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How we estimate percentiles: Missouri 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 Missouri Department of Elementary and Secondary Education's public Missouri Assessment Program (MAP) results, as published in the yearly files on moschooldata.org. They cover the MAP end-of-course tests: English I, English II, Algebra I, Geometry, Algebra II, Biology, Physical Science, Government and American History, for the school years ending in 2019 and 2021 through 2025 (there was no spring 2020 test). For each school, district and the state, the files report:

We checked that estimate against the real statewide averages printed in Missouri's technical reports for 2019, 2021 and 2022: for every test, the estimated statewide average is within 1.6 points of the real one, and the estimated spread within 1.7 points.

Who is counted

These counts are the students who took this end-of-course test during the school year, in the summer, fall and spring testing windows together. Middle-school students who take a high-school course test early (most often Algebra I) are included, counted at their middle school.

A course test is taken by whoever is in the course that year, so a percentile compares a score with that year's takers of the same test, not with every student of the same age. Some tests have few takers statewide: about 650 to 1,150 a year for Physical Science, 1,150 to 3,700 for Geometry, and 1,300 to 1,900 for American History, against 60,000 to 75,000 for Algebra I, English II, Biology and Government.

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

Missouri publishes the exact scale-score range for each performance level (e.g. on Algebra I, “Proficient” is 400-408). 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.

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.

About one school result in seventeen gets a wide default curve for that reason, most of them Government results, where few students land at Below Basic or Advanced. A few middle schools have nearly every Algebra I student at Advanced; their curve sits at the top of the scale.

Levels Missouri hides

To protect privacy, Missouri leaves a level blank when only a few students are in it, and then blanks a second level too, so the first can't be worked out by subtraction. From 2021 on, no printed level holds fewer than 5 students. For a school or district with blank levels we fill them with the most likely split of the hidden students, given the levels that are printed, the number tested, and the statewide split for that test. The printed levels are kept exactly. Results with every level blank (16 students or fewer) are left out.

Why estimates are still useful: the performance-level percentages are real for each group, and so is the number tested. The average score shown is estimated from how students split across the levels, 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, 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

Every MAP end-of-course test is scored from 325 up, with 400 the start of Proficient on every test. The other two cut scores differ by test; the score range for each level is on the score guides. Missouri has kept the same cut scores on each test since it was set (English and math in 2017-18, Biology and Physical Science in 2018-19, Government and American History in 2020-21), and its guides confirm them through 2025-26.

Missouri sets no maximum score: the highest score depends on each year's test form. The top of the range shown here is the highest score any form of that test reached in Missouri's technical reports for 2019 through 2022 (for example 471 on Algebra I and 490 on English II). Missouri has not posted a technical report since, so a later form's highest score may differ; scores that high are very rare.

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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