Chapter 2.1 · The classroom staircase

Test scores, class and race

Average achievement in third through eighth grade differs by 2.54 grade levels between the 5th and 95th percentile of counties, and it rises with county income, with a positive slope in 45 of 45 states.

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

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, with counties 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, among 3,000 counties whose math and reading results cover the school years 2009 to 2019. Counting each county once puts the two ends at −1.57 and +1.01, a spread of 2.58.

Average achievement moves with county income. Across 2,999 counties its correlation with the log of median household income is +0.59 (95% CI 0.43 to 0.76), and each doubling of income goes with 1.28 (95% CI 0.94 to 1.72) more grade levels. 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.

Inside the same school districts, white students score 0.64 (95% CI 0.61 to 0.67) standard deviations above Black students in math, about 2.0 (95% CI 1.9 to 2.1) grade levels, and students who are not economically disadvantaged score 0.58 (95% CI 0.55 to 0.61) standard deviations above those who are, about 1.8 (95% CI 1.7 to 1.9) grade levels. 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, and 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, and 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, and one standard deviation equals 3.3 grade levels in the county averages and 3.2 in the math gaps. 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: 74% of the lowest tenth of counties are there, against 43% of all counties (Figure 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 moves both ends of the spread down, since the lowest-scoring counties tend to have few tests and the highest-scoring ones many.

Figure 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

Loading county values

Average of math and reading achievement (grade levels from the national average)

Below the national averageAbove the national average

Values outside −2.0 to +2.0 take the end colors.

No data (3,143 counties)

Select a class to show only those places.

Find a county

Hover or tap a county for its value, or search by name. Zoom with the buttons on the map, then drag to move it.

Counties toward the high end of the key cluster in the Northeast and the Midwest, and counties toward the low end are concentrated in the South and include rural Alaska and parts of the Dakotas. The map plots each county's average of math and reading achievement on a scale centered on the national average, and the 73 counties more than 2 grade levels away take the end colors of the key. The 142 gray places have no average, and the tooltip gives the reason for each.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)

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 (Figure 2). 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, and the test results are for 2009 to 2019, so it stands in for income during the test years.

Figure 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

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. The cloud is wide: the standard deviation of county averages around the income line is 0.63 grade levels. Markers plot weighted mean achievement within tenths of counties by income, with 95% intervals from a bootstrap over states; the line through all counties has slope 1.28 grade levels per doubling of income.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

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. Figure 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, and 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)).

Figure 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

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Data for 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
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

Every dot lies to the right of zero. The 95% interval, from robust standard errors with t intervals, clears zero in 40 of the 45 states and includes zero in Kentucky, Wyoming, Utah, New Hampshire and North Dakota. Each dot is the slope from a weighted regression across the counties of one state, and states run from the shallowest slope at the top to the steepest.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

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, and at 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 2.3, Learning growth and starting level (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. Figure 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, and 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. White students score above Black students in 99.8% of the 5,729 districts that report both.

Figure 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

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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
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 Hispanic gap is smaller, and the white–Asian dot lies left of zero because Asian students score higher. Each dot is the mean over the districts that report that gap, weighted by the tests of the two groups, so the rows cover different districts: 11,815 report the income gap and 5,729 the white–Black gap, and in the 5,658 that report both the means are 0.64 and 0.60. The bar is the spread of district gaps, the interquartile range or, in the second view, the 5th to 95th percentile, and it is not an interval for the mean.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

The income gap is reported by more districts than the white–Black gap (11,815 against 5,729), and 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 Figure 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. 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. 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.

Figure 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

Race and ethnicity

Economic status

Math achievement relative to the national average of all students (standard deviations)

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Data for In math, Asian students average +0.66 standard deviations from the national average and Black students −0.53
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

Stems run from the national average at zero to each group's mean. Asian and white students lie above it, and Hispanic, Native American and Black students below; not disadvantaged students lie above it and disadvantaged students below. Each mean weights counties by the group's tests, with a 95% interval from a bootstrap over states. Counting each county once pulls every level toward zero, and the table gives both.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

Counting each county once instead of weighting by the group's tests pulls every level toward zero: +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, and +0.23 for students who are not economically disadvantaged and −0.28 for students who are. 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, 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, which is 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 (Figure 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.

Figure 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

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Dots slope up from left to right, and the markers for tenths of counties by segregation rise from 0.47 in the least segregated tenth to 0.90 in the most. Markers are weighted mean gaps with 95% intervals from a bootstrap over states. Within states, a county one standard deviation higher on the index has a gap wider by 0.11 standard deviations.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

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] A county regression with four measures at once, 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, with state fixed effects, 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 standard deviations of the gap per standard deviation of the measure, across 1,849 counties. 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, and 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, so this is 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 (Figure 7). Across 2,092 counties the two correlate at +0.80 (95% CI 0.75 to 0.84), a line through them has slope 0.99 (95% CI 0.91 to 1.08), and 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.

Figure 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

Loading data

Dots follow the diagonal, which marks equal gaps, and the markers for tenths of counties by income gap run along it, above it in the lowest tenth. Dots are counties and markers are weighted mean race gaps with 95% intervals from a bootstrap over states. A line through the counties has slope 0.99, and the income gap accounts for 64% of the variance of the race gap.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

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 3.3, 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 (Figure 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 2.2, Gender gaps in reading and math, has a spread of 0.06 (95% CI 0.05 to 0.07), and 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).

Figure 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

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

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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
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. The second view shows the same spreads in standard deviations, where the white–Black, white–Hispanic and income bars are several times longer than the reading bar because those gaps are also larger. Each bar is a weighted spread across the same 2,020 counties, with a 95% interval from a bootstrap over states.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

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, so 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 evidenceRegression discontinuity

Head Start funding and children's later outcomes

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.

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, and 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] which 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, and 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 3.1, School discipline and incarceration.

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

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.

Figures explained here: Figure 5, Figure 4 and Figure 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).

Figures explained here: Figure 2, Figure 3, Figure 6 and Figure 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.

Figure explained here: Figure 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.

References

Reardon, Sean F.; Kalogrides, Demetra; Shores, Kenneth (2019). The Geography of Racial/Ethnic Test Score Gaps. American Journal of Sociology 124(4): 1164-1221. doi:10.1086/700678
Card, David; Rothstein, Jesse (2007). Racial Segregation and the Black-White Test Score Gap. Journal of Public Economics 91(11-12): 2158-2184. doi:10.1016/j.jpubeco.2007.03.006
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. doi:10.1162/qjec.122.1.159
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. doi:10.1093/qje/qjv036
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.

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.}
}

One scale for every state's tests

Where county averages are highest and lowest

Average achievement rises with county income

County income and achievement inside each state

Gaps between groups inside the same districts

Where each group stands

School segregation and the white–Black gap

The income gap and the white–Black gap

How much each gap varies across counties

Two studies of Head Start and school spending

What these data cannot show

Data sources

Methods

Which students, grades and years the scores cover

How grade levels, standard deviations and gaps are defined

Where the income and segregation measures come from

How counties and groups are weighted

Which places are drawn

How uncertainty and spread are measured

References

How to cite

Reading paths