What does the chart show?
The chart shows the probability of achieving a given grade within ten GCSE subjects. The black bars show the distribution of grades for all candidates in the sample. When a selection is made, the purple bars in the dependent subjects indicate the grade distribution for the candidates achieving this result. For example, 79.3% of candidates achieving an A* in Physics also received an A* in Mathematics.
The data come from the 2016 National Pupil Database, which contains the details of 588,973 GCSE candidates in 86 unique subjects. Approximately 24% of these candidates took ten or more subjects. We counted the number of candidates who took each possible combination of ten subjects; the subjects displayed here were the most common and were taken by 2664 candidates.
The structure of the network was determined using a Bayesian network (via the bnlearn R package). This technique identifies the conditional dependencies between subjects. In the example above, we can say that one's result in Mathematics is conditionally dependent on the result achieved in Physics; however the result in Mathematics is independent of a candidate's result in French.
Why is the chart interesting?
The structure of the network illustrates that Biology is a bridging subject between the sciences and humanities. Success in Biology requires skills that lead to strong performance in other sciences, but this effect is attenuated as one moves towards subjects with greater mathematical complexity (i.e. the dependent subjects are, in order, Chemistry, Physics, and Mathematics). However Biology also requires candidates to recall large amounts of information and present it clearly in short answer or essay responses, a trait shared with many humanities subjects.
The chart also reveals some interesting predictions. For example, if a candidate achieved an A* in History, then their probability of achieving an A or A* in English Language would be very similar (46.3% and 42.9% respectively). However they would have a much higher probability of achieving an A* in Religious Studies (64.8% versus 27.8% for an A). At the other extreme, a grade of less than D in Physics means that a candidate still has a 45% chance of getting a C or higher in Mathematics, an important achievement for accessing many forms of further education.