How we estimate percentiles

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 Hawaii State Department of Education assessment data (Smarter Balanced for ELA & Math in grades 3-8; Science in grades 5 and 8, grades 4 and 8 in 2018-2019). These files report, for each school / grade / year:

the percentage of students in each performance level, for every school, complex, complex area, and the state. Hawaii doesn’t publish how many students tested below the state level, so a school’s number is its enrollment in that grade (special-education students included) times its own participation rate, scaled so the statewide total matches Hawaii’s published number tested, 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 ELA and Math, 2022-2025, we use Hawaii’s own published average and spread instead.

Important: the public data does not contain individual student scores, only these group summaries. So no tool can compute a true rank of one child against every other child. What we provide is a well-grounded estimate.

How the percentile is estimated

Hawaii publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Met the Standard” is 2436-2500). Given your child's 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 level counts, centered on that estimated average score. 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: the performance-level percentages are Hawaii’s own for every group. The number of students behind them is modeled from enrollment, so a group’s size is approximate but its percentages are not. The average score shown is estimated from how students split across the levels (Hawaii’s own figure for the state in ELA and Math, 2022-2025), and, as with every state, the only other assumption is how scores are distributed inside a level, a small and bounded range. Across a whole school, complex, complex area, 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.

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.
Some school/grade cells are suppressed by the state (for privacy, small groups) and won't appear.
Smarter Balanced scale scores run roughly 2000-3000 (the range varies by grade) and are stable across years. HSA Science is a separate test on its own scale, and that scale changed: science was reported on a 100-500 scale in 2018 and 2019 (grades 4 and 8), then on a 400-600 scale from 2021 under the Next Generation Science Standards (grades 5 and 8). Science scale scores are not comparable across that change, but percentiles are, because each year is compared against that year’s own cohort.
Charter schools are grouped under HIDOE's own "Charter Schools" Complex and Complex Area, and are included in the school, complex, complex area, and statewide comparisons like any other school.

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