How we estimate percentiles: California 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 California CAASPP research files for the grade 11 Smarter Balanced ELA and Math tests (2018, 2019 and 2021 to 2026) and the high-school California Science Test, CAST (2019 and 2021 to 2026). These files report, for each school, district, county and the state:

the number of students tested and their mean scale score (real, reported figures), and
how many students landed in each performance level, a real, reported count for 2024 onward. For 2018-2023 the files published percentages instead, which we convert to counts (percentage × number tested) so that every count rounds back to the percentage California printed.

Who is counted

ELA and Math: the Smarter Balanced tests taken by 11th graders. Science: the California Science Test (CAST), which students take once in high school, in grade 10, 11 or 12; each year counts every high-school student who took it that year, whatever their grade.

For 2019 the files have no all-high-school CAST row, so each school's grade 10, 11 and 12 rows are added together; a school with any of those rows hidden for privacy is left out that year, so 2019 science has about a quarter fewer schools than other years. A percentile compares a score with that year's takers of the same test.

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

California publishes the exact scale-score range for each performance level (e.g. for grade 11 Math, Level 4 “Standard Exceeded” is 2718-2900). 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. 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 real reported counts, anchored to the group’s real reported mean. 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: both the performance-level counts and the mean score are real, reported figures. The only assumption anywhere in this pipeline 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

Grade 11 ELA: Standard Not Met to 2492, Nearly Met 2493-2582, Met 2583-2681, Exceeded from 2682;
Grade 11 Math: Standard Not Met to 2542, Nearly Met 2543-2627, Met 2628-2717, Exceeded from 2718;
High School CAST Science: Standard Not Met 550-575, Nearly Met 576-614, Met 615-635, Exceeded 636-650.

The lowest and highest possible ELA and Math scores were 2299-2795 (ELA) and 2280-2862 (Math) through 2019 and 2300-2900 / 2280-2900 from 2021, as California prints them. In 2026 California renamed the four levels Minimal, Developing, Proficient and Advanced; the cut scores did not change. Ranges are from ETS's CAASPP scale score range tables.

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 results are suppressed by the state (for privacy, small groups) and won't appear.
No statewide test was given in 2020 (COVID). In 2021 testing was optional: about half the usual number of students took grade 11 ELA and Math, and about a quarter took CAST, so 2021 compares a smaller group that is not representative of the state. CAST had no scored high-school results in 2018 (its field-test year).
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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