Chapter 3.1 · The classroom staircase

Test scores, class and race

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.

Author: Vishal Singh
Affiliation: NYU Stern
Published: 9 October 2026

The county at the 5th percentile of average achievement averages −1.27 grade levels from the national average, and the county at the 95th percentile averages +1.27. These are averages of math and reading in third through eighth grade, pooled over the school years 2009 to 2019, among 3,000 counties weighted by the tests counted. The two are 2.54 grade levels apart. One grade level is the national average gain from one grade to the next, and a county at zero matches the nation.

County average achievement rises with county income

Counties with higher median household income have higher average achievement. Across counties with both an average and an income estimate, each doubling of median household income goes with 1.28 (95% CI 0.94 to 1.72) more grade levels. Counties at any income level still scatter around that line, with a standard deviation of 0.63 grade levels, so income alone does not place a county (Figure 1).

Figure 1

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

Loading data

Dots drift up from left to right, and the marker for the highest tenth of counties by income lies above the marker for the lowest tenth. Each dot is a county, sized by the tests counted, against median household income on a log scale. The markers are weighted mean achievement within tenths of counties by income, with 95% intervals from a bootstrap over states. Values in Table 2.

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

A slope across all counties could come from comparing rich states with poor ones, with no link inside any state. Fitted one state at a time, the estimated slope is positive in 45 of the 45 states with 10 or more counties. Its 95% interval includes zero in Kentucky, Wyoming, Utah, New Hampshire and North Dakota. How many intervals lie above zero depends on how the intervals are built and on the minimum number of counties. Wyoming's slope is close to zero, and with the Census Bureau's 2019 income estimate in place of the 2022 one it turns slightly negative.

How we know

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. Counties are weighted by the tests counted, where a test is one student's result in one subject, grade and year. The archive publishes empirical-Bayes estimates, which pull the figure for a place with few tests toward the average of similar places, so the spreads here understate the spread of the true values. Virginia has no math estimates in the archive, so none of its counties has an average. The income measure is the Census Bureau's modeled estimate for 2022, after the test years, so it stands in for a county's income during them. Intervals come from a bootstrap that resamples whole states, because counties in one state resemble each other. The report gives every estimate with its interval and sample size.

Gaps inside the same districts, on a second scale

A county average blends every group of students in the county. SEDA also reports the gap between two groups in the same geographic school district. Inside the same districts, white students score 0.64 (95% CI 0.61 to 0.67) standard deviations above Black students in math. In math, students who are not economically disadvantaged score 0.58 (95% CI 0.55 to 0.61) standard deviations above those who are (Figure 2).

These gaps are in standard deviations of the national cohort, the scale the archive recommends for research, while the county averages above are in grade levels. On the archive's own grade-level gap, the white–Black math gap is about 2.0 (95% CI 1.9 to 2.1) grade levels, and the chapter never puts the two scales on one axis. Each gap is averaged over the districts that report it, weighted by the tests of the two groups, so the two means cover different districts. In the districts that report both, the white–Black gap is the larger, by 0.04 (95% CI 0.02 to 0.06) standard deviations. States define economic disadvantage in their own ways, so the income gap compares groups that are defined differently from state to state.

Figure 2

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

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Data for 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, Interquartile range of districts
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

The white–Black and income gaps sit furthest right, the white–Hispanic gap is smaller, and the white–Asian dot lies left of zero because Asian students score higher. Each dot is the mean gap in math over the districts that report it, and the bar is the interquartile range of district gaps, not an interval for the mean. Values in Table 4.

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

How much each gap varies with place

A gap between two groups differs from one county to the next. Take the counties that report the white–Black, white–Hispanic and income gaps in math and the gap between boys and girls in reading. In standard deviations, the white–Black gap varies 4.1 (95% CI 3.3 to 5.2) times as much across them as the reading gap. That reading gap serves as a yardstick, and its own size is the subject of Chapter 3.2, Gender gaps in reading and math. A larger gap has more room to vary, so the comparison that matters is the spread relative to the average gap. Relative to its average, the white–Black gap varies 1.34 (95% CI 1.08 to 1.76) times as much as the reading gap (Figure 3).

Figure 3

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

Spread across counties relative to the average gap (standard deviation divided by the mean)

Show data

Data for 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, Relative to the average 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

The white–Hispanic bar is longest, the white–Black bar next, and the income and reading bars are shortest and close in length. Each bar is the weighted standard deviation of a gap across counties divided by its average gap, with a 95% interval from a bootstrap over states; the second view shows the spreads in standard deviations. Values in Table 8.

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

The white–Hispanic gap varies most relative to its average, and the income gap about as much as the reading gap. Relative to their size, then, these data do not show that race and class gaps depend on place much more than the gender gap does. The income pattern is also a description of places. A slope across counties compares places, not students, and a county average reflects everything that happens to children in and out of school. The slope therefore 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 (planned).

What these county averages cannot tell you

Every figure describes counties or districts, and a pattern across counties need not hold for the students inside them (ecological inference). 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. The income estimate comes from years after the tests, and the comparison assumes that a county's position changed little in between. None of the slopes says what would happen to a county's students if its income changed.

Go deeper

The report: every estimate with its interval and sample size.
Tables: every figure of the report as a table.

Reading paths that include this chapter:

Data sources

Stanford Education Data ArchiveStanford 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 groupsYears: 2009-2019 (version 6.0) · Weights: tests counted; each analysis names its weight · License: CC BY 4.0 (Stanford CEPA); cite SEDA
County Health RankingsCounty 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 residentsYears: 2024 release · Weights: none (published county measures); analyses weight counties by SEDA tests counted · License: CC BY 4.0 (University of Wisconsin Population Health Institute)

All data sources

How to cite

@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.}
}