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How we compute percentiles: Montana 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 ACT results dashboard of the Montana Office of Public Instruction (GEMS), for the ACT with Writing that every Montana junior takes: ELA and math in 2018, 2019 and 2022 to 2025, and science in 2022 to 2025. For each school, district, county and the state, and for each subject and year, it gives:

That second part is rare: most states publish only how many students fall in each level. Because Montana publishes the count at every score, a percentile here is read straight from real students rather than estimated from a curve.

Hidden numbers. Montana hides any cell of 5 or fewer students but still prints each group’s total. A hidden level count is worked out where only one split fits the printed numbers; a school or district where more than one split fits is left out of that year’s list (about 7% of test takers; 2% for counties). Every student is in the statewide results. A hidden score cell (1 to 5 students) is filled so that its level adds up to the level count.

Who is counted

A percentile compares a score with that year’s Montana public school juniors who took the ACT with Writing, by the school where they tested: about 9,600 students in 2025. The ELA score is the ACT’s English Language Arts score, from the English, reading and writing tests; it appears on a student’s ACT report when they take the writing test. Students who took Montana’s alternate assessment instead are not counted.

Important: the public data does not contain individual student records, only these group counts. Montana’s score counts make the percentiles close to exact for most groups; a group with hidden score cells can be off by a little, never by more than its hidden students.

How the percentile is computed

Given an ACT score, we:

  1. identify which performance level the score falls in, and count everyone in the lower levels as scoring below;
  2. within the score’s own level, count the students at or below the score from Montana’s own score counts.

That gives the percentile: the share of students in the group who scored at or below the entered score. We checked it against the statewide score counts in every subject and year: the largest difference is under 0.1 percentile point. The method most states need, a smooth curve fitted to the level counts, would be off by up to 18 points here, because ACT scores bunch up just below the cut scores instead of spreading evenly across a level.

About the smooth curve

The bell-like curve on each chart is a truncated-normal distribution fitted to the level counts, there only to visualize the shape of the group’s scores. In Montana it plays no part in the percentile.

Cut scores

Each test has four levels: Novice, Nearing Proficiency, Proficient and Advanced. Proficient and above count as proficient.

These are from the Office of Public Instruction’s “Statewide Assessment Proficiency Levels” table, and they reproduce Montana’s own level counts from its score counts in every year. Montana set them in a 2017 standard setting (its technical report prints the ELA Advanced cut as 25 in one table; the adopted cut is 24). 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.

Limitations to keep in mind

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

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