How we estimate percentiles: New Jersey 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 New Jersey Department of Education’s statewide assessment reports: one results file per test and year, for every school, every district and the state. Each file gives the number of students with a valid score, the group’s average (mean) scale score, and the percentage of students in each performance level. We turn the percentages into student counts that print back exactly as New Jersey printed them, and center each group’s curve on New Jersey’s own average. New Jersey does not publish county results, so a county here is the sum of its districts.

• Grade 9 ELA: 2018, 2019 and 2022 to 2025. Grade 10 ELA: 2018 and 2019. Grade 11 ELA: 2018. New Jersey stopped giving the grade 11 ELA test after 2018 and the grade 10 test after 2019.
• Algebra I, Geometry and Algebra II: end-of-course tests, 2018, 2019 and 2022 to 2025.
• Grade 11 Science: 2019 (the test’s first year) and 2022 to 2025.

The 2018 tests were PARCC and the later ones NJSLA. Both use the same 650 to 850 scale and the same cut scores, so a 2018 score and a 2025 score mean the same thing. There was no state test in 2020 or 2021. Spring 2026 results are not published yet.

The grade 11 graduation test (NJGPA) is not included. It reports only two levels, Graduation Ready or Not Yet Graduation Ready, and one cut score is too little to place a score well: checked against the statewide score distributions in New Jersey’s technical reports, the estimate was off by about 3 to 6 percentile points for a typical score, where the five-level tests here are off by under 1. New Jersey’s NJGPA files also leave a school blank when nearly all of its students landed on the same side of the cut (no school shown has more than 90% in either level), which removes about 4 in 10 schools from the ELA results, many of them the highest-scoring.

Who is counted

These numbers are the spring test only. For Algebra I, Geometry and Algebra II, they include every student who took the test that school year, in any grade: middle-school students who take Algebra I or Geometry early are included and counted at their middle school (about a third of Algebra I testers are in grades 7 and 8, and about 15% of Geometry testers from 2022). In 2018 the course tests also include students in grades 11 and 12. From 2019 New Jersey’s files leave out the grade 11 students who took these tests, and from 2022 grades 11 and 12 as well, because the tests were optional for them. So Algebra II in particular counts far fewer, mostly younger students from 2019 on (78,429 students in 2018, about 7,700 in 2025).

The grade 9, 10 and 11 ELA tests and the grade 11 science test count the students in that grade. Schools with fewer than 10 tested students, and a few schools whose number of tested students New Jersey does not print, are not shown, but their students are counted in their district and the state.

How the percentile is estimated

New Jersey publishes the exact scale-score range for each performance level (e.g. for Algebra I, Level 4 “Met Expectations” is 750-804). 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. Checked against the statewide score distributions in New Jersey’s 2023 to 2025 technical reports, the statewide estimate lands within about 1 percentile point of the true value for a typical score.

About the smooth curve

The bell-like curve on each chart is a truncated-normal distribution centered on the group’s real average score and fitted so that its area within each performance level matches the level counts. 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.

Cut scores

ELA and the math tests have five levels: Did Not Yet Meet, Partially Met, Approached, Met and Exceeded Expectations. Levels 2, 3 and 4 start at 700, 725 and 750 on every test; Level 5 starts at 791 for grade 9 ELA, 794 for grade 10 ELA, 792 for grade 11 ELA, 805 for Algebra I, 808 for Algebra II and 783 for Geometry. Level 4 and above means the student met expectations. These cuts are the same in every year shown.

Grade 11 Science is a separate test on a 100 to 300 scale with four levels, which New Jersey calls simply Level 1 to Level 4: 100-157, 158-199, 200-249 and 250-300. Levels 3 and 4 are proficient.

Each year’s table is read from that year’s official documents: the PARCC technical report for the 2018 tests (New Jersey was a PARCC state), New Jersey’s Score Interpretation Guides for 2019 and 2022, and New Jersey’s NJSLA technical reports for 2023 to 2025 (for science, the 2019 and 2022 guides and the NJSLA-Science technical reports). The score range for each level, by year, is on the score guides.

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.

• Lines join only the same kind of comparison. A grade-level test (ELA in grades 9, 10 and 11, and grade 11 science) is taken by every student in that grade, so one subject’s grade-level results form a line across the years. A course exam (Algebra I, Geometry or Algebra II) is taken by the students in that course that year, a different group for each course, so each one is its own point.
• Earlier years are compared statewide only. You can add your child’s grades 3-8 scores in the same subjects. The tool doesn’t know which middle school or district they attended, so those years are compared with every student in the state in that grade, not with this high school or its district.
• The report opens on the statewide view, the one level with a result for every test.

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. New Jersey hides results for schools with fewer than 10 tested students.
• The course tests compare a student with everyone who took that course that year, not with everyone in the same grade. An 8th grader’s Algebra I score is compared with 9th graders too, and the Algebra II group from 2019 on is mostly younger students ahead in math.
• In 2018, about 1 in 4 students registered for the grade 11 ELA test did not get a valid score, so that year’s grade 11 group is smaller than the full class.
• New Jersey moved to a new adaptive test (NJSLA-Adaptive) in spring 2026, on a new scale with new cut scores. When those results are posted they will be added with their own cut scores; scores from the new scale won’t line up with the 650 to 850 scale, but percentiles will.

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