What is a scale score?
All of the academic assessments in NZCER Assist are based on the use of the Rasch scale to report student achievement and progress. There are separate PAT scales for each subject. A scale score is the conversion of a raw test score to a location on a scale that has been aligned with the curriculum levels. This is possible because the questions are on the same scale, and each test groups it's questions against a specific area/range of the scale. The scale can tell the story of a student's position now and provide progress steps over several years.
Students cannot get a stanine without first getting a scale score. It is the student's scale score plus their Year Level that produces a stanine.
Scale scores in any one test are based the level of scale difficulty of the questions within that test.
- All question are located on the scale based on the knowledge and skill required to answer it. In any one test, the scale range of question difficulty can be two years plus/a full curriculum level range.
- The same scale runs throughout all tests in a subject. This means that students' scale scores can be compared directly to each other, even if students sit different tests.
- Each unit on a PAT scale represents the same amount of progress no matter where the student is located on the scale - they are 'equal interval scales'. For example, a student who increases from 20 to 30 patm units is considered to have made the same amount of progress as a student who moves from 50 to 60 patm units. This property makes the PAT scales ideal for tracking student achievement over time.
- The reliability of the scale allows schools to match the test to student ability level E.G. students in Year 6 who are well above or well below their expected level can sit different tests and yet the whole of Year 6 will be represented on the same scale. Alternatively, for subjects with adaptive testing, tests will deliver students questions tailored to their ability level and those results can also be compared as they are on the same scale.
Progress on the scale
Each PAT scale uses its own measurement unit to measure progress. For instance, the PAT Pāngarau | PAT Mathematics uses a unit called “patm” (short for PAT: Mathematics unit). Each unit on a PAT scale represents the same amount of progress no matter where the student is located on the scale - they are 'equal interval scales'. For example, a student who increases from 20 to 30 patm units is considered to have made the same amount of progress as a student who moves from 50 to 60 patm units. This property makes the PAT scales ideal for tracking student achievement over time. Students’ scale scores can be compared from test to test to show their growing levels of knowledge and skill.
Scale score progress over time
NZCER Assist provides scale benchmarks for each test subject to describe 12months of progress, i.e half a curriculum level approximately. For testing undertaken in Term 1 and Term 4 of the same year, a calculation would be required for 75% of the progress benchmark. This information is provided for individual learners, year levels, and identified cohorts using report filters.
Scale Descriptors
The progressions of the scale are detailed in the descriptors for each subject. (Maths descriptors, Reading Comp descriptors). The descriptors detail the concepts that are tested. All concepts are considered vital for successful student progression.
A sample of the PAT Pāngarau | Mathematics Descriptors
Question difficulty using the scale
The relative difficulty of every question in each test is described by its location on the scale, based on the knowledge and skill associated with the question. A student’s achievement can therefore be reported in terms of the knowledge and skill required to correctly answer questions that are located at or below the student’s own scale score location. Students are more likely to have developed the knowledge and skills described at and below their own scale location. The scale is defined so that a student whose scale score is at the same position as a particular set of questions is expected to answer correctly 50 percent of these questions, and far more than 50 percent of the questions located further down the scale.
The scale range of the questions in any one test covers a minimum of two years progression in difficulty. They are generous to include students who are just below or just above the average expectation for their year level.
Comparing achievement with national norms
Once a raw score has been converted to a scale score it becomes possible to compare a student’s achievement with the achievement of national reference samples at different year levels. A scale score of 50 patm units, for instance, represents very high achievement for a Year 4 student (stanine 9), but represents below average achievement for a student in Year 10 (stanine 4). It is important to remember that data from the reference samples were collected in March (June for S:TwE).