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 Ohio Department of Education and Workforce assessment data (OST, ELA & Math, grades 3-8). These files report, for each school / grade / year:

the percentage of students in each performance level (school rows) or the real count (district/state rows), plus the number tested, and
from those figures, a mean we estimate from the count-weighted midpoint of each performance level’s scale range, which we then fit a curve around.

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

Ohio publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 700-724). 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 a mean estimated from the count-weighted midpoint of each level. 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 performance-level counts are real and complete for each group. The mean figure shown is approximated from where students fall within each level, and, as with every state, the only other assumption is how scores are distributed inside a level, a small and bounded range. 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.
Ohio's State Tests (OST) report a scale score with its own range for each grade and subject, across five performance levels: Limited, Basic, Proficient, Accomplished, and Advanced, with Proficient marking the state proficiency line (Proficient always starts at 700 and Basic always ends at 699, so only the Basic floor and the top two cuts move by grade and subject). Ohio publishes the real percentage of students at each level and a real number of test-takers statewide; school and district figures are estimated from each school's real reported proficiency rate and real grade enrollment, by fitting a normal distribution against the state's own scale-score standard deviation for that grade and subject. Science is given in grades 5 and 8. Ohio is compared at the school, district, and state levels (no county tier).
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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