from

Income is County Health Rankings' 2024 median household income (Census SAIPE for 2022); school segregation is its Theil's index of the spread of students of every racial and ethnic group across a county's schools (0 to 1, NCES Common Core of Data, school year 2022 to 2023 per the 2024 Technical Document); residential segregation is the Black-white index of dissimilarity (0 to 100, ACS 2018 to 2022).

Explains Table 2, Table 3, Table 6 and Table 7.

### How counties and groups are weighted

Weights: county averages by the math and reading tests counted for all students; a group's level by that group's math tests; a gap by the math tests of the two groups; the class-race comparison by all-student tests.

### Which places are drawn

Connecticut is drawn as its eight legacy counties; Puerto Rico is not drawn.

Explains Table 1.

### How uncertainty and spread are measured

Correlations, slopes and means across counties use a bootstrap that resamples whole states (2,000 draws, seed 12345), because counties in a state resemble one another; slopes within one state use robust errors with t intervals, each county its own cluster; regressions with state fixed effects cluster on state.

Spreads of county averages and of district gaps are percentiles or standard deviations, not intervals, and the archive's shrinkage lowers them.

## What these data cannot show

The figures describe counties and districts, and a county average blends every child in it (ecological inference). A pattern across counties need not hold for the students inside them. An average level is not a school's contribution, since it reflects families, neighborhoods, health and schools together. Reardon found that the income gap in achievement is already large when children enter kindergarten and does not widen much during the school years.[5] That fits a gap that is mostly in place at school entry, though county averages for third through eighth grade cannot show when each gap arises.

The achievement estimates are state tests placed on a national scale, pooled over a decade of cohorts. They are empirical-Bayes estimates, so small places are pulled toward the mean and the spreads here understate the spread of the true values, most for places with few tests. Virginia has no math estimates and DC no county rows. The groups come from state reports, states define economic disadvantage differently, and the data do not cross race with income.

The covariates come from other years than the tests. Median income is for 2022, the school segregation index for the 2022 to 2023 school year and the residential index for 2018 to 2022, while the tests are for 2009 to 2019, so the comparisons assume that a county's position changed little in the years between. The school segregation index covers every racial and ethnic group, not only Black and white students. The correlations and slopes are associations across places. The state fixed effects remove differences between states but not differences between counties, so none of them says what would happen to a county's students if its income or segregation changed. How schools discipline students, and what follows, is the subject of Chapter 3.4, School discipline and incarceration (https://vishalsingh.org/zipcode/school-discipline-and-incarceration).

## References

1. Reardon, Sean F.; Kalogrides, Demetra; Shores, Kenneth (2019). The Geography of Racial/Ethnic Test Score Gaps. American Journal of Sociology 124(4): 1164-1221. https://doi.org/10.1086/700678
2. Card, David; Rothstein, Jesse (2007). Racial Segregation and the Black-White Test Score Gap. Journal of Public Economics 91(11-12): 2158-2184. https://doi.org/10.1016/j.jpubeco.2007.03.006
3. Ludwig, Jens; Miller, Douglas L. (2007). Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design. The Quarterly Journal of Economics 122(1): 159-208. https://doi.org/10.1162/qjec.122.1.159
4. Jackson, C. Kirabo; Johnson, Rucker C.; Persico, Claudia (2016). The Effects of School Spending on Educational and Economic Outcomes: Evidence from School Finance Reforms. The Quarterly Journal of Economics 131(1): 157-218. https://doi.org/10.1093/qje/qjv036
5. Reardon, Sean F. (2011). The Widening Academic Achievement Gap Between the Rich and the Poor: New Evidence and Possible Explanations. In Greg J. Duncan and Richard J. Murnane (eds.), Whither Opportunity? Rising Inequality, Schools, and Children's Life Chances, pp. 91-116. New York: Russell Sage Foundation.

## Provenance

- Pipeline version: 0.1.0
- Build script: book2/chapters/test-scores-class-and-race/build.py (sha256 29de886272fb6330964489d56c5ef47b1057490454547685990192499c08c6ca)
- Built on: 2026-10-07
- Site commit: c2b1ff3309cb4a10833f884da91ac0057a66ad0a

Inputs:

| File | Size (bytes) | SHA-256, first 1 MB | SHA-256, last 1 MB |
| --- | ---: | --- | --- |
| book2/chapters/test-scores-class-and-race/seda.py | 33,494 | f4f0b05e4a3ad768df827cce4120f2ee17feb040d8062984836c50cced7d27e9 | f4f0b05e4a3ad768df827cce4120f2ee17feb040d8062984836c50cced7d27e9 |
| data/staged/education/seda_county_poolsub_6.0.parquet | 3,604,804 | 730134713ed3cae8983a255caa2a1be786a2d50688a949b11372f86e90065976 | 356fb555b2de0cc487cb4c37c95f29cee0497a96b4f7385fa6f10b9975bee58d |
| data/staged/education/seda_geodist_poolsub_6.0.parquet | 12,344,123 | 48de785e0dc62aacfc4608757670e6912b318c6c02baa3a716ef4c131c0eb6b5 | 5a22f706cfd0295923dd169d985d44d0da9076236e3afe38d59c5f6dd3e518a6 |
| data/staged/health/chr_county_2024.parquet | 8,776,933 | 619795f7ecfec8aff10694b649eaee5e421dbeffbe4be47af4161b51ceefa5cd | c69357f1bcf630407bb9716cb445618838999558c019aaaf77d4681b6bf45c56 |
| data/staged/income/saipe_county_2003_2023.parquet | 3,353,599 | 9c5b5e7b6921841caeeddfc1d582f638a1bd73320edf86de8a7c71b58ab44779 | 41e3bf3a4d8d9dea49709b4e790a66ae9a34d0937e8c3b219772a12c145bb760 |

Outputs:

| File | SHA-256 |
| --- | --- |
| facts.json | 161fb9daeca96d4198ccc6aa225f9d80757de196e99cc3d23690f3e41d8ec6c4 |
| figures/class_gap_vs_race_gap.json | d13790c2ba5a956bec45bf46c44672cfa20cd95a662f8d06bb4c70e5b7b726fc |
| figures/gap_distribution.json | c55ec368097035dd5dea00f0acb1b8a19c6b862533301bc386da7fb628f61fa2 |
| figures/gap_vs_segregation.json | 32a7a9f6dc1d305c44c9583ab647e0581ac8d9250ccf7a270e540e10dcde4317 |
| figures/group_levels.json | ef08d907d3eb458fd540fc03dabee103ffef635a1e3c9313138117b698bdd48c |
| figures/income_slopes_by_state.json | c2605808594a6879940ea3a9cc0e68d7699319be0b751fbda0a748cbc06c1fa4 |
| figures/place_made_gaps.json | 98ec8200b2c13bb745c111c3bdc1a907d11bbc5e692c115acad2ee988cc9dc66 |
| figures/scores_map.json | ae4443eafcf360040f178fad3cc90a0ac4f44db24626dcc948d4250840d66e6f |
| figures/scores_vs_income.json | e97f4c2aa78353616df54e8c216f5343ff611849f580dcaf0f4db8212cc96ef8 |
| meta.json | 301bd2655f4490faf63da8c885479c1b94c95de34eb01c5da4e6aa64f8b9ad4b |
| public/data/test-scores-class-and-race/class_gap_vs_race_gap.json | 1624d8ce14499a4039542fc0f90f03bf081e4748b7cc8d8908b2f87001ee1b9b |
| public/data/test-scores-class-and-race/gap_vs_segregation.json | 43a86c93850d3e0d5b00fd1074df96be590c0b3e654486228249a837e18e0e0d |
| public/data/test-scores-class-and-race/scores_map.json | f09ba9fd4341c9551b5274219b0d35c53765e42382216815d79f3eca4b9de31b |
| public/data/test-scores-class-and-race/scores_vs_income.json | 5a71d5c5e08322fbf43ce7d9060a681e5a616ff68eec3efb0bd86ac8960611a3 |
| refs.json | 8456854d14e1dfee87d5de8fe9a053a972b6ad0cbba84262ef3758f31539ebfa |

## Machine formats

- Report (HTML): https://vishalsingh.org/zipcode/test-scores-class-and-race/report
- Report (Markdown): https://vishalsingh.org/zipcode/test-scores-class-and-race/report.md
- Every estimate (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/facts.json
- Table 1, figure "scores_map" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/scores_map.json
- Table 2, figure "scores_vs_income" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/scores_vs_income.json
- Table 3, figure "income_slopes_by_state" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/income_slopes_by_state.json
- Table 4, figure "gap_distribution" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/gap_distribution.json
- Table 5, figure "group_levels" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/group_levels.json
- Table 6, figure "gap_vs_segregation" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/gap_vs_segregation.json
- Table 7, figure "class_gap_vs_race_gap" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/class_gap_vs_race_gap.json
- Table 8, figure "place_made_gaps" (JSON): https://vishalsingh.org/zipcode/report/test-scores-class-and-race/figures/place_made_gaps.json
- Payload of "scores_map" (JSON): https://vishalsingh.org/zipcode/data/test-scores-class-and-race/scores_map.json
- Payload of "scores_vs_income" (JSON): https://vishalsingh.org/zipcode/data/test-scores-class-and-race/scores_vs_income.json
- Payload of "gap_vs_segregation" (JSON): https://vishalsingh.org/zipcode/data/test-scores-class-and-race/gap_vs_segregation.json
- Payload of "class_gap_vs_race_gap" (JSON): https://vishalsingh.org/zipcode/data/test-scores-class-and-race/class_gap_vs_race_gap.json
- Index of every report: https://vishalsingh.org/zipcode/llms.txt; all reports in one file: https://vishalsingh.org/zipcode/llms-full.txt