University offer rates for candidates from different ethnic categories

Abstract

Previous research suggested that candidates from some black and minority ethnic groups were less likely to receive an offer of a place from an ‘old’ university. These findings were disputed in a re-analysis carried out for HEFCE which found that only Pakistani candidates were significantly less likely to receive offers (from both ‘old’ and ‘new’ universities). In this paper we return to the question of ethnic differences in university offer rates, examining UCAS admissions data for 2008. We use a cross-classified multi-level modelling approach to predict the probability that applications from candidates from different ethnic groups will receive an offer. Controlling for variables seeking to capture the academic quality of applications we find significant differences between offer rates for different ethnic groups. Significantly lower offer rates remained for the main ethnic groups when social characteristics were also taken into account in the model (social class background, gender and school type). However, offer rates for candidates from mixed ethnic groups were not significantly different from those for white British candidates. Our analysis did not find evidence of differences in offer rates from higher and lower status institutions for black and minority ethnic candidates relative to white British applicants.

Keywords:

• higher education
• ethnicity
• offer
• quantitative

Acknowledgements

We would like to thank Professor Harvey Goldstein for his methodological expertise and support throughout this project and for comments on earlier drafts of this paper. The authors are grateful to the Nuffield Foundation for funding this research project. The Nuffield Foundation is an endowed charitable trust that aims to improve social well-being in the widest sense. It funds research and innovation in education and social policy and also works to build capacity in education, science and social science research. The Nuffield Foundation has funded this project, but the views expressed are those of the authors and not necessarily those of the Foundation. UCAS provided the data for this study though similarly UCAS cannot accept responsibility for any inferences or conclusions derived from the data by third parties—nevertheless, thanks to Kim Dukes of UCAS for helpful comments on an earlier draft of this paper. Errors and omissions are thus the responsibility of the authors.

Notes

1. The use of actual rather than predicted A level grades would be particularly problematic if candidates from black and minority ethnic groups were more likely to have overly pessimistic predictions compared with white candidates. However this is not the case (Everitt & Papageorgiou, 2011).

2. Coe et al. (2008) ranked subjects according to their average difficulty score calculated through five methods including Rasch models, subject pairs analysis and reference tests. Subject rankings across the different methods showed substantial agreement.

3. Shiner and Modood (2002) overcame this problem by randomly selecting one application for each applicant included in the dataset.

4. In short, in a multi-level model, unexplained variance is clustered at higher levels. In the case of our binary logistic model, the model could predict a high probability that a particular application would receive an offer. For example, this could be the case for an application with a relatively good academic record—yet in fact the application did not receive an offer. Such a case would have a large negative residual (the difference between the actual outcome, 0, and the predicted probability of the application receiving an offer). For some courses there may be a large number of such applications—that is, many good quality applications did not lead to offers being made. In a multi-level model such unexplained variation is partitioned between the different levels of the model. Thus, in this example, the course would have a negative residual indicating that, taking into account the characteristics of applications to the course, a smaller number of applications received offers than was predicted by the independent variables included in the model. That is, the course level residual captures the unexplained course level probability of receiving an offer. Similarly, unexplained variation clustered at candidate level captures the unexplained candidate level probability of receiving an offer.

5. Formally, using the general notation for multilevel models (Goldstein, 2011), the model may be represented as:

6. Subject dummy variables were particularly valuable in producing more normally distributed course level residuals. One of the model assumptions is that higher level residuals are normally distributed.

7. This interpretation is of course somewhat speculative and could not be tested using the data available.

8. In order to check the robustness of the findings compared with the approach of Gittoes and Thompson (2005), measures of course popularity were added to the model as course level predictor variables. In each case the model fit and the substantive results relating to differences between ethnic groups remained the same. In addition, the model was run on a dataset excluding applications to medicine and dentistry but once again the conclusions remained substantively the same.

9. For each ethnic group a substantial portion of candidates’ social class was recorded as ‘not known’.

10. The process of converting estimates of log odds into probabilities is more complex in multi-level logistic regression than in single level models. In a single level logistic regression, predicted probabilities are often computed for exemplar individuals, illustrating the fact that a fixed effect implies a non-linear effect on a probability scale and that different combinations of fixed effects imply different non-linear functions. In a multi-level model higher level residuals have a similar non-linear effect on a probability scale. The effect of a predictor variable on the predicted probability of receiving an offer is unique to each higher level cluster and the effects for predictor variables are estimated taking into account the clustering of that residual variation. Effects for predictor variables are consequently said to have a ‘cluster-specific’ interpretation. However, a ‘population averaged’ effect may be obtained by taking the mean probability over a simulated set of higher level residual values (see Steele, 2008).