How we estimate percentiles

A clear explanation of the data and the method, so you can judge how much weight to give the numbers.

What the data is

Every number here comes from official public test-results files: the Delaware Department of Education assessment data (Smarter Balanced, ELA & Math, grades 3-8). For each school / grade / year, Delaware reports two real, summary figures:

the number of students tested and their real, reported mean scale score, and
the real, reported percentage proficient, the share scoring at Level 3 or above.

We use those two figures to build the full four-level picture: we fit a normal distribution whose mean matches Delaware’s real reported average exactly, and whose spread is set so the modeled share above the Level-3 cut matches the real reported proficiency rate. When a group’s mean sits close to that cut, common for Delaware’s statewide 2018-2019 figures, that equation alone can’t reliably pin down the spread. A district or the state then takes the spread its own schools imply (each school’s spread plus how far apart the schools’ averages are), and a school borrows a typical spread from other schools in the same grade, subject and year. Either way the level bars keep Delaware’s real proficiency rate exactly.

Where Delaware publishes the real level counts, we use them instead. Delaware’s online school report card shows how many students scored at each of the four levels, but only for its current year. So for 2026, ELA, Math and Science use Delaware’s own counts for every school, district and the state. The report card hides a count below 5 students; we fill it back in from the published number tested and number proficient when only one count in that half is hidden, and when both are hidden we split that half’s known total by the fitted curve. The report card also shows each school’s counts for all its grades combined back to 2022, which is one grade’s counts at a school that tests only that grade, so 2022-2025 Science at most schools (and a few ELA and Math cells) uses real counts too. Everything else, 2018-2025 and 2026 Social Studies, is modeled as described above. Checked against the 2026 real counts, the model lands within about 1.5 percentage points at every level for the state in ELA and Math, with a median worst-level gap of about 3 points for a district and about 4.7 for a school. For 2022-2025, the combined-grades counts show the model is about as close in those years as in 2026. Those combined counts also fix how many of a school’s students sit in the lowest level and how many in the highest, across all its grades, so where a school tests several grades we adjust each grade’s modeled split until the grades add up to Delaware’s totals. Tested on 2026 first, where the real per-grade counts are known, that lowers a school grade’s median worst-level gap from about 4.8 to about 4.1 points.

For 2022-2025, districts and the state are then built up from the schools. A district’s grade is exactly its schools’ students added together, and the state’s is its districts’. So where at least half of a district’s students are in schools whose counts are Delaware’s own or adjusted as above, its lowest-level and highest-level counts are the sum of its schools’, and the state’s are the sum of its districts’. The number tested, the average and the proficiency rate are still Delaware’s own figures for that district or the state. A few students are in schools too small for Delaware to publish; we know how many there are, how many are proficient and their average from the district’s own totals, so they are split using their own numbers rather than the district’s. Tested on 2026 first, this lowers a district’s median worst-level gap from about 2.3 to about 1.7 points, and the state’s worst from about 1.4 to about 1.0 in ELA and Math (Science gains more). It also means a district with only one school in a grade now shows exactly that school’s bars for it, as it should.

Important: the public data does not contain individual student scores, only these group summaries. So no tool can compute a true rank of one child against every other child. What we provide is a well-grounded estimate.

How the percentile is estimated

Delaware publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Met the Standard” is 2436-2500). Given your child's score, we:

identify which performance level the score falls in;
count everyone in the lower levels as scoring below;
within the score's own level, spread that level's students along the group's fitted curve (below) rather than evenly across the level's range. Students bunch up toward the middle of the scale, so an even spread would put too many of them out at the far ends of the lowest and highest levels. Checked against published statewide score distributions, this lands within about one percentile point of the true value for a typical score.

That gives the percentile: the estimated share of students in the group who scored at or below the entered score.

About the smooth curve

The bell-like curve on each chart is a truncated-normal distribution anchored to Delaware’s real reported mean. Where the level counts are Delaware’s own, its spread is the one that best fits them; elsewhere it is the modeled spread described above. It's there to visualize the shape of the group's scores. The level counts set the headline percentile (steps above); the curve only decides where inside the student's own level the line falls.

When a group's students all sit in one or two levels, the counts can't say how spread out their scores are, and the fitted curve can come out far too narrow. Those curves are drawn no narrower than one fifth of the statewide spread, which is about the size of the test's own measurement error, and inside the student's level the percentile spreads that level's students evenly instead.

Why estimates are still useful: the mean and number tested are real, reported figures, and the reconstruction always matches Delaware’s real mean, and its level bars always match the real proficiency rate. Outside the real-count cells described above, what’s modeled is the split between the four levels itself, not just the spread inside a level like most other states, since Delaware’s open data file centers on the mean and proficiency rate rather than a level-by-level breakdown. Across a whole school, district, or the state, that assumption averages out well, so the comparison ("above/below average here vs. statewide") is reliable even though the exact percentile is approximate.

Limitations to keep in mind

Percentiles are estimates, not official rankings. Treat a "62nd percentile" as "roughly the top 40%," not an exact standing.
Small schools have small counts, so their estimates are noisier.
Delaware’s open data file hides some school and grade results: very small groups, groups with fewer than 5 students on one side of the proficiency line, and some larger groups hidden so the small ones can’t be worked out. When a hidden result follows exactly from totals Delaware does publish (a school’s all-grades total minus its other grades, or a district’s total minus its other schools), we fill it back in, about 180 results from 2019 on. We never show a group of fewer than 15 students, Delaware’s own reporting minimum. The other hidden results won’t appear.
DeSSA uses the Smarter Balanced scale, which runs roughly 2000-3000 (the range varies by grade, and the widest range applies from 2024) and is stable across years. No statewide test was given in 2020 (COVID). Delaware is compared at the school, district, and state levels (its school districts, not its three counties, are the reporting unit).
Charter schools appear as their own districts in the state files and are included in the school, district, county and statewide comparisons.

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