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 Montana Office of Public Instruction assessment data (SBAC / MAST / MSA, 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

Montana publishes the exact scale-score range for each performance level (e.g. for Grade 5 Science, Proficient is 506-530). 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.
Montana's ELA and Math results span two tests. Through spring 2023 they use the Smarter Balanced consortium scale (roughly 2100-2800, varying by grade), a common multi-state scale whose four levels are Novice, Nearing Proficient, Proficient, and Advanced. Starting spring 2025 Montana uses its own MAST (Montana Aligned to Standards Through-year) assessment on a 250-400 scale, whose four levels are Novice, Partially Proficient, Proficient, and Advanced. Science uses the Montana Science Assessment on a 400-600 scale in grade 5 and a 700-900 scale in grade 8, with levels Novice, Nearing Proficiency, Proficient, and Advanced, and is given in grades 5 and 8. Proficient marks the state proficiency line in every subject. Montana publishes the percentage of students at each level and the number tested for every school, district, and the state, from which the exact level counts are recovered and the curve is fit. No statewide test was given in spring 2020 (COVID), and spring 2024, the MAST transition year, is not yet included. Montana is compared at the school, district, county, and state levels.
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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