DorothyIn order to get a perfect assessment method, are we at risk of developing systems that are ever more complex and time-consuming? Dorothy Bishop looks at the differences between readily available measures to award research funding and the highly complicated RAE formula. An evaluation system need not be perfect – it just needs to be ‘good enough’ to provide a basis for disbursement of funds that can be seen to be both transparent and fair, and which does not lend itself readily to gaming.

The UK’s Research Excellence Framework (REF) is like a walrus: it is huge, cumbersome and has a very long gestation period. Most universities started preparing in earnest for the REF early in 2011, with submissions being made late in 2013. Results will be announced in late December, just in time to cheer up our seasonal festivities.

Like many others, I have moaned about the costs of the REF: not just in money, but also the time spent by university staff, who could be more cheerfully and productively engaged in academic activities. The walrus needs feeding copious amounts of data: research outputs must be carefully selected and then graded in terms of research quality. Over the summer, those dedicated souls who sit on REF panels were required to read and evaluate several hundred papers. Come December, the walrus digestive system will have condensed the concerted ponderings of some of the best academic minds in the UK into a handful of rankings.

walrusImage credit: John Tenniel‘s illustration for Lewis Carroll‘s poem “The Walrus and the Carpenter” (Wikipedia, Public Domain)

But is there a viable alternative? Last week I attended a fascinating workshop on the use of metrics in research. I had earlier submitted comments to an independent review of the role of metrics in research assessment from the Higher Education Funding Council for England (HEFCE), arguing that we need to consider cost-effectiveness when developing assessment methods. The current systems of evaluation have grown ever more complex and expensive, without anyone considering whether the associated improvements justified the increasing costs. My view is that an evaluation system need not be perfect – it just needs to be ‘good enough’ to provide a basis for disbursement of funds that can be seen to be both transparent and fair, and which does not lend itself readily to gaming.

Is there an alternative?

When I started preparing my presentation, I had intended to talk just about the use of measures of citations to rank departments, using analysis done for an earlier blogpost, as well as results from this paper by Mryglod et al. Both sources indicated that, at least in sciences, the ultimate quality-related research (QR) funding allocation for a department was highly correlated with a department-based measure of citations. So I planned to make the case that if we used a citation-based metric (which can be computed by a single person in a few hours) we could achieve much the same result as the full REF process for evaluating outputs, which takes many months and involves hundreds of people. However, in pondering the data, I then realised that there was an even better predictor of QR funding per department: simply the number of staff entered into the REF process.

Before presenting the analysis, I need to backtrack to just explain the measures I am using, as this can get quite confusing. HEFCE deserves an accolade for its website, where all the relevant data can be found. My analyses were based on the 2008 Research Assessment Exercise (RAE).  In what follows I used a file called QR funding and research volume broken down by institution and subject, which is downloadable here. This contains details of funding for each institution and subject for 2009-2010. I am sure the calculations I present here have been done much better by others and I hope they will not by shy to inform me if there are mistakes in my working.

The variables of interest are:

  • The percentages of research falling in each star band in the RAE. From this, one can compute an average quality rating, by multiplying 4* by 7, 3* by 3, and 2* by 1 and adding these, and dividing the total by 100. Note that this figure is independent of department size and can be treated as an estimate of the average quality of a researcher in that department and subject.
  • The number of full-time equivalent research-active staff entered for the RAE. This is labelled as the ‘model volume number’, but I will call it Nstaff. (In fact, the numbers given in the 2009-2010 spreadsheet are slightly different from those used in the computation, for reasons I am not clear about, but I have used the correct numbers, i.e. those in HEFCE tables from RAE2008).
  • The departmental quality rating: this is average quality rating x Nstaff. (Labelled as “model quality-weighted volume” in the file). This is summed across all departments in a discipline to give a total subject quality rating (labelled as “total quality-weighted volume for whole unit of assessment”).
  • The overall funds available for the subject are listed as “Model total QR quanta for whole unit of assessment (£)”. I have not been able to establish how this number is derived, but I assume it has to do with the size and cost of the subject, and the amount of funding available from government.
  • QR (quality-related) funding is then derived by dividing the departmental quality rating by the total subject quality rating and multiplying by overall funds. This gives the sum of QR money allocated by HEFCE to that department for that year, which in 2009 ranged from just over £2K (Coventry University, Psychology) to over £12 million (UCL, Hospital-based clinical subjects). The total QR allocation in 2009-2010 for all disciplines was just over £1 billion.
  • The departmental H-index is taken from my previous blogpost. It is derived by doing a Web of Knowledge search for articles from the departmental address, and then computing the H-index in the usual way. Note that this does not involve identifying individual scientists.

Readers who are still with me may have noticed that we’d expect QR funding for a subject to be correlated with Nstaff, because Nstaff features in the formula for computing QR funding. And this makes sense, because departments with more research staff require greater levels of funding. A key question is just how much difference does it make to the QR allocation if one includes the quality ratings from the RAE in the formula.

Size-related funding

To check this out, I computed an alternative metric, size-related funding, which multiplies the overall funds by the proportion of Nstaff in the department relative to total staff in that subject across all departments. So if across all departments in the subject there are 100 staff, a department with 10 staff would get .1 of the overall funds for the subject.

Table 1 shows: the correlation between Nstaff and QR funding (r QR/Nstaff) and how much a department would typically gain or lose if size-related funding were adopted, expressing the absolute difference as a percentage of QR funding (± % diff).

Table 1: Mean number of staff and QR funding by subject, with correlation between QR and N staff, and mean difference between QR funding and size-related funding

SubjectMean NstaffMean QR £Kr QR/ Nstaff± % diff
Cardiovascular Medicine26.37940.90623
Cancer Studies38.11,3300.93913
Infection and Immunology43.71,5060.97122
Other Hospital Based Clinical Subjects58.21,9450.98623
Other Laboratory Based Clinical Subjects21.86850.95241
Epidemiology and Public Health26.69490.98625
Health Services Research21.96590.924
Primary Care & Community Based Clinical 10.43700.7929
Psychiatry, Neuroscience & Clinical Psychology46.71,4020.98715
Nursing and Midwifery184870.9332
Allied Health Professions and Studies20.44240.88436
Biological Sciences45.11,6490.97819
Pre-clinical and Human Biological Sciences49.41,9440.88718
Agriculture, Veterinary and Food Science33.29990.97621
Earth Systems and Environmental Sciences28.61,1280.97114
Pure Mathematics18.44890.95724
Applied Mathematics206140.98819
Statistics and Operational Research12.64060.95319
Computer Science and Informatics22.97690.95426
Electrical and Electronic Engineering23.88920.98217
General Engineering; Mineral/Mining Engineering28.91,0730.95830
Chemical Engineering26.61,1620.96815
Civil Engineering23.21,0050.9619
Mech., Aeronautical, Manufacturing Engineering35.71,3700.98714
Metallurgy and Materials21.18070.94824
Architecture and the Built Environment18.74360.96123
Town and Country Planning15.13060.91127
Geography and Environmental Studies22.85050.96921
Economics and Econometrics25.75810.96820
Accounting and Finance11.71560.98219
Business and Management Studies38.76300.96427
Library and Information Management16.32440.93526
Politics and International Studies22.43330.95531
Social Work and Social Policy & Administration19.13240.94426
Development Studies21.73680.93625
Sports-Related Studies13.52310.95237
American Studies and Anglophone Area Studies10.91910.98811
Middle Eastern and African Studies17.73930.97817
Asian Studies15.92580.93826
European Studies20.12530.78730
Russian, Slavonic and East European Languages8.71380.97322
German, Dutch and Scandinavian Languages8.41290.96617
Iberian and Latin American Languages9.11560.93717
Celtic Studies0328
English Language and Literature20.93740.98226
Classics, Ancient History, Byzantine and Modern Greek Studies19.43640.99222
Theology, Divinity and Religious Studies11.41740.95832
Art and Design22.74190.95537
History of Art, Architecture and Design10.72130.9618
Drama, Dance and Performing Arts9.82210.86436
Communication, Cultural and Media Studies11.91950.8629


Correlations between Nstaff and QR funding are very high –above .9. Nevertheless, this analysis shows that, as is evident in Table 1, if we substituted size-related funding for QR funding, the amounts gained or lost by individual departments can be substantial. In some subjects, though, mainly in the Humanities, where overall QR allocations are anyhow quite modest, the difference between size-related and QR funding is not large in absolute terms. In such cases, it might be rational to allocate funds solely by Nstaff and ignore quality ratings.  The advantage would be an enormous saving in time – one could bypass the RAE or REF entirely. This might be a reasonable option if the amount of expenditure on the RAE/REF by the department exceeds any potential gain from inclusion of quality ratings.

Is the departmental H-index useful?

If we assume that the goal is to have a system that approximates the outcomes of the RAE (and I’ll come back to that later) then for most subjects you need something more than Nstaff. The issue then is whether an easily computed department-based metric such as the H-index or total citations could add further predictive power. I looked at the figures for two subjects where I had computed the departmental H-index: Psychology and Physics.  As it happens, Physics is an extreme case: the correlation between Nstaff and QR funding was .994. Adding an H-index does not improve prediction because there is virtually no variance left to explain. As can be seen from Table 1, Physics is a case where use of size-related funding might be justified, given that the difference between size-related and QR funding averages out at only 8%.

For Psychology, adding the H-index to the regression explains a small but significant 6.2% of additional variance, with the correlation increasing to .95.

But how much difference would it make in practice if we were to use these readily available measures to award funding instead of the RAE formula? The answer is more than you might think, and this is because the range in award size is so very large that even a small departure from perfect prediction can translate into a lot of money.

Table 2 shows the different levels of funding that departments would accrue depending on how the funding formula is computed. The full table is too large and complex to show here, so I’ll just show every 8th institution. As well as comparing alternative size-related and H-index-based (QRH) metrics with the RAE funding formula (QR0137), I have looked at how things change if the funding formula is tweaked: either to give more linear weighting to the different star categories (QR1234), or to give more extreme reward for the highest 4* category (QR0039) – something which is rumoured to be a preferred method for REF2014. In addition, I have devised a metric that has some parallels with the RAE metric, based on the residual of the H-index after removing effect of departmental size. This could be used as an index of quality that is independent of size; it correlates with r = .87 with the RAE average quality rating. To get an alternative QR estimate, it was substituted for the average quality rating in the funding formula to give the Size.Hres measure.

Table 2: Funding results in £K from different metrics for seven Psychology departments representing different levels of QR funding



To avoid invidious comparisons, I have not labelled the departments, though anyone who is curious about their identity could discover them quite readily. The two columns that use the H-index tend to give similar results, and are closer to a QR funding based that treats the four star ratings as equal points on a scale (QR1234). It is also apparent that a move to QR0039 (where most reward is given for 4* research and none for 1* or 2*) will increase the share of funds to those institutions who are already doing well, and decrease it for those who already have poorer income under the current system. One can also see that some of the Universities at the lower end of the table – all of them post 1992 universities – seem disadvantaged by the RAE metric, in that the funding they received seems low relative to both their size and the H-index.

The quest for a fair solution

So what is a fair solution? Here, of course, lies the problem. There is no gold standard. There has been a lot of discussion about whether we should use metrics, but much less discussion of what we are hoping to achieve with a funding allocation. How about the idea that we could allocate funds simply on the basis of the number of research-active staff? In a straw poll I’ve taken, two concerns are paramount.

First, there is a widely held view that we should give maximum rewards to those with highest quality research, because this will help them maintain their high standing, and incentivise others to do well. This is coupled with a view that we should not be rewarding those who don’t perform. But how extreme do we want this concentration of funding to be? I’ve expressed concerns before that too much concentration in a few elite institutions is not good for UK academia, and that we should be thinking about helping middle-ranking institution become elite, rather than focusing all our attention on those who have already achieved that status. The calculations from RAE in Table 2 show how a tweaking of the funding formula to give higher weighting to 4* research will take money from the poorer institutions and give it to the richer ones: it would be good to see some discussion of the rationale for this approach.

The second source of worry is the potential for gaming. What is to stop a department from entering all their staff, or boosting numbers by taking on extra staff? The first point could be dealt with by having objective criteria for inclusion, such as some minimal number of first- or last-authored publications in the reporting period.  The second strategy would be a risky one, since the institution would have to provide salaries and facilities for the additional staff, and this would only be cost-effective if the QR allocation would cover it. Of course, a really cynical gaming strategy would be to hire people briefly for the REF and then fire them once it is over. However, if funding were simply a function of number of research-active staff, it would be easy to do an assessment annually, to deter such short-term strategies.

How about the departmental H-index? I have shown that it not only is a fairly good predictor of RAE QR funding outcomes on its own, incorporating as it does both aspects of departmental size and research quality, but it also correlates with the RAE measure of quality, once the effect of departmental size is adjusted for. This is all the more impressive when one notes that the departmental H-index is based on any articles listed as coming from the departmental address, whereas the quality rating is based just on those articles submitted to the RAE.

There are well-rehearsed objections to the use of citation metrics such as the H-index: first any citation-based measure is useless for very recent articles. Second, citations vary from discipline to discipline, and in my own subject, Psychology, within sub-disciplines.. Furthermore, the H-index can be gamed to some extent by self-citation, or scientific cliques, and one way of boosting it is to insist on having your name on any publication you are remotely connected with – though the latter strategy is more likely to work for the H-index of the individual than for the H-index of the department. It is easy to find anecdotal instances of poor articles that are highly cited and good articles that are neglected.  Nevertheless, it may be a ‘good enough’ measure when used in aggregate: not to judge individuals but to gauge the scientific influence of work coming from a given department over a period of a few years.

The quest for a perfect measure of quality

I doubt that either of these ‘quick and dirty’ indices will be adopted for future funding allocations, because it’s clear that most academics hate the idea of anything so simple. One message frequently voiced at the Sussex meeting was that quality is far too complex to be reduced to a single number.  While I agree with that sentiment, I am concerned that in our attempts to get a perfect assessment method, we are developing systems that are ever more complex and time-consuming. The initial rationale for the RAE was that we needed a fair and transparent means of allocating funding after the 1992 shake-up of the system created many new universities. Over the years, there has been mission creep, and the purpose of the RAE has been taken over by the idea that we can and should measure quality, feeding an obsession with league tables and competition. My quest for something simpler is not because I think quality is simple, but rather because I think we should use the REF just as a means to allocate funds. If that is our goal, we should not reject simple metrics just because we find them oversimplistic: we should base our decisions on evidence and go for whatever achieves an acceptable outcome at reasonable cost. If a citation-based metric can do that job, then we should consider using it unless we can demonstrate that something else works better.

I’d be very grateful for comments and corrections.

Mryglod, O., Kenna, R., Holovatch, Y., & Berche, B. (2013). Comparison of a citation-based indicator and peer review for absolute and specific measures of research-group excellence Scientometrics, 97 (3), 767-777 DOI: 10.1007/s11192-013-1058-9

This piece originally appeared on Dorothy Bishop’s personal blog and is reposted with permission.

Note: This article gives the views of the authors, and not the position of the Impact of Social Science blog, nor of the London School of Economics. Please review our Comments Policy if you have any concerns on posting a comment below.

About the Author

Dorothy Bishop is Professor of Developmental Neuropsychology and a Wellcome Principal Research Fellow at the Department of Experimental Psychology in Oxford. The primary aim of her research is to increase understanding of why some children have specific language impairment (SLI). Dorothy blogs at BishopBlog and is on Twitter @deevybee.

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