How we estimate percentiles

Plain-English 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, ELA & Math, grades 3-8). These files report, for each school / grade / year:

the percentage of students in each performance level (school rows) or the real count (district/state rows), plus the number tested, and
from those figures, a mean we estimate from the count-weighted midpoint of each performance level’s scale range, which we then fit a curve around.

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, use linear interpolation across that level's count, assuming scores are spread evenly across the level's range.

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, anchored to a mean estimated from the count-weighted midpoint of each level. It's there to visualize the shape of the group's scores. The headline percentile comes from the counts (step above), not from the curve.

Why estimates are still useful: the performance-level counts are modeled from real inputs, not directly reported. Hawaii publishes each school's real Language Arts/Math proficiency rate per grade (School Status and Improvement Report) and real per-school enrollment by grade, but not a public four-level breakdown. We place each school's average score so it reproduces that real proficiency rate, using the state's own official average and spread for that grade and year as the shape, then split the real enrollment across the four levels using that curve. Across a whole school, district, or the state, that shape 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 2000-2800 (the range varies by grade) and are stable across years.
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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