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 Louisiana Department of Education assessment data (LEAP, 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

Louisiana publishes the exact scale-score range for each performance level (e.g. for Grade 3 Math, Level 4 “Mastery” is 750-789). 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 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 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 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.
Louisiana prints any level under 5% as “<5”. When only one level in a row is hidden, the other four give it exactly, because the five add up to 100. When two or more are hidden, we split what is left between them. Hidden levels on the same side of the group's scores follow its fitted curve, so the level farther out gets fewer students. Hidden levels at opposite ends (a few students in both Unsatisfactory and Advanced) get equal shares. We checked this on states that print every level, hiding their small levels the way Louisiana does: it lands about 30% closer to the real shares than splitting evenly. A hidden level is never shown at more than 4%, except in the few rows where the printed levels leave more than that to share.
LEAP reports a scale score from 650 to 850 for English Language Arts and Mathematics, stable across years. The five levels are Unsatisfactory, Approaching Basic, Basic, Mastery, and Advanced, with Mastery marking the state proficiency line. Louisiana publishes the percentage of students at each level rather than student counts, so figures are shown as percentages. No statewide test was given in 2020 (COVID). Louisiana is compared at the school, district, and state levels (its school systems, which include parish, city, and charter systems, are the district tier).
Charter schools appear as their own districts in the state files and are included in the school, district and statewide comparisons.

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