Data: A single set of class marks
In this release of Assessment CAST, we will look at a single set of class marks in isolation.
Interesting information can also be obtained from comparisons of different sets of marks (different classes or different years) or by looking at a series of assessments from the same students. However graphical and numerical methods for these data structures are more complicated, so it is best to start with the simplest scenario — a single set of marks.
Causes of variability
An important characteristic of marks is variability. Variability arises from several sources.
- Variability between classes. This could be caused by differences between teachers or differences between the backgrounds of the students (especially if the classes are from different areas of the town with different socio-economic characteristics).
- Variability between students. Some students are more intelligent than others or have simply understood the material that is being tested better. This is usually the major cause of variability of marks within a class.
- Test-to-test variability. Even if given two equivalent tests, students will not usually perform identically. This may be caused by guessing some answers or other chance features of the test that the student knows or does not know.
It is important to recognise these three causes of variability.
Variability between classes
This would be of most interest to a principal, head of department or board of trustees. Does one teacher's class perform worse than the classes of others?
Variability between students
This is of most interest to a teacher. This component of variability tells which students are performing best.
Test-to-test variability
This aspect of variability is just a nuisance since it tells you nothing about how well a student understands the material. The better designed the test, the lower the randomness in the results that are obtained. In general, short tests tend to have more variable results — longer tests tend to give a more consistent measure of ability.
Distinguishing causes of variability
Unfortunately it is impossible to distinguish these three sources of variability from a single set of class marks. If sets of marks are available from different classes, or we have different assessments from the same class, it is possible to get some handle on the different sources of variability. However, from a single set of marks, we must simply be aware of the issue when interpreting the data.