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 Missouri Department of Elementary and Secondary Education assessment data (MAP, ELA & Math in grades 3-8, and Science in grades 5 and 8). These files report, for each school / grade / year:

the percentage of students in each performance level and the real number tested, for every school, district, and the state; we turn the percentages into student counts. Where Missouri hides one or two small levels for privacy, they are filled in from the rest, 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.

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

Missouri publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 362-389). 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, 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 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 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.

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.
The MAP Grade-Level Assessment reports a scale score with its own range for each grade and subject (English Language Arts spans 160 at Grade 3 up to 650 at Grade 8, Mathematics 185 up to 660, and Science runs 100-540 at Grade 5 and 285-710 at Grade 8), across four performance levels: Below Basic, Basic, Proficient, and Advanced, with Proficient marking the state proficiency line (proficient means scoring Proficient or Advanced). The ranges were set for the current Missouri Learning Standards and are fixed across administrations, so scores are comparable year to year. Missouri publishes the percentage of students at each level and a real number of test-takers for every school and grade; it reports percentages rather than an average scale score, so the curve's center is estimated by fitting a normal distribution to those percentages across the official score ranges. Science is given in grades 5 and 8. No test was given in 2020 (COVID). Missouri is compared at the school, district, and state levels (it has no county tier).
Charter schools appear as their own districts in the state files and are included in the school, district and statewide comparisons.

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