I was recently at a presentation where the success rates for EPSRC fellowships were given by theme. The message of the talk was that Engineering fellowships were under-subscribed and so we should all be preparing our applications. But just because a theme is under-subcribed doesn’t mean that you’ve got a better chance of getting funded.

A more sensible way of thinking about the problem is by using a funnel plot. Funnel plots allow you to compare the outcomes of “random” events in organizations of different sizes. For example, you might want to compare the performance of healthcare institutions or the feedback rate of student surveys within different departments. I say “random” because, in this case, we’re assuming that the chance of getting funded can be modelled as a binomial distribution with a probability of success *p*.

The results are shown below and reinforce the EPSRC’s message, though for different reasons. The plot shows that, yes, there are fewer engineering fellowship applications than in some other themes. But more importantly, the probability of being funded is better than the average EPSRC success rate for fellowships. On the other hand, if your engineering research might be classified under the Manufacturing the Future theme, then your odds look even better there.

For more details on the method, please see this paper by Cambridge’s David Spiegelhalter. Alternatively the full data and my analysis code in R are available on Github.