1.3 Score Interpretation: Scaled Scores, Percentile Ranks, Stanines, NCEs & Grade Equivalents

Reading a Stanford 10 Score Report

Stanford 10 has no passing score. A report instead shows how a student performed compared with a national norm group, using several score types. Pearson's sample reports let schools choose up to five types for each subtest from Number Correct, Scaled Score, Grade Equivalent, National Percentile Rank-Stanine, National Normal Curve Equivalent and local versions of those comparisons. The Arkansas Department of Education's Stanford 10 interpretation guide explains each one; this section follows its definitions.

Number Correct and the Scaled Score

The number correct (NC), or raw score, is simply how many questions the student answered correctly. Stanford 10 does not subtract points for wrong answers, so students should answer every question. Raw scores cannot be compared across subtests, because subtests differ in length and difficulty: 20 correct in Reading Comprehension does not mean the same thing as 20 correct in Mathematics Problem Solving.

The scaled score (SS) fixes this within a subject. Scaled scores are designed to represent roughly equal units on a continuous scale, and each subtest's scale spans all of its levels. The Arkansas guide notes, for example, that Reading Comprehension is linked across 11 test levels from Primary 1 through TASK 3. That is why scaled scores are the best Stanford 10 score for tracking growth in one subject over time, even when a student moves from one test level to the next.

Two limits matter:

• Scaled scores are not comparable across subtests. A Reading Comprehension scaled score and a Spelling scaled score are on different scales even when the numbers look similar.
• Scaled scores are not reported for battery totals. In a sample Intermediate 2 report published by Seton Testing Services, subtest scaled scores range from 664 to 748, while the Total Battery shows "N/A" for scaled score.

National Percentile Rank (PR)

A percentile rank ranges from 1 to 99, with 50 as average. It shows the percentage of students in the norm group who scored at or below the student's score, among students in the same grade tested at a comparable time of year. A PR of 75 means the student did as well as or better than 75% of the comparison group.

A percentile rank is not a percent correct. A PR of 42 does not mean the student answered 42% of the questions correctly; it is a rank. Percentile ranks are also not equal units: because most students score near the middle, a small change in raw score near the 50th percentile can move the PR several points, while the same change near the top moves it less. For that reason, percentile ranks should not be averaged.

Reports state which norms were used. Pearson publishes fall and spring grade-based norms, and reports print labels such as "2018 National Spring" or "2018 National Midyear." Testing providers assign the season by test date. For example, one homeschool provider treats August-December as fall, January-March as midyear and April-July as spring.

Stanines

Stanines ("standard nines") divide the normal curve into nine bands with a mean of 5 and a standard deviation of 2. They are broad enough that small, meaningless fluctuations do not change them, and unlike percentile ranks they represent roughly equal steps of achievement.

Reports usually print percentile rank and stanine together as PR-S, for example "73-6" for the 73rd percentile and stanine 6.

Normal Curve Equivalents (NCE)

The normal curve equivalent is a normalized standard score with a mean of 50 and a standard deviation of 21.06:

$$\text{NCE} = 50 + 21.06z$$

NCEs run from 1 to 99 and match percentile ranks at 1, 50 and 99, but they are equal-interval, so they can be averaged across a class or used in research. The Arkansas conversion table shows, for example, that PR 10 = NCE 23.0 and PR 90 = NCE 77.0. NCEs were developed for evaluating federally funded Title I programs, which is why districts still use them for group averages.

Grade Equivalents (GE)

The score key printed with Stanford 10 reports (reproduced in Seton Testing Services' school information file) defines the grade equivalent as the "grade placement at which the number correct (raw score) is average." A GE of 6.2 is read as sixth grade, second month.

The common mistake is to treat a high GE as proof of higher-grade mastery. Suppose a third grader takes Primary 3 in the spring and earns a mathematics GE of 6.2. The student was not tested on sixth-grade content; the GE means that a typical student in the second month of sixth grade would be expected to get about that raw score on the same third-grade-level test. The correct reading is "very strong command of the content on this test," not "ready for sixth-grade mathematics." Very high grade equivalents can appear as PHS (Post High School) instead of a number.

Percentile Bands and Lexile Measures

National Grade Percentile Bands appear as bars on many reports. Each band spans plus or minus one standard error of measurement, showing the range in which the student's true score probably falls. Pearson's guidance is that bands which do not overlap usually indicate a real difference between subjects; overlapping bands usually do not.

Students who take the full-length Reading Comprehension subtest at Primary 1 through TASK 3 can also receive a Lexile measure, a reading-level score used to match students with books. The Seton sample Intermediate 2 report, for example, shows a Lexile measure of 1290L.