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How we estimate percentiles: Kansas 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 Kansas State Department of Education (KSDE) results for the Kansas Assessment Program (KAP): grade 10 ELA, grade 10 Math and grade 11 Science, for 2018, 2019 and 2021 to 2026 (grade 11 Science has no 2025 results, see below). For each school, district and the state, KSDE reports:

A county’s figures add up the actual students of its own schools. KSDE’s files do not include each group’s average score, so the average shown is estimated from how the students split across the levels.

Who is counted

ELA and Math: the grade 10 KAP tests, taken by 10th graders. Science: the grade 11 KAP science test, taken by 11th graders. Each year counts the students who took that test that spring. Students with the most significant cognitive disabilities (about 1 in 100) take a separate alternate test and are not included, and English learners in their first year in a U.S. school take Math and Science but not ELA.

The statewide figures cover public schools. Accredited private schools that give the KAP, such as Catholic diocese high schools, are shown as their own districts, so you can compare against them, but they are not part of the statewide figure and have no county. A percentile compares a score with that year’s takers of the same test.

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

Kansas publishes the exact scale-score range for each performance level (e.g. for grade 10 Math in 2026, Level 3 “Proficient” is 540-599). Given a score, we:

  1. identify which performance level the score falls in;
  2. count everyone in the lower levels as scoring below;
  3. 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.

That gives the percentile: the estimated share of students in the group who scored at or below the entered score. We checked it against the statewide score percentiles in KSDE’s yearly technical reports (2018, 2019 and 2021 to 2025). For a score in Level 2 or above, it lands within about 2 percentile points of the published value. In Level 1 it can run high: on the 220-380 scale, grade 10 Math scores in Level 1 bunch up just below the Level 2 cut, so a low Math score from 2018 to 2024 can show 7 to 17 points above its true statewide percentile, and a low grade 11 Science score 2 to 11 points above.

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, centered on that estimated average score. 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 student counts in each level are real for each group. The average score shown is estimated from how students split across the levels, and 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

The score range for each level, by year, is on the score guides. Scores in Level 3 and Level 4 meet Kansas’s standard. Through 2024 the levels were named Limited, Basic, Effective and Excellent; from 2025 they are Limited, Basic, Proficient and Advanced.

The ranges are from KSDE’s KAP technical reports, its guide to scale scores and cut scores for families, its 2025-26 guide to score reports, and the State Board’s meeting materials and minutes for the 2025 and 2026 cut scores.

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 state, and charts each subject across the years.

Limitations to keep in mind

This site stores nothing you type. Scores are used only in your browser to draw your charts.

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