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 Arkansas Division of Elementary and Secondary Education assessment data (ATLAS, 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

Arkansas publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 1060-1072). 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.
ATLAS (the Arkansas Teaching, Learning and Assessment System) reports a scale score that runs from 1000 up to about 1120 for each grade and subject, across four performance levels numbered 1 through 4, with Level 3 marking the state proficiency line. Level 3 “proficient” always begins at 1060; the other cuts shift only slightly by grade and subject. Arkansas publishes the real percentage of students at each level and a real number of test-takers for every school, district, and the state, so the level counts come straight from the state's own numbers; no mean scale score is published, so the curve's center is estimated by fitting a normal distribution to those percentages across the official score ranges. Science is given in every grade 3 through 8. ATLAS began in spring 2024, replacing ACT Aspire; for Math and Science, results also go back to 2018 using ACT Aspire, which used a different 400 to 460 scale and four readiness levels (In Need of Support, Close, Ready, Exceeding, with Ready marking readiness). The two tests are on different scales, so the scale scores are not comparable, but the percentiles are, because each year places the child against that grade's cohort. ELA is only from 2024 on, since ACT Aspire did not report a single ELA score. No test was given in 2020 (COVID). Arkansas 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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