The effect of subject choice on the apparent relative difficulty of different subjects

Abstract

Periodically there is interest in whether some GCSE and A level subjects are more 'difficult' than others. Because students choose which subjects they take from a large pool of possible subjects, the matrix of data to be analysed contains a large amount of non-random missing data - the grades of students in subjects that they did not take. This makes the calculation of statistical measures of relative subject difficulty somewhat problematic. It is also likely to make subjects that measure something different to the majority of other subjects appear easier. These two claims are illustrated in this article with a simple example using simulated data.