What is a scale score?

The 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. 
  • The questions the students answer are placed on the same scale. Each test groups the questions against a specific area/range of the scale to align with curriculum expectations.  
  • 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 the scale scores of students in the same year level can be compared directly to each other, even if students sit different tests. 
  • The scale is an 'equal interval scale' which means that it takes an equal amount of knowledge and skill to move from one unit to the next. EG: 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 and cohort progress.
  •  Students’ scale scores can be compared from test to test to show their growing levels of knowledge and skill.
  • The margin of error associated with the student’s score is to show that  if the test was repeated, we would expect the student to score in the range indicated by the highlighting, about two thirds of the time. Students who achieve very highly or very poorly on a test will have a larger error associated with their score and it is less reliable. The student has clearly been given the wrong test and, if maths, the ākonga would benefit from sitting the adaptive test next time.


Progress on the scale

Each PAT scale uses its own measurement unit to show position and measure progress.

  • PAT Pāngarau | PAT Mathematics uses a unit called “patm” (short for PAT: Mathematics unit). 
  • Pat Pānui | Pat Reading Comp uses patc
  • PAT Tuhutuhi | PAT Writing  uses patw



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.


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. 
  • Each test defines a range of scaled questions. Students whose achievement  level is within the scale range  of questions is expected to answer correctly 50% of these questions, most below their own scale score line on the individual report.
  • The adaptive test presents questions closer to the students level as it adjusts each question and students are expected to answer 60% correctly.


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
Using 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).