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 Kentucky Department of Education assessment data (KSA, ELA & Math, grades 3-8). These files report, for each school / grade / year:

the percentage of students in each performance level per school/grade/subject. We treat these published percentages as a group of 100 students to preserve their shape, and derive an implied count scale, mean, and spread from them using the same statistical fit described below.

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

Kentucky publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 3 “Proficient” is 521-541). 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 percentage-derived counts, anchored to a mean we derive from those same percentages. 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 percentages are real for each group. Because this state’s files center on those percentages alone, both the implied student count and the mean shown are derived from them, using a consistent method across every school and grade, so the comparison (“above/below average here vs. statewide”) still holds up well even though these figures carry more modeling than most other states in this tool.

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.
The Kentucky Summative Assessment (KSA) reports a scale score from 400 to 600 for Reading (shown here as ELA) and Mathematics, stable across years. The four levels are Novice, Apprentice, Proficient, and Distinguished, with Proficient marking the state proficiency line. Kentucky publishes the percentage of students at each level rather than student counts, so figures are shown as percentages. KSA began in spring 2022 (replacing K-PREP); there are no comparable statewide results for 2020 or 2021. Kentucky is compared at the school, district, and state levels.
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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