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 Wyoming Department of Education assessment data (WY-TOPP, 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

Wyoming publishes the exact scale-score range for each performance level (e.g. for Grade 4 Math, Level 3 “Proficient” is 466-490). 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.
The Wyoming Test of Proficiency and Progress (WY-TOPP) reports a grade-embedded scale score (each grade and subject has its own range, e.g. grade 4 ELA is 430-790 and grade 4 Math is 310-610), stable across years since the July 2018 standard-setting. The four levels are Below Basic, Basic, Proficient, and Advanced, with Proficient marking the state proficiency line. The three cut scores separating those levels come directly from WDE's official published cut-score tables for every grade. The outer endpoints of each grade's scale (the lowest and highest obtainable score) are published by WDE only for grade 4; for the other grades this site estimates them from WDE's own published statewide mean and standard deviation for the 2017-18 base year (mean plus or minus four standard deviations, rounded to the nearest ten), a rule that reproduces three of grade 4's four known endpoints exactly and the fourth within ten points. Those estimated endpoints only affect where a score falls within the lowest or highest level; level assignment itself always uses the real published cuts. Wyoming publishes the percentage of students at each level for every school and the number tested as a rounded range, from which the exact count is recovered by matching the published percentages. No statewide test was given in spring 2020 (COVID). Wyoming is compared at the school, district, county, and state levels (each regular district's county is part of its official name).
Charter schools appear as their own districts in the state files and are included in the school, district, county and statewide comparisons.

This site stores nothing you type. Scores are used only in your browser to draw your charts.

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