What is a scale score?

The NZCER Assist scale scores report student achievement. There are separate PAT scales for each assessment. A scale score represents the conversion of a raw test score to a location on a described scale designed to measure progress over several year levels.  The PAT Pāngarau | PAT Mathematics scale, along with a sample of descriptors from different content categories, is shown below.


Scale scores take into account the difficulty of the questions in the tests. All question difficulties can also be located on the scale. This means that scale scores can be compared directly, regardless of which test in a series was originally administered. This allows schools to match the test to student ability level if appropriate. Alternatively, the adaptive test will deliver students questions tailored to their ability level.


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 (this is the equal interval property described above). 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. 


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.


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).


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.