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How we estimate percentiles: Arizona 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 yearly test-results files of the Arizona Department of Education, for the high-school tests Arizona has given since 2018: the ACT, which juniors take at school (its ELA and Math scores, 2022 to 2026), the AzSCI science test in grade 11 (2022 to 2025), and in 2018 and 2019 the AzMERIT end-of-course tests (ELA 9, ELA 10, ELA 11, Algebra I, Geometry and Algebra II). These files report, for each school, school district or charter holder, county and the state, and for each test and year:

Hidden numbers. To protect small groups, Arizona hides any number that could reveal a group of 10 or fewer students, so many schools show only some of their four levels. When a school shows its passing rate and some of the levels, the missing ones are worked out from what is shown: the four levels add up to 100%, and Proficient plus Highly Proficient equals the passing rate. When both levels on one side of the passing line are hidden, they are split the way schools with the same passing rate split them in that year’s file, among the schools that show all four. Where the file hides the passing rate too, we use the rate from Arizona’s school report card site when it has one. We tested this on schools whose four levels are all shown, hiding their numbers the way real schools’ numbers are hidden: the filled-in levels land within about 1 to 2 percentage points of the real ones on average, and about 2 to 4 points when only the passing rate is known. A school that shows only its number of students, or nothing at all, does not appear.

2022 is percentages only. For spring 2022 Arizona’s file hides the number of students tested for almost every school while still showing the percentages, so 2022 results show the share of students at each level rather than student counts.

Who is counted

ACT ELA and ACT Math are Arizona’s high-school test since spring 2022: every public school student in the grade 11 class takes the ACT with Writing at school in the spring, and ACT ELA is the average of the English, Reading and Writing scores. Science is the AzSCI science test, taken by the same grade 11 class each spring (2022 to 2025). The 2018 and 2019 tests are AzMERIT end-of-course tests: ELA 9, 10 and 11 at the end of each year’s English course, and Algebra I, Geometry and Algebra II at the end of each course. They count every test given that school year (summer, fall and spring), with each student’s highest score, and the math courses include middle-school students who took the course early (about one Algebra I tester in five was in grade 8), counted at their middle school. In 2019 about 12,000 juniors at 54 schools took the ACT or SAT in place of the grade 11 tests, so they are not in the 2019 grade 11 results. Every result counts students enrolled in an Arizona public school (district or charter), at the school where they tested. For 2022 Arizona published only the percentage of students at each level, not how many students tested, so 2022 results are shown as percentages.

The ACT and grade 11 science are taken by the whole junior class (about 79,000 students for ACT ELA in 2026), so a percentile compares a score with Arizona public school juniors who took it at school that spring. It is not the same as the national rank on an ACT score report, which compares with test takers across the country. Algebra I, Geometry and Algebra II are course tests, taken by whoever is in the course that year, so a percentile compares a score with that year’s students in the course, not with every student of the same age.

The statewide row is Arizona’s own statewide total for public schools. Since 2023 Arizona’s county totals add up to slightly more than its statewide total (by less than 1%), most likely because a student who tested at more than one school is counted at each one but only once statewide.

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

Arizona publishes the exact scale-score range for each performance level (e.g. for ACT Math, “Partially Proficient” is 16-18, and for Algebra I, “Proficient” is 3681-3719). 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 all sit in one or two levels, the counts can't say how spread out their scores are. A curve that comes out too narrow is 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. About one school result in twenty here gets a wide default curve instead, which places a score inside its level close to an even spread. Most of these are Algebra I and Geometry results at middle schools, where nearly every student who takes the course early scores Proficient or above.

ACT scores are whole numbers from 1 to 36, and some levels span only a few of them (ACT Math “Partially Proficient” is 16 to 18). So a one-point change in an ACT score can move the percentile noticeably, and the curve is a smoothed picture of a score scale that really moves in steps.

Why estimates are still useful: the share of students in each performance level comes from Arizona’s own numbers for each group (worked out from the published parts where some are hidden), and so does the number tested. The average score shown is estimated from how students split across the levels, 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.

Cut scores

Every test here has four levels: Minimally Proficient, Partially Proficient, Proficient and Highly Proficient. Proficient and Highly Proficient count as passing.

The ACT reports each score on a 1-36 scale. Arizona’s State Board of Education set its levels in July 2022: for ACT ELA, 1-14, 15-18, 19-24 and 25-36; for ACT Math, 1-15, 16-18, 19-24 and 25-36. These come from the Arizona Department of Education’s “ACT Cut Scores” document, which its ACT page has linked every year since and still links after the spring 2026 results. Arizona applies the same table to the updated ACT given from spring 2026. The ACT ELA score is the average of the English, Reading and Writing scores, so a student needs the Writing test to have one.

AzSCI grade 11 science runs from 1200 to 1500, with Proficient from 1350, from the State Board’s July 2022 “AzSCI Cut Scores” document; each year’s AzSCI technical report (2022 to 2025) prints the same table.

The 2018 and 2019 AzMERIT ranges come from each year’s AzMERIT technical report, which prints every test’s ranges, lowest and highest possible scores included; both years use the same table. Arizona revised its high-school cut scores in August 2019 for the next version of the test (a grade 10 test, first given in 2021), after these results. 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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