How we estimate percentiles: Vermont high school

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 the Vermont Agency of Education’s Education Dashboard assessment files, for Vermont’s high-school tests: ELA and math in grade 9 (Smarter Balanced in 2018, 2019, 2021 and 2022, VTCAP from 2023) and science in grade 11 (the New England science test, NGSA, in 2019, 2021 and 2022, VTCAP science from 2023). For each school, supervisory union and the state, and for each subject and year, these files give:

the number of students tested and the share in each of the four performance levels, and
the average scale score, which centers each group’s curve.

Hidden numbers. Vermont hides a small school’s results entirely. Each row of its files also carries the school’s supervisory union and the state, so a hidden school is estimated from its supervisory union’s results (or, failing that, the state’s) applied to the school’s own grade enrollment. The supervisory union and statewide rows are Vermont’s own published figures, never sums.

Who is counted

Vermont tests ELA and math in grades 3 to 9 and science in grades 5, 8 and 11; it has no grade 10 or 11 ELA or math test. A percentile compares a score with that year’s Vermont public school students in that grade who took the test, by the school where they tested: about 5,300 students in grade 9 ELA and math and about 5,200 in grade 11 science in 2025.

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

How the percentile is estimated

Vermont publishes the exact score range for each performance level (e.g. for grade 9 VTCAP Math, Proficient is 1750-1861). Given a 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.

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 centered on the group’s published average score, with its spread fitted so that its area within each performance level matches the level shares. It's there to visualize the shape of the group's scores. The level shares set the headline percentile (steps above); the curve only decides where inside the student's own level the line falls.

Why estimates are still useful: the level shares and averages are Vermont’s own published numbers for each group. We checked them against a second figure Vermont prints separately for every group, the share proficient and above, and they agree within rounding everywhere. The only assumption is how scores are distributed inside a level, a small and bounded range, so the comparison ("above/below average here vs. statewide") is reliable even though the exact percentile is approximate.

Cut scores

Each test has four levels: Substantially Below Proficient, Partially Proficient, Proficient and Proficient with Distinction. Proficient and above count as proficient.

Grade 9 ELA: VTCAP (2023 on) 1500-1663, 1664-1749, 1750-1860, 1861-2000; Smarter Balanced (2018-2022) 2299-2488, 2489-2570, 2571-2671, 2672-2795
Grade 9 Math: VTCAP (2023 on) 1500-1654, 1655-1749, 1750-1861, 1862-2000; Smarter Balanced (2018-2022) 2280-2516, 2517-2600, 2601-2675, 2676-2862
Grade 11 Science: VTCAP (2023 on) 1500-1709, 1710-1749, 1750-1893, 1894-2000; NGSA (2019-2022) 1-35, 36-59, 60-70, 71-120

The VTCAP ranges are from Vermont’s VTCAP Score Interpretation Guide. The Smarter Balanced grade 9 cut scores are the consortium’s validated grade 9 cuts, with its high-school lowest and highest scores; the NGSA ranges are from the New England science test’s technical report, which Vermont gave jointly with Rhode Island. Vermont prints the proficiency cut on every row of its files, and it matches these ranges in every year. The tests changed in 2023, so a scale score before then doesn’t compare with one after, but a percentile does. The score range for each level, by year, is on the score guides.

The high-school progress report

The paid progress report puts every high-school test your child took in one table, with the percentile at each level from the school to the state, and charts each subject across the years.

One line per subject. Grade 9 ELA and math continue the grades 3-8 lines, and grade 11 science continues the grade 5 and 8 science line. Each point is a percentile among that year’s students in that grade, so the points compare.
Earlier years are compared statewide only. You can add your child’s grades 3-8 scores. The tool doesn’t know which middle school or supervisory union they attended, so those years are compared with every student in the state in that grade, not with this high school or its supervisory union.
The report opens on the statewide view, the one level with a result for every test.

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, and a hidden school’s figures are borrowed from its supervisory union, so their estimates are noisier.
Not included: 2020 (no test, COVID), science in 2018 (no file), and 2026, not yet published.
Vermont is compared at the school, supervisory union and state levels.

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