How we estimate percentiles: Connecticut 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 Connecticut State Department of Education’s public EdSight reports, for the two tests every Connecticut grade 11 student takes: the Connecticut School Day SAT (its Reading and Writing section and its Math section, 2018, 2019 and 2022 to 2026) and the NGSS Science test (2019 and 2022 to 2026). These reports give, for each school, district and the state, and for each test and year:

• the real number of students in each achievement level, the number with a score, and the number who met or exceeded the standard. We use those counts exactly as Connecticut printed them, and
• the group’s real average score, which sets the center of each group’s bell curve.

Who is counted

The SAT results include the grade 11 students who took the SAT at school on Connecticut’s School Day, in the spring. Scores from weekend SAT administrations are not included. The Science results include the grade 11 students who took the NGSS Science test. Students who take Connecticut’s alternate tests and students with a medical exemption are not counted, and for the SAT neither are English learners in their first two years in U.S. schools (CSDE’s report notes for each test). A student is counted at the school where they were enrolled when they tested.

Both tests are taken by the whole grade 11 class (about 35,600 students with an SAT score and 35,800 with a Science score in 2026), so a percentile compares a score with Connecticut juniors who took the test that spring. 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.

The statewide row is Connecticut’s own statewide total. District results also count their students placed in approved private special education programs, which have no school row, so a district’s schools add up to a little less than the district (in districts where every school is published, a median of 1 student less).

How the percentile is estimated

Connecticut publishes the exact scale-score range for each achievement level (e.g. for SAT Math, “Level 2: Approaching” is 420-520, and for Science, “Level 3: Met” is 1099-1140). Given a score, we:

1. identify which achievement 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 centered on the group’s published average score, with its spread fitted so that its area within each achievement 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. A curve that comes out too narrow is drawn no narrower than one fifth of the statewide spread, and inside the student's level the percentile spreads that level's students evenly instead.

Hidden counts

To protect privacy, Connecticut hides any count of 5 or fewer students, and then hides a second count so the first can’t be worked out by subtraction. In a district whose high school sits beside a very small program (an alternative or transition program, for example), it also hides the high school itself, so the program can’t be worked out from the district total. That is why some large high schools show no counts in Connecticut’s own reports. We never change a number Connecticut published, and we fill in the hidden ones like this:

• A few levels hidden: the hidden students are the school’s total minus the levels shown. Connecticut also prints how many students met or exceeded the standard, which tells exactly how many of them are in the top two levels. Within that, they are split by the school’s curve around its published average. When we hid two levels of schools whose counts are all published and filled them back this way, the result was exact for most schools and off by at most about 2% of the school’s students for nine in ten.
• A whole high school hidden: its counts are the district’s published counts minus the district’s other schools. What remains also holds the district’s tiny hidden programs, so it is trimmed to the school’s size in the way that best agrees with the school’s published average score. When we hid large schools whose counts are all published and recovered them this way, a typical school was off by about 1% of its students in any level, and nine in ten by under about 3.5%.

About a quarter of the students in the school results are in a level filled in this way, most of them at the large schools recovered from their district. A district result with a hidden level is filled the same way as a school; the state results are published in full.

Cut scores

The SAT reports each section on a 200-800 scale, in steps of 10. Connecticut sets four levels on it: Level 1 Not Met, Level 2 Approaching, Level 3 Met and Level 4 Exceeded, with Met as the state’s achievement standard. For Reading and Writing they are 200-410, 420-470, 480-620 and 630-800; for Math, 200-410, 420-520, 530-640 and 650-800. Met starts at College Board’s own college-readiness benchmarks (480 and 530). The table is printed in CSDE’s CT School Day SAT Report Notes, and it is the same in the 2016, 2022 and March 2026 editions, so the same ranges apply from 2018 to 2026, including the digital SAT used from 2024.

NGSS Science grade 11 is reported on a 1000-1199 scale, with the same four levels: 1000-1072, 1073-1098, 1099-1140 and 1141-1199. Connecticut educators set these levels in summer 2019 from the first spring 2019 results, and CSDE’s NGSS Assessment Interpretive Guide prints the same table in its 2022 and Spring 2026 editions. 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. Both tests here are grade-level tests, taken by every grade 11 student. Science continues the grade 5 and grade 8 NGSS Science tests from the grades 3-8 tool.
• 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.
• Programs too small for Connecticut to publish an average score don’t appear (about a third of the rows in its school reports, nearly all with a handful of students or none tested), and neither do about four high schools a year that are hidden alongside another hidden school in the same district. The district and state results still count those students; the schools shown hold 96% to 98% of each year’s students.
• Not included: 2020 (no test, COVID); 2021, which Connecticut does not publish in these reports; and Connecticut’s alternate tests.
• Connecticut is compared at the school, district and state levels.

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