residuals in value-added GCSE result assessments

We are into some fairly heavy statistics here. It’s all to do with Pupil Referencing which involves comparing one set of GCSE results with another, in a way that irons out differences resulting from socio-economic or other extraneous factors.

Let’s start with the simplest example: comparing a pupil’s performance in a particular GCSE subject with their performance in other subjects. First, we add up their points score in the usual way (ie A* = 8, A = 7, through to G = 1, and X = 0). Then we calculate their average score (eg total 40 points across 8 subjects = average 5 points). Next, we subtract the pupil’s average score from their score for the particular subject. The result may be zero, + X, or - Y. This is the residual. For example, our pupil with an average score of 5, but who achieved a B (6 points) in English, has a residual for English of +1.

The next calculation might be to calculate a school’s residual for a given subject. This is the average of the individual pupils’ residuals. Then you might carry out a similar calculation to arrive at the LEA’s residual for the subject, or even the national residual for the subject. When you have all this information, you can see how an individual’s, or a subject department’s, or a school’s or even an LEA’s performance compares with others’. Clearly, positive residuals are good news.

Now, your question was about residuals in value-added GCSE result assessments. “Value-added” is, of course, a measure of how much progress a pupil (or school, or whatever) has made since the last time they were assessed. It is a fairer measure of achievement than simply saying what grades have been achieved because the pupil may have been at a high standard in the first place. To progress from 10 A* GCSEs to four A levels at grade A is a great achievement but is, arguably, less impressive than progressing from five GCSEs at grade C to three A levels at grade B.

Clearly, once you have the value-added figures for individual pupils, you can work out the residuals, as described above.

There are some limitations to this method. For example, if a school does particularly well in one or two main subjects, this will pull down the residuals for other subjects, making them appear worse than they are. And, of course, vice versa. This won’t affect comparisons within a school but it may affect comparisons between schools or with LEA or national residuals. Another limitation may apply to minority subjects. For example, if all pupils taking GCSE Music are prodigies, this will distort the residuals. Common sense should enable schools to allow for this sort of distortion.