How we estimate percentiles: Massachusetts 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 official public test-results files: the Massachusetts DESE MCAS results for grade 10 ELA and Math (2018, 2019 and 2021 to 2026), Biology and Introductory Physics (2018, 2019 and 2021 to 2026), and the older Chemistry and Technology and Engineering tests (through 2023). These files report, for each school, district and the state:

the real number of students at each achievement level and the number tested, and
from 2019 for grade 10 and from 2022 for science, the average scale score, which the curve is centered on. Earlier (legacy) years publish no average, so there it is estimated from how students split across the levels.

Who is counted

Grade 10 ELA and Math count 10th graders who took the spring test; retests are not counted. Students take a high school science test in grade 9 or 10, so a year's Biology or Introductory Physics group mixes 9th and 10th graders; DESE's reporting rules for 2022 to 2025 count only students taking that test for the first time. In 2021 the science tests were open only to 9th graders and former students. Two older tests, Chemistry and Technology and Engineering, were last given in 2023 and few students took them. Students who took the alternate assessment (MCAS-Alt) are counted in the achievement levels but not in the average score, and a school counts only students enrolled there since October.

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

Massachusetts publishes the exact scale-score range for each performance level (e.g. for grade 10 Math, “Exceeding Expectations” is 530-560). 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 real reported counts, anchored to the group’s real reported mean. 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: both the performance-level counts and the mean score are real, reported figures. The only assumption anywhere in this pipeline 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

Next-generation MCAS (grade 10 ELA and Math from 2019, Biology and Introductory Physics from 2022) is scored 440-560: Not Meeting Expectations 440-469, Partially Meeting 470-499, Meeting 500-529 and Exceeding 530-560. Earlier years, and Chemistry and Technology and Engineering in every year, use the legacy 200-280 scale with cuts at 220, 240 and 260 (Failing, Needs Improvement, Proficient, Advanced). Scale scores on the two scales don't line up; percentiles do, because each year is compared to its own students.

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. Chemistry and Technology and Engineering were taken by very few students (in some years only a few hundred statewide).
Results for groups of fewer than 10 students are not published. No MCAS tests were given in 2020. The grade 10 “science” figure DESE also reports is a best score across different science tests, so it is not included.

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