School Scores in context.
Household income is the biggest factor determining whether students meet state math and language standards.1 2 3
Test scores leave out this context. A meaningful comparison asks whether students perform better or worse than income predicts.
Across Chicago
Community boundaries: City of Chicago · Scroll or pinch to zoom
The underlying relationship
Achievement above or below the model
Studentized residuals · ordered from highest to lowest
* Tested count is the smaller of the two subject counts.
A higher or lower residual means higher or lower proficiency than the model predicts. The prediction is based on student economic disadvantage, which is strongly associated with academic achievement and is among the strongest predictors of differences in school-level test scores1 2 3. However, the residual still represents an association, not a direct measure of a school’s causal impact on student achievement or its overall quality.
One school over time
Select a school to see its residual history.
Loading historical residuals…
Zero = predicted performance. Positive residuals are above prediction; negative residuals are below. Each year uses that school year's income data and a separate regression for the assessment, level and subject. Bars, where available, show approximate 95% conditional sampling intervals. Points without bars have unavailable sampling intervals because tested counts are missing. Gaps are not interpolated: 2020 testing was canceled; the source has no 2017 SAT results. Changes reflect relative position within each year's model, not causal improvement or an equivalent scale across assessments.
Annual actual, predicted and residual values
A clearer comparison.
A still-limited model.
The difference between where a school should land, and where it does land, is exciting and illuminating. But it’s foolish to believe the school is responsible for the entire difference. Parents, families, neighborhood culture, and how screens are warping their heads matters more. A teacher can make a difference! But let’s not kid ourselves.
Can states, regions and tests be compared?
Comparison population: Chicago Public Schools. Select Statewide for Illinois IAR and SAT comparisons.
Illinois assessment standards apply to the results shown here. Each state sets its own assessment system and proficiency thresholds. The same percentage proficient in two states can represent different standards. Test changes within a state also break direct comparisons. Studentizing residuals does not turn these results into a common achievement scale.
Every model is tied to its source population, year, assessment, level and subject. A region filter and the population used for the regression are distinct choices; the current comparison population is named at the start of this section. Low-income measures retain their source definitions, which may differ between states and reporting systems.
The Illinois pilot imports the 2024 Report Card's separate IAR and SAT rates. Statewide IAR rankings use tested counts published by Education Data Center v3.1 from ISBE records. Grade counts must be exact, cover all expected tested grades, and reconcile to the Report Card rate within 0.11 percentage points. Missing, suppressed or inconsistent counts are excluded. SAT residual rankings are available without sampling intervals because verified tested counts are unavailable. Statewide IAR history covers 2023–2024; SAT history covers 2019 and 2021–2024. Each year uses its own income data and regression. Earlier IAR school aggregates remain unavailable: grade percentages cannot be averaged without valid weights. The 2023 outcome is aggregated from ISBE grade-level proficiency with verified EDC tested counts; rounding differs slightly from the 2024 published school rate. The Chicago view continues to use its matched CPS sources and annual models.
Illinois Report Card Data Library · 2024 assessment and income definitions
What are we comparing?
Spring 2024 The percentage of tested students meeting or exceeding the state standard for their assessment. This is the actual result compared with the model’s prediction.: Illinois Assessment of Readiness. Illinois’s ELA and math assessment for grades 3–8; it supplies the recent grade-school results on this site. grades 3–8 for grade schools; A College Board assessment used for Illinois grade 11 results in the years shown here. This site uses the percentage meeting state standards, rather than average scores or college-admission cutoffs. SAT is the test’s name, not a current acronym. grade 11 state standards for high schools. English Language Arts: literacy skills assessed through texts and language. The ELA control uses IAR ELA results for grade schools and the SAT EBRW measure for high schools. (English Language Arts) uses IAR ELA or the SAT Evidence-Based Reading and Writing, the SAT subject label in the historical CPS data. These results appear under ELA on this site. section. The average of the math and ELA proficiency percentages, giving each subject equal weight. It does not mean the percentage of students meeting both standards. is the equally weighted mean of the two proficiency percentages, not the percentage proficient in both.
The history chart shows Actual proficiency minus predicted proficiency, scaled using a measure of school-to-school variation calculated without that school and adjusted for its position in the income data. Positive values are above prediction; negative values are below., fitted separately by year, assessment, level and subject. Chicago grade school assessments cover 2015–2019 and 2021–2024; high school assessments cover 2015–2016 Partnership for Assessment of Readiness for College and Careers. The earlier assessment represented in this site’s history, before IAR for grade schools and SAT for high schools. Each year and assessment gets its own model. and 2018–2019 / 2021–2024 SAT. All eligible schools in each annual source enter the model, including schools absent from today's directory. A school serving both levels can enter each separate assessment The group of schools compared in one model: the same assessment year, school level, test and subject. Its membership can change from year to year.. Search filters do not refit the models.
In the statewide view, income is the same-year published Illinois Report Card Low Income percentage. In the Chicago view, income percentages come from Chicago Public Schools, the district that publishes the school, assessment and income reports used here.'s annual An enrollment snapshot taken on the twentieth school day. This site uses that school year’s counts to calculate each school’s low-income percentage. demographic reports, matched by school ID and school-year ending year: spring 2024 assessments use 2023–24 income counts. We measure The share of enrolled students counted as low income in CPS demographic reports. These counts provide the model’s measure of economic disadvantage. as the percentage of enrolled students in these low-income counts. Demographics describe the entire school, while assessments cover tested grades. Changing reporting, participation and cohort composition can affect trends.
How is the residual calculated?
For each level and subject, A method for fitting the prediction line by minimizing squared differences between actual and predicted proficiency. Each eligible school has equal weight here. fits proficiency = α + β × low-income percentage + ε. Each eligible school has equal weight. A school’s raw residual is actual minus predicted proficiency, in The subtraction of two percentages: an actual result of 60% and a prediction of 50% give a residual of +10 percentage points..
The externally studentized residual is tᵢ = eᵢ / (s₍₋ᵢ₎ √(1 − hᵢᵢ)), using a A measure of how widely schools’ actual results differ from the prediction line. It supplies the scale used to studentize residuals. estimate that excludes that school and adjusts for How unusual a school’s income percentage is compared with the other schools in its model. Unusual values can have more influence on the fitted line; studentization accounts for this.. Zero is the fitted prediction; positive values are above it. The straight-line model may predict outside 0–100%; predictions are not clipped.
Name and school-type filters change what you see, not the regression. Models use all eligible schools of the chosen level within the selected comparison population. Grade and high school residuals are never ranked together. Program labels follow CPS’s school-level classification; a school can offer multiple admissions programs.
How do school size and uncertainty enter?
Tested-student counts drive approximate Approximate ranges based on the tested-student count and proficiency rate. They show one source of statistical uncertainty; smaller tested groups generally produce wider ranges., propagated through the fitted regression and expressed on the studentized scale. Smaller tested groups generally have wider intervals. Rates of 0% and 100% use A small adjustment to estimated proficiency rates when calculating uncertainty. It prevents a reported 0% or 100% rate from being treated as perfectly certain. to avoid zero estimated uncertainty.
Intervals hold the studentizing denominator fixed. They are The displayed ranges account for tested-sample uncertainty while holding parts of the fitted model fixed. They do not cover all uncertainty or measure a school’s causal effectiveness., not full confidence intervals for school effectiveness; they omit cohort, demographic, model-choice and student-dependence uncertainty. Combined uses the conservative maximum positive How two measurements vary together. Since student-level math and ELA overlap is unavailable, the combined interval assumes the strongest positive relationship to avoid understating this part of uncertainty. because student-level subject overlap is unavailable.
No Methods that pull less precise estimates, often from small schools, toward an overall average. They are not applied here; the chart uses studentized residuals and sampling intervals. is applied in this version. Studentization adjusts leverage; it does not itself adjust for enrollment. Avoid treating small differences or overlapping intervals as definitive rankings.
Sources, coverage and limitations
A result withheld in the published source, often to protect privacy when groups are small. It is treated as unavailable, never as zero., missing or invalid rates, missing demographics, and known tested counts under 10 are excluded from fitting and ranking. Statewide SAT uses unsuppressed published rates when counts are unavailable; sampling intervals are then unavailable for the entire cohort. Schools without eligible data remain in the directory. Pre-K-only / other school levels are excluded. This is a historical snapshot, not a current admissions directory.
- Statewide SAT history: source values and workbook checksums · NCES school locations and map provenance
- Education Data Center v3.1: statewide IAR tested counts · Count validation and provenance
- CPS historical assessment reports
- CPS annual income reports, 2014–15 through 2023–24
- CPS school profiles, SY2023–24
- CPS Community Eligibility Provision history · Illinois Low Income criteria · IAR assessment guide · SAT guide
- Chicago community-area boundaries
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Background research on income and academic achievement
- Stanford Educational Opportunity Project — socioeconomic disparities in academic achievement
- Dahl & Lochner (2012), “The Impact of Family Income on Child Achievement,” American Economic Review 102(5): 1927–1956
- Marsh et al., “The Role of Household Chaos in Understanding Relations Between Early Poverty and Children’s Academic Achievement”
- Download current assessment source CSV · Download historical source CSV · Download modeled JSON · Annual income CSV · All schools and years: residuals and exclusions
Historical source terminology: Some CPS reports label the income counts Free/Reduced Lunch (FRPL); others use Economically Disadvantaged. The model uses these published income counts.
Selection into schools, prior achievement, grade mix, disability, language, resources and other factors are not controlled. This exploratory model cannot identify why a school differs from its prediction. The 2024 snapshot avoids mixing the redefined 2025 performance standards with earlier rates.