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 Arizona Department of Education assessment data (AASA / AzSCI, 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

Arizona publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 3531-3572). 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 real and complete for each group. The mean figure shown is approximated from where students fall within each level, 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, district, county, 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.
Arizona's statewide tests report a scale score with its own range for each grade and subject: the AASA in English Language Arts and Mathematics (grades 3-8), and AzSCI in Science (grades 5 and 8). Both use four performance levels -- Minimally Proficient, Partially Proficient, Proficient, and Highly Proficient -- with Proficient marking the state proficiency line. The scale-score ranges were set with the 2019 cut-score revision (carried forward when the test was rebranded AASA in 2021) and are fixed across administrations, so scores are comparable year to year. Arizona publishes the percentage of students proficient and a real number of test-takers for every school, district, and the state, but not an average scale score or a full level split, so the level shares and the curve's center are estimated by fitting a normal distribution to each group's real proficiency rate across the official score ranges, using the state's own scale-score standard deviation for that grade and subject; the statewide figures use Arizona's own published averages where available. ELA and Math cover spring 2021 through 2024 (2021 and 2022 were given as AzM2, 2023 on as AASA on the same scale), and Science covers 2023 and 2024; no test was given in 2020 (COVID). Arizona is compared at the school, district, and state levels (it has no county tier).
Charter schools appear as their own districts in the state files and are included in the school, district, county and statewide comparisons.

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