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 Vermont Education Dashboard (Smarter Balanced / VTCAP, ELA & Math, grades 3-8). For each school / grade / year, Vermont reports:

the number of students tested, their real, reported average scale score, and the real, reported percentage of students in each of the four performance levels, and
alongside every school's own row, the real average and level percentages for the school's supervisory union (Vermont's district-equivalent) and for the state, reported in the same file.

When a school's own numbers are withheld for privacy (a small tested group), we apply its supervisory union's real average and level percentages to the school's own real grade enrollment (reported separately by the Agency of Education and never suppressed), so the school still shows a grounded estimate built from real, published figures rather than a guess. If the union's own numbers are also withheld, we use the state's real figures the same way.

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

Vermont publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 1750-1851 in VTCAP years). 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, use linear interpolation across that level's count, assuming scores are spread evenly across the level's range.

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 fitted so that its area within each performance level matches the level counts, anchored to the group's real (or, for a suppressed school, its union's real) average scale score. It's there to visualize the shape of the group's scores. The headline percentile comes from the counts (step above), not from the curve.

Why estimates are still useful: the average scale score and the level percentages are real, published figures for almost every school, and for a suppressed school they are its real supervisory union's figures applied to the school's own real enrollment. The only modeled step anywhere in this pipeline is how scores are distributed inside a level, a small and bounded range. Across a whole school, union, 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.
Vermont used the Smarter Balanced consortium scale (roughly 2000-2800, varying by grade) through spring 2022. Starting spring 2023, Vermont moved to its own VTCAP test, which reports every grade and subject on the same 1500-2000 scale, with Proficient always beginning at 1750. Both tests share the same four levels: Substantially Below Proficient, Partially Proficient, Proficient, and Proficient with Distinction, with Proficient marking the state proficiency line. Vermont is compared at the school, supervisory union, and state levels (it has no county tier).
A small number of school/grade/year cells have no usable data (the school's own figures are withheld and no matching real enrollment count could be found) and won't appear.

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