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 Maryland State Department of Education assessment data (MCAP, ELA & Math in grades 3-8, Science in grades 5 and 8, and Social Studies in grade 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 (Maryland’s 24 local school systems and the SEED School), and the state; we turn the percentages into student counts. Where Maryland shows a small level only as “5.0% or less,” the count is worked out from the state's other published numbers: the levels add up to the number tested, Maryland also publishes how many students were proficient, and each school's all-grades row (from 2023) and each district's row add up the rows under them. Most of the time that leaves only one possible answer. Where it leaves a few, the remaining students are split along the bell curve of the group's published levels, which puts fewer of them in the outer level. Every count rounds back to the percentage Maryland printed, and a district's counts are chosen together with its schools' so the two add up (for a district of thousands of students, a one-decimal percentage can match a few different counts), 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.

How the percentile is estimated

Maryland publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient Learner” is 750-789). Given your child's 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. 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.

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. In 2022 and 2023 Maryland also hid the split between the two lowest levels wherever 5% or fewer students were proficient, mostly in Math. Those groups appear only where the school's other published rows pin the split down; about 1,500 school and district results from those two years are left out.
• Maryland's tests report on a 650-850 scale. Since 2022 MCAP has four levels: Beginning Learner, Developing Learner, Proficient Learner, and Distinguished Learner, with Proficient marking the state proficiency line. In ELA and Math the lower cuts sit at 725 and 750 for every grade and only the top “Distinguished” cut moves by grade; those cuts were set in October 2022. In 2018 and 2019 ELA and Math were reported on the earlier PARCC-era table with five levels (Did Not Yet Meet, Partially Met, Approached, Met, and Exceeded Expectations, proficient from 750), so scale scores from those years don't line up exactly with later ones; percentiles do. Science has used the same cut scores since 2018. The shortened 2021 test was reported in three levels, and only its Science results are carried here: 2021 ELA and Math were scored on short point scales with no other year to calibrate against. Maryland publishes the real percentage of students at each level and a real number of test-takers for every school, district, and the state, so the level counts come from the state's own numbers; no mean scale score is published, so the curve's center is estimated by fitting a normal distribution to those percentages. Science is given in grades 5 and 8, Social Studies in grade 8 (from 2023). No test was given in 2020 (COVID). Maryland is compared at the school, district (its 24 school systems, one per county plus Baltimore City, and the SEED School), and state levels (no separate county tier).
• Charter schools are listed under the local school system that authorized them, which is how Maryland reports them; the SEED School of Maryland, a statewide public boarding school, is its own district.

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