How we estimate percentiles: Idaho 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 the assessment data of the Idaho State Department of Education / Idaho Report Card, for the grade 11 ISAT: ELA and math in 2023 to 2026, and science in 2022 to 2026. For each school, school district and the state, and for each subject and year, these files give:

• the real number of students in each of the four performance levels and the number tested, and
• from those counts, an estimated average score: Idaho does not publish an average, so the center of the curve is the one that best matches the share of students below each level’s cut score.

Hidden numbers. Where Idaho hides a small level for privacy, it still prints a bound on it (for example “under 27%”). Together with the number tested, the number proficient, and the school’s and district’s totals, those bounds usually pin every hidden level to an exact whole number of students. Where they leave a choice of a few students, the split follows the school’s or district’s own results, with all of a district’s open counts chosen together so its schools still add up to the district totals Idaho published. Groups under 20 students with most levels hidden are left out; the schools shown hold about 96% of each year’s test takers, and every student is in the statewide results.

Who is counted

Idaho gives the ISAT in ELA, math and science to its grade 11 students. A percentile compares a score with that year’s Idaho public school students counted in grade 11, by the school where they tested: about 22,300 students in each subject in 2026. A student can take the ELA or math test early, in grade 9 or 10 (Idaho’s “Challenge Up”), and have that score count for grade 11. Charter schools appear as their own districts in the state files and are included in the school, district and statewide comparisons.

How the percentile is estimated

Idaho publishes the exact score range for each performance level (e.g. for grade 11 Math, Proficient is 2628-2717). Given a score, we:

1. identify which performance level the score falls in;
2. count everyone in the lower levels as scoring below;
3. 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.

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 nearly all sit in one or two levels, as at some alternative schools and some very high-scoring ones, the counts can't say how spread out their scores are. About 3% of high-school groups are like this. Their curves are drawn no narrower than one fifth of the statewide spread, and inside the student's level the percentile spreads that level's students evenly instead.

Cut scores

Each test has four levels: Below Basic, Basic, Proficient and Advanced. Proficient and above count as proficient.

• Grade 11 ELA: 2102-2492, 2493-2582, 2583-2681, 2682-3032
• Grade 11 Math: 2118-2542, 2543-2627, 2628-2717, 2718-3085
• Grade 11 Science: 1000-1081, 1082-1107, 1108-1145, 1146-1200

These come from the Idaho State Department of Education’s “Cut Scores for ISAT” table (its 2023 and 2024 editions print the same grade 11 rows). The ELA and math tests are Smarter Balanced tests, and their grade 11 cut scores match the Smarter Balanced consortium’s own published table. The score range for each level, by year, is on the score guides.

The high-school progress report

The paid progress report puts every high-school test your child took in one table, with the percentile at each level from the school to the state, and charts each subject across the years.

• One line per subject. The grade 11 ISAT is taken by the whole class, so ELA, math and science continue the grades 3-8 lines in the same subject (science is tested in grades 5 and 8). Grade 11 ELA and math are on the same Smarter Balanced scale as grades 3-8; science has its own scale in each grade, but each point is a percentile among that year’s students in that grade, so the points compare.
• Earlier years are compared statewide only. You can add your child’s grades 3-8 scores. The tool doesn’t know which middle school or district they attended, so those years are compared with every student in the state in that grade, not with this high school or its district.
• The report opens on the statewide view, the one level with a result for every test.

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, and some are hidden.
• Not included: ELA and math in 2021 and 2022, when Idaho tested them in grade 10. Idaho’s grade 10 cut table and the Smarter Balanced consortium’s differ at two cut scores, and we have not found which one Idaho used in those years. Also not included: science in 2021 (no performance levels published), 2020 (no test, COVID), and years before 2021, which the report card’s data export does not carry.
• Idaho is compared at the school, district and state levels (its districts do not map to counties).

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