How we estimate percentiles: Ohio 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 Ohio Department of Education and Workforce’s report card downloads and its yearly Statistical Summary of Ohio’s State Tests, for the end-of-course tests given in high school from 2021 to 2026: Algebra I, Geometry, Integrated Math I and II, English II, Biology, American History and American Government. Ohio publishes:

for every school and district, the percent of students proficient or above on each of these tests;
for every school, the number of tests at each of the five levels (Limited, Basic, Proficient, Accomplished, Advanced) and the number of tests taken, but added up by subject: all of a school’s math tests together, all its English tests together, and so on; and
for the state, each test’s number of students, average score, spread and level percentages.

Real counts, and where we split a subject

At most high schools Biology is the only science test and English II the only English test, so the subject’s level counts are that test’s counts, and the bars show them as Ohio printed them. Ohio hides a count under 10; we fill it back in from the published number of tests taken and the school’s own proficiency rate, which pin it exactly when only one count is hidden.

Math (Algebra I, Geometry, Integrated Math) and social studies (American History and American Government) are printed together, and so is a middle school’s Algebra I with its grade 7 and 8 math. For those we split the subject’s real counts between its tests. The split reproduces every number Ohio prints: the subject’s count at each level, its total, and each test’s own proficiency rate. What it models is how each half (below Proficient, and at or above it) divides between the tests, using a curve for each test centred on its own rate. We measured how well that works where the answer is known, by pooling a school’s real Biology and English II counts and splitting them back apart: the split lands within about 1.3 percentage points of the true share at each of the two lower levels and 1.5 to 2.5 at the upper ones (about 9 points in all over the five levels), against about 14 points for a curve placed from the proficiency rate alone.

Districts are added up from their schools; checked against Ohio’s own district proficiency rates, the sums land within a median 0.3 points. The state is Ohio’s published statewide table for each test.

Two corrections to Ohio’s files

Mislabelled columns. In the 2023 and 2026 school files, the columns labelled Accomplished, Advanced and Advanced Plus hold Advanced, Advanced Plus and Accomplished. We read them in the right order; Ohio’s per-school Performance Index shares, published separately, confirm it (the corrected reading fits them many times more closely than the labels as printed).
The acceleration bonus. Ohio counts a student on a written acceleration plan one level higher on its report card when they score Proficient or above (Proficient becomes Accomplished, Accomplished becomes Advanced, Advanced becomes “Advanced Plus”). That is a reward in Ohio’s school ratings, not a different score, and it matters most for middle-school Algebra I takers. We move those students back to the level their score earned, using the size of the bonus measured from Ohio’s own statewide figures. It never changes anyone’s proficient-or-not status.

Who is counted

A school’s results count the students it tested in that course that year, the way Ohio’s report card counts them: once per student per year at their best score, without retakes of a course already counted, and including approved AP and IB exams taken in its place. Students who take Algebra I or Geometry in middle school count at their middle school, which is why a middle school can appear here. The statewide distribution is Ohio’s published one for every test taken, retakes included, so it sits a little lower than the schools’ results added together.

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

Ohio publishes the exact score range for each level (e.g. for Algebra I, Proficient is 700-724). Given a score, we:

identify which 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.

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 to the group’s level counts. It’s there to visualize the shape of the group’s scores. The level counts set the headline percentile; the curve only decides where inside the student’s own level the line falls.

Cut scores

Each test has five levels; Proficient and above is proficient. Ohio prints the same ranges every year from 2021 to 2026.

Algebra I and Integrated Math I: Limited 618-681, Basic 682-699, Proficient 700-724, Accomplished 725-753, Advanced 754-814.
Geometry: Limited 604-677, Basic 678-699, Proficient 700-724, Accomplished 725-755, Advanced 756-810.
Integrated Math II: Limited 594-676, Basic 677-699, Proficient 700-724, Accomplished 725-757, Advanced 758-813.
English II: Limited 597-678, Basic 679-699, Proficient 700-724, Accomplished 725-741, Advanced 742-808.
Biology: Limited 617-684, Basic 685-699, Proficient 700-724, Accomplished 725-734, Advanced 735-823.
American History: Limited 619-683, Basic 684-699, Proficient 700-724, Accomplished 725-737, Advanced 738-800.
American Government: Limited 642-686, Basic 687-699, Proficient 700-724, Accomplished 725-738, Advanced 739-774.

These are from Table 2 of Ohio’s Statistical Summary for each year. 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 whole state.

Each test is its own point. Algebra I, Geometry, English II, Biology and the social studies tests are different tests on different scales, so each is shown on its own rather than joined into a line.
Earlier years are compared statewide only. You can add your child’s grades 3-8 scores. The tool doesn’t know which middle school they attended, so those years are compared with every Ohio student in that grade.
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.
Where a subject is split between tests, the level bars are partly modeled, as described above; the proficiency share is always Ohio’s own.
Small schools have small counts, so their estimates are noisier, and groups under 10 students are hidden.
Not included: 2018 and 2019 (Ohio’s level file for those years has percentages without the number of tests, and its report card then gave school results for Algebra I and English only); 2020 (no spring test); English I, which Ohio was phasing out (about 5,800 students in 2021 and none after 2023); and the alternate assessments.

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