How we estimate percentiles: Washington high school

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 Washington OSPI Report Card assessment data for grade 10 Smarter Balanced ELA and Math, and the grade 11 Washington Comprehensive Assessment of Science (WCAS), for 2018, 2019 and 2022 to 2026. These files report, for each school, district and the state:

the percentage of students in each performance level and the number tested; we turn the percentages into student counts. Where OSPI hides a small group’s number tested but keeps its percentages, the number is recovered from the percentages, the school’s other subject, its own count in other years, or what its district leaves unaccounted for. That only changes the student count shown, never the percentages or the percentile. A county is the sum of the districts in it, and
from those figures, an estimated average score: the center of the bell curve that best matches the share of students below each level’s cut score. Washington publishes no average score.

Who is counted

ELA and Math count the 10th graders who took the Smarter Balanced test that spring. Students in 11th or 12th grade may retake it for a graduation pathway, and those retakes are not counted. Science counts the 11th graders who took the WCAS that spring; 12th graders who retake it are not counted. Students who take the alternate assessment (WA-AIM) are not included. There is no 2020 (testing was cancelled) and no 2021: the spring 2021 tests were given in the fall of 2021 to students one grade older, so that year is left out.

Important: the public data does not contain individual student scores, only these group summaries. So no tool can compute a true rank of one student against every other student. What we provide is a well-grounded estimate.

How the percentile is estimated

Washington publishes the exact scale-score range for each performance level (e.g. for grade 10 Math, Level 4 is 2697-3085). Given a 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.

That gives the percentile: the estimated share of students in the group who scored at or below the entered score. For the state, we checked this against OSPI’s own statewide score distributions for every year shown: the student counts, the share below each cut score and the percentiles all line up.

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, centered on that estimated average score. 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. The average score shown is estimated from how students split across the levels, and 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.

Cut scores

The same ranges apply in every year shown. Level 3 and above meets the standard.

Grade 10 ELA (2102-3032): Level 1 2102-2490, Level 2 2491-2576, Level 3 2577-2677, Level 4 2678-3032.
Grade 10 Math (2118-3085): Level 1 2118-2532, Level 2 2533-2613, Level 3 2614-2696, Level 4 2697-3085.
Grade 11 Science (WCAS) (390-1190): Level 1 390-649, Level 2 650-699, Level 3 700-790, Level 4 791-1190.

Washington set its own grade 10 cut scores in 2018 (they differ slightly from other Smarter Balanced states’ high-school cuts). Sources: the State Board of Education’s January 2018 threshold-score decision, OSPI’s spring 2022 technical report, its yearly score-report guides, and OSPI’s current scale-score page.

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. Groups of fewer than 10 students are not published.
For some small schools the student count shown is recovered rather than published (see above); it can be off, but the percentages and the percentile are not affected.

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

Back to the tool