Small Numbers and Strong Statements: Analysing offers to black students at Oxford

By Jack Blundell

Under immense pressure over transparency, Oxford University last month released its latest and most-detailed-ever tranche of undergraduate admissions data. These statistics have been heavily drawn on in a series of articles and statements, notably by the MP for Tottenham David Lammy (Link) who focuses on the representation of black British students. The goal of this post is to help inform this particular debate by analysing relevant features of this treasure-trove of data, pointing out where we can infer true differences from patterns in the data. Unless otherwise noted, the source of all analyses below is Oxford’s May 2018 Annual Admissions Statistical Report and the associated datasets released.

To summarise my discussion, I find that:

  • Among Oxford offer holders, black students are under-represented relative to the overall population but over-represented once we restrict to those achieving the top school grades.
  • Out of those who apply, black students have a significantly lower probability of receiving an offer.
  • Just under half of this gap can be attributed to black students being more likely to apply to more-competitive subjects than other applicants.
  • The remainder of the gap is due to lower probabilities of application success within courses.

Firstly, to set the scene and before diving into the detail, we ask whether there are fewer black students receiving offers than we would expect given the population numbers. As pointed out in the media the raw numbers are very low, with many constituent colleges of Oxford not admitting a single black British student. However, as with any discussion of minority representation it is difficult to have an intuition of how low these numbers really are without looking at the population figures. Focusing on the latest data, black students are actually slightly over-represented relative their proportion among high-scoring pupils in England and Wales. According to the most recent year of data available, 1.8% of pupils achieving AAA or above at A-level were black, relative to Oxford’s 2.2% of offer holders. But how about the broader population? My own calculations using data from the England and Wales 2011 census suggest that among 17-20 year olds, approximately 4.5% of the population is black. Relative to the total population of people of university age, black students are under-represented at Oxford. Therefore it really depends whether you consider the general age-adjusted population or just those with the required grades. It should be noted that the 2.2% figure above should be taken with caution as 3.3% of offer holders in the Oxford data who do not declare their ethnicity are included in the denominator. In the work below, I continue include these with ‘all other’ students.

Secondly, by looking at overall counts of applicants and offers, we can test whether black applicants are less likely to be given an offer than others. For this and all calculations that follow, I aggregate the previous ten years of data and look at all applicants irrespective of A-level grades. In total, these years saw 2,547 black UK-domiciled students apply to Oxford and 398 given offers, corresponding to an offer success rate of just under 16%. This is well below the average success rate of 25% for all other applicants over the same period. Moreover this difference is significant in a statistical sense meaning that we can reject the hypothesis that the offer rates are the same. The evidence here is fairly clear, black applicants to Oxford are less likely to receive offers than other applicants. For the remainder of this post I focus on subject selection, a single aspect of application behaviour which has been suggested as a potential cause of this disparity.

Previous commentators have noted that ethnic minorities are more likely to apply for “professional” subjects such as Medicine, Law and Economics & Management (Link ). Do we see this among black students in the Oxford data? In the graph below, each point represents a subject. On the vertical axis we have the proportion of black applicants, and on the horizontal we have the proportion of all other applicants. The diagonal line illustrates where all points would fall if application rates were the same for both groups. I have highlighted some subjects of interest, and placed subjects into three broad groups. This shows that black applicants are more than twice as likely to apply for Medicine and Law than other students. In fact, these two subjects make up almost half of all applications from black students over the ten-year period. Other students apply more broadly, with particularly strong differences for arts and humanities subjects. I find that these differences in subject selection are highly statistically significant.

Figure 1


While this is interesting in its own right, could this have something to do with the low offer rates we saw on aggregate among black students? If black students disproportionately apply for competitive subjects, even if rates where identical across ethnicities we would see lower total offer rates for this group. The graph below plots the difference between black and all other application rates against the total offer rate for a set of courses. Courses positioned above 0 on the vertical axis are more popular among black applicants. The further to the right, the less competitive a course is.

Figure 2


Here we see that the courses which are disproportionately applied to by black students are indeed the most competitive. The three professional courses are among the lowest in terms of offer rates. Courses which have higher offer rates such as Music, Classics and Chemistry tend to have fewer black applicants.

To round up my analysis I calculate the proportion of the difference in offer rates between black and non-black applications which can be attributed to different course selection.  This is purely a statistical exercise and not a policy experiment, nonetheless it is instructive for understanding the importance of the above differences in course choice. To decompose the difference, I ask what happens to aggregate offer rates of black applicants if application subject patterns were identical to those of non-black students. I find that the offer rate under the thought experiment of equal application proportions would be 20%, up from the actual observed rate of 15.6%. This is still below the 24.8% offer rate experienced by non-black students. According to this back-of-the-envelope calculation then, just under half the difference in offer rates between black and non-black students can be attributed to subject choice. The remaining half can be attributed to lower application success within courses. Course selection, while important, cannot fully explain differences in offer rates.

As I hope to have illustrated here, the release of Oxford’s detailed data represents a boon for researchers interested in questions of elite university access. I have shown that representation depends on what you consider to be the relevant population, and that differences in course choice can explain almost half of the lower application success rates for black Oxford applicants. This second issue has been recognized by Oxford, who have taken steps to open up some of their less-competitive courses to pupils from broader backgrounds. Classics for example is now in theory available to the vast majority of us who have not studied ancient languages at school. Nonetheless, more emphasis should be placed both in the media and among policymakers on this particularly important aspect for understanding minority representation at Oxford.



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