How we estimate percentiles: New Hampshire 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 Hampshire Department of Education’s assessment data for its two grade 11 tests: the School Day SAT (its Reading and Writing section and its Math section) and the NH SAS Science test, in 2018, 2019 and 2021 to 2026. For each school, district and the state, and for each test and year, these files give:

• the percentage of students in each performance level. The number of students is printed only as a five-student range of full-year students (such as 45-50, which means 45 to 49). Because every percentage has to round to what is printed, the exact number of students can usually be worked out, and we use it (otherwise the middle of the range). When a level is shown only as “under 10%” or “over 90%”, we work out how many students it holds from what is printed: every level, and the share at Proficient or above, has to round to the whole percent New Hampshire prints, and the figures for boys and girls (and, from 2024, for other pairs of student groups) have to add up to the whole group. When the printed numbers still allow more than one split, we split what is left using a curve centred on the group’s published average; and
• New Hampshire’s own published average score for each group, which sets the center of its bell curve.

Who is counted

New Hampshire gives the SAT at school, on its spring School Day, to its grade 11 students as the state’s high-school test in reading and writing and in math, and gives them the NH SAS Science test. A student is counted at their school if they were enrolled there for the full school year. A percentile compares a score with that year’s New Hampshire public school juniors: about 10,600 students took each SAT section and 9,700 took Science in 2026. An SAT percentile here is not the same as the national percentile on a College Board score report, which compares with test takers across the country.

How the percentile is estimated

The score range for each performance level is published (e.g. for SAT Math, Level 3 is 530-640). 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 centered on the group’s published average score, with its spread fitted so that its area within each performance level matches the level percentages. It's there to visualize the shape of the group's scores. The percentages set the headline percentile (steps above); the curve only decides where inside the student's own level the line falls.

Cut scores

The SAT reports each section on a 200-800 scale, in steps of 10. New Hampshire reports four levels on it, Level 3 being its proficiency benchmark: for Reading and Writing 200-410, 420-470, 480-620 and 630-800; for Math 200-410, 420-520, 530-640 and 650-800. These levels were set in 2016 by Connecticut, Delaware, Maine and New Hampshire together (the “2016 SAT Multi-State Standard Setting” report). The Department’s SAT School Day FAQ prints the Level 3 benchmarks, 480 and 530, says the four states use the same levels and that they stay the same from year to year unless the states adjust them. New Hampshire’s own 2018 statewide percentages match the levels the 2016 report projected for New Hampshire to within about one point. Connecticut and Delaware still print the same table for the digital SAT in 2026.

NH SAS Science grade 11 is reported on a 1100-1200 scale: Below Proficient 1100-1145, Approaching Proficient 1146-1152, Proficient 1153-1175 and Above Proficient 1176-1200. These come from the NH SAS technical reports (2018-19, 2022-23 and 2024-25) and the Department’s NH SAS performance levels table. 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.

• One line per subject. Both tests are taken by the whole grade 11 class. The SAT sections continue the grades 3-8 ELA and math lines, and Science continues the grade 5 and grade 8 science tests. The scales differ, but each point is a percentile among that year’s students in that grade, so the points compare.
• Earlier years are compared statewide only. You can add your child’s grades 3-8 scores. 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.
• New Hampshire prints whole percentages and a range for the number of students, so a small school’s results are rounded and noisier.
• Not included: 2020 (no test, COVID).
• New Hampshire is compared at the school, district and state levels.

This site stores nothing you type. Scores are used only in your browser to draw your charts.