How we estimate percentiles: Pennsylvania Keystone Exams

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 Pennsylvania Department of Education Keystone Exams results for Algebra I, Literature and Biology (2018, 2019 and 2021 to 2025). These files report, for each school, district and the state:

the percentage of students at each performance level (Below Basic, Basic, Proficient, Advanced) and the real number scored; we turn the percentages into student counts that round back to the percentages Pennsylvania printed. Counties are the sum of their districts, and charter and career-centre schools without a district row are summed from their schools, and
from those figures, an estimated average score: the center of the bell curve that best matches the share of students below each level’s cut score.

Who is counted

Pennsylvania reports the Keystone Exams for its 11th graders. Each junior with a score is counted once, with their best Keystone score so far, whatever grade or test session it came from: a student can take an exam before 11th grade and can take it again. So a percentile here compares a score with juniors' best scores, and a school's numbers are its own 11th graders, wherever they tested. Fewer juniors are counted in 2021 to 2023, because the spring 2020 exams were cancelled, students who missed them did not have to test later, and fewer students tested in 2021. PDE says the 2021 results are not a representative sample.

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

Pennsylvania publishes the exact scale-score range for each performance level (e.g. for Keystone Algebra I, Proficient is 1500-1545 and Advanced is 1546 and up). 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. Checked against published statewide score distributions, this lands within about one percentile point of the true value for a typical score.

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 converted counts, anchored to a mean we derive from those same percentages. It's there to visualize the shape of the group's scores. The level counts set the headline percentile (steps above); the curve only decides where inside the student's own level the line falls.

When a group's students all sit in one or two levels, the counts can't say how spread out their scores are, and the fitted curve can come out far too narrow. Those curves are drawn no narrower than one fifth of the statewide spread, which is about the size of the test's own measurement error, and inside the student's level the percentile spreads that level's students evenly instead.

Why estimates are still useful: the performance-level percentages are real and complete for each group; converting them to counts (percentage × number tested) is arithmetic, not a model. The mean figure shown is derived from those percentages using a statistical fit, 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.

Cut scores

Keystone Exams are scored from 1200 to 1800 with Proficient starting at 1500, on cut scores the State Board approved in July 2011 and every technical report since repeats:

Algebra I: Below Basic 1200-1438, Basic 1439-1499, Proficient 1500-1545, Advanced 1546-1800;
Literature: Below Basic 1200-1443, Basic 1444-1499, Proficient 1500-1583, Advanced 1584-1800;
Biology: Below Basic 1200-1459, Basic 1460-1499, Proficient 1500-1548, Advanced 1549-1800.

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. Pennsylvania hides results for groups of fewer than 11 students, so a county total can be a little short.
2021 and 2022 count far fewer juniors than usual (the spring 2020 exams were cancelled and 2021 testing was reduced), so those years compare a smaller, selected group; the tool shows a note on them.
No exams were given in spring 2020. The 2026 results have not been posted yet.

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