Scaled Study Score Interpolation in the Study Score Archive

As I previously mentioned, this year’s release of the Study Score Archive will feature estimated scaled scores alongside raw scores. Helpfully, VTAC provides scaling data in the annual Scaling Report, but correspondences between raw scores and scaled scores for each subject are provided only for scores that are greater than 20 and are multiples of 5 (that is, for the raw scores of 20, 25, 30, 35, 40, 45 and 50). As such, it is necessary to somehow estimate the correspondences for the remaining raw scores. This process in general is called interpolation.

A simple method of interpolation is linear interpolation. This is the approach used by Daniel15’s VCE ATAR Calculator, and it is the approach that I will be using in the 2010 release of the Study Score Archive. Other methods might produce more accurate results, but they are harder to implement and without more data it’s not possible to verify which method of interpolation produces the best results.

To illustrate the process, let’s take a look at the scaling of Further Mathematics in 2010 (for scores of 40 and above).

From the Scaling Report, we can see that 40 scales to 38, 45 scales to 44 and 50 scales to 50.

The difference between 44 and 38 is 6. So, the scaled score needs to increase by 6 points over 5 raw score points. We divide 6 by 5, giving 1.2, which is the increase for each raw score:

38 + (0x1.2) = 38
38 + (1×1.2) = 39.2
38 + (2×1.2) = 40.4
38 + (3×1.2) = 41.6
38 + (4×1.2) = 42.8
38 + (5×1.2) = 44

Repeating the process for the scores between 45 and 50, the difference is again 1.2.

44 + (0x1.2) = 44
44 + (1×1.2) = 45.2
44 + (2×1.2) = 46.4
44 + (3×1.2) = 47.6
44 + (4×1.2) = 48.8
44 + (5×1.2) = 50

So, the raw to scaled score correspondences are:

If you have any thoughts as to what might be a better type of interpolation for this sort of data, I’m keen to hear them.