How we estimate percentiles

Plain-English 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 school or district’s mean happens to sit very close to that cut, common for Delaware’s statewide 2018-2019 figures, that equation alone can’t reliably pin down the spread, so we borrow a typical spread from other schools/districts in the same grade/subject/year instead of guessing.

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, 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 modeled counts, anchored to Delaware’s real reported mean, with its spread modeled as described above. 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 mean and number tested are real, reported figures, and the reconstruction always matches Delaware’s real mean and real proficiency rate exactly. What’s modeled is the shape between the four levels itself, not just the spread inside a level like every other state, since Delaware’s figures center on the mean and proficiency rate rather than a level-by-level breakdown. Across a whole school, district, county, 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.
Some school/grade cells are suppressed by the state (for privacy, small groups) and won't appear.
DeSSA uses the Smarter Balanced scale, which runs roughly 2000-2800 (the range varies by grade) 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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