How we estimate percentiles: Hawaii 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 Hawaii State Department of Education’s assessment data for the grade 11 Smarter Balanced tests in ELA and math, in 2018, 2019 and 2021 to 2026. For each school, complex, complex area and the state, and for each subject and year, these files give:

• the percentage of students in each of the four performance levels. Hawaii doesn’t publish how many students tested below the state level. Its percentages are cut off (not rounded) at one decimal, though, so only certain group sizes can produce them, and Hawaii publishes no group smaller than 20. A school’s number is the size that reproduces its own percentages, picked closest to its grade 11 enrollment (special-education students included) times its participation rate. Checked against the federal count of test takers for 2018, 2019 and 2021, it is exact for about 9 in 10 high schools and within 30% for all but one. High schools are large, and the bigger the group, the more sizes fit the same percentages, so this is less exact than in grades 3-8. The number of students only sets the counts shown; the percentile comes from the percentages; 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. For the state in 2022-2025, we use Hawaii’s own published average and spread instead.

Who is counted

Hawaii gives the Smarter Balanced ELA and math tests to its grade 11 students. A percentile compares a score with that year’s Hawaii public school students in grade 11, by the school where they tested: about 11,200 students in each subject in 2025. As in Hawaii’s own reports, students who took the alternate assessment (HSA-Alt) or the Hawaiian-language assessment (KA‘EO) are counted in. Charter schools are grouped under Hawaii’s own “Charter Schools” complex and complex area.

How the percentile is estimated

Hawaii publishes the exact score range for each performance level (e.g. for grade 11 Math, Level 3 “Met Standard” is 2628-2717). 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 fitted so that its area within each performance level matches the level percentages, centered on that estimated average score. 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

Each test has four levels: Did Not Meet Standard, Nearly Met Standard, Met Standard and Exceeded Standard. Met Standard and above count as proficient.

• Grade 11 ELA: 2102-2492, 2493-2582, 2583-2681, 2682-3032
• Grade 11 Math: 2118-2542, 2543-2627, 2628-2717, 2718-3085

These come from Hawaii’s own Smarter Balanced technical reports (2021-22 to 2024-25), which print the cut scores and the lowest and highest possible scores. The cut scores are the same in every Smarter Balanced state and match the consortium’s own published 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. The grade 11 tests are taken by the whole class, so ELA and math continue the grades 3-8 lines, on the same Smarter Balanced scale. Each point is a percentile among that year’s students in that grade.
• 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 complex they attended, so those years are compared with every student in the state in that grade, not with this high school or its complex.
• 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, and groups under 20 students are not published.
• Not included: 2020 (no test, COVID); high-school science (Biology), which Hawaii reports by the student’s grade with no combined result and no student counts, so a school’s Biology results can’t be put together; and the Algebra end-of-course exams, which are not in the public data. In 2021 some schools tested few students (Maui High tested about 3% of its grade 11), and Hawaii published no result for them.
• Hawaii is compared at the school, complex, complex area and state levels.

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