Rough stats: What is everyone studying?

With the recent news surrounding the proposed rise in tuition fees in the UK, I thought I'd see how many more students we have these days. The claim is that with more than ever before going to university it's impractical for every student to be funded by the taxpayer, but how many more are there?

I've rifled through the Higher Education Statistics Agency for figures, and my first graph is of total students numbers since 1996/97:

A pretty clear trend, then. Although there are a couple of caveats. The main one is that I have plotted total undergraduates, which doesn't separate international students from UK ones, which obviously muddies the water a bit. The other is that my y-axis starts at 1 million, so the increase looks a little more dramatic than it is (although a 25% increase is still pretty big).

What I find most interesting about this graph, however, are the two places where the trend gets interrupted. They represent when key changes were made to how much a degree would cost - the first being when tuition fees were initially introduced, and the second when top-up fees (trebling the cost of most courses) came in. It doesn't seem that these two measures have had long-term impacts on the increasing number of students, but eyeballing it is obviously pretty dangerous, and since we don't have data prior to 1996 we can't really say much about earlier trends either.

So we know there are more students, but what are they studying? Again, I've looked at undergraduates only, and plotted the numbers of students studying various subjects from 2002/03 to 2008/09. There are subject-by-subject data, but to try and make it close to comprehensible I've used HESA's 19 subject 'areas'. For reference, I've listed which subjects each subject area includes at the bottom, as it can explain a lot of the relative popularity of each.

It's not a particularly good graph, I know (and you probably need to click on it to see it properly), but I just wanted an overview to see if anything leapt out. (Don't worry about some of the colours being quite similar - the legend is arranged to match up with the order the lines appear on the far right of the plot, so it should be just about decipherable.)

First of all, why only from 2002/03? The answer is because there seems to be a dramatic change in how degrees were classified in the datasets I found. Prior to 2002 around 100,000 students were categorised as doing a 'combined' subject, but this suddenly dropped to just 10,000. At the same time various other subjects saw massive jumps in numbers - clearly most of the combined subjects were now being counted amongst other categories, and so it's easiest to just look at the data from this point onwards.

What are the main trends? Most subjects seem to be gradually increasing, as we might expect, but there are some that stay roughly constant, and some that drop considerably. In particular, computer science is having a terrible time of it, with a huge drop over the last seven years.

A better way to look at these data, however, is to consider what proportion of undergraduates are studying which subjects, rather than their absolute numbers. This gives us a clearer picture of the changes in the makeup of our student population, and should highlight which subjects are just increasing in line with the overall surge in student numbers, and which are losing out or doing better still.

It might not look like too much has changed, but you can see plenty of subjects' lines aren't quite as steep as they were. One can now identify with slightly more confidence which subjects are getting more than their fair share of new students.

As you've probably noticed, this 'analysis' is pretty rough and not particularly scientific. The main warning I should probably provide is that you shouldn't read too much into the subject area headings. For instance, something like biological sciences seems to be getting a bigger share of the pie, but this doesn't mean biology is. From 2002/03 to 2008/09 biology increases from 17,390 undergraduates to 18,885, whereas sports science goes from 15,755 to 31,370.

A subject-by-subject analysis might be forthcoming, should I get bored enough over the festive period, but for now I must resist. All the data are available for free here, though. So if you're super keen you could poke around it yourself. You never know, you might be able to work out why statistics has dropped from 1,680 undergraduates to 1,325. It seems totally inexplicable to me...

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Those subject areas in full...

Business & administrative studies: Broadly-based programmes within business & administrative studies; Business studies; Management studies; Finance; Accounting; Marketing; Human resource management; Office skills; Hospitality, leisure, tourism & transport; Others in business & administrative studies

Subjects allied to medicine: Broadly-based programmes within subjects allied to medicine; Anatomy, physiology & pathology; Pharmacology, toxicology & pharmacy; Complementary medicine; Nutrition; Ophthalmics; Aural & oral sciences; Nursing; Medical technology; Others in subjects allied to medicine

Creative arts & design: Broadly-based programmes within creative arts & design; Fine art; Design studies; Music; Drama; Dance; Cinematics & photography; Crafts; Imaginative writing; Others in creative arts & design

Social studies: Broadly-based programmes within social studies; Economics; Politics; Sociology; Social policy; Social work; Anthropology; Human & social geography; Others in social studies

Biological sciences: Broadly-based programmes within biological sciences; Biology; Botany; Zoology; Genetics; Microbiology; Sports science; Molecular biology, biophysics & biochemistry; Psychology; Others in biological sciences

Engineering & technology: Broadly-based programmes within engineering & technology; General engineering; Civil engineering; Mechanical engineering; Aerospace engineering; Naval architecture; Electronic & electrical engineering; Production & manufacturing engineering; Chemical, process & energy engineering; Others in engineering; Minerals technology; Metallurgy; Ceramics & glasses; Polymers & textiles; Materials technology not otherwise specified; Maritime technology; Biotechnology; Others in technology

Languages: Broadly-based programmes within languages; Linguistics; Comparative literary studies; English studies; Ancient language studies; Celtic studies; Latin studies; Classical Greek studies; Classical studies; Others in linguistics, classics & related subjects; French studies; German studies; Italian studies; Spanish studies; Portuguese studies; Scandinavian studies; Russian & East European studies; European studies; Others in European languages, literature & related subjects; Chinese studies; Japanese studies; South Asian studies; Other Asian studies; African studies; Modern Middle Eastern studies; American studies; Australasian studies; Others in Eastern, Asiatic, African, American & Australasian languages, literature & related subjects

Law: Broadly-based programmes within law; Law by area; Law by topic; Others in law

Computer science: Broadly-based programmes within computer science; Computer science; Information systems; Software engineering; Artificial intelligence; Others in computing sciences

Physical sciences: Broadly-based programmes within physical sciences; Chemistry; Materials science; Physics; Forensic & archaeological science; Astronomy; Geology; Science of aquatic & terrestrial environments; Physical geographical sciences; Others in physical sciences

Education: Broadly-based programmes within education; Training teachers; Research & study skills in education; Academic studies in education; Others in education

Historical and philosophical studies: Broadly-based programmes within historical & philosophical studies; History by period; History by area; History by topic; Archaeology; Philosophy; Theology & religious studies; Others in historical & philosophical studies

Medicine & dentistry: Broadly-based programmes within medicine & dentistry; Pre-clinical medicine; Pre-clinical dentistry; Clinical medicine; Clinical dentistry; Others in medicine & dentistry

Mass communications & documentation: Broadly-based programmes within mass communications & documentation; Information services; Publicity studies; Media studies; Publishing; Journalism; Others in mass communications & documentation

Architecture, building & planning: Broadly-based programmes within architecture, building & planning; Architecture; Building; Landscape design; Planning (urban, rural & regional); Others in architecture, building & planning

Mathematical sciences: Broadly-based programmes within mathematical sciences; Mathematics; Operational research; Statistics; Others in mathematical sciences

Agriculture & related subjects: Broadly-based programmes within agriculture & related subjects; Animal science; Agriculture; Forestry; Food & beverage studies; Agricultural sciences; Others in veterinary sciences, agriculture & related subjects

Combined

Veterinary science: Pre-clinical veterinary medicine; Clinical veterinary medicine & dentistry

(There were occasional changes to these lists throughout the years in our dataset, with these being the details of the 2008/09 data. Probably an unimportant detail, but worth bearing in mind.)

Doing it by Degrees

When it comes to looking at university education, many do not have to think too hard about what they want to study, the bigger dilemma is where to study it. That said, university prospectuses will often tout various statistics to try and lure potential students into plumping for a particular course, with employability one of the more commonly seen figures. But is this a reliable metric of how 'valuable' a degree is? Or is it yet another example of STATISTICS ABUSE? (roll opening credits)

Every year AGCAS produces a report looking at destinations of graduates six months after graduation. The latest report, from 2009, is the result of questionnaires sent to all graduates from the 2007/8 academic year, and can be downloaded here. The report itself contains quite a lot of interesting data, with destination breakdown (how many graduates are employed, unemployed, or studying for further degrees) as well as stats on the types of job those in employment have found themselves in. With these statistics available for a number of subjects (or subject areas), we can get a feel for which subjects seem the most or least valuable.

The report provides details on the following subjects/subject areas:

Science

Biology; Chemistry; Environmental, Physical Geographical and Terrestrial Sciences; Physics; Sports Science

Mathematics, IT and Computing

Computer Science and Information Technology; Mathematics

Engineering and Building Management

Architecture and Building; Civil Engineering; Electric and Electronic Engineering; Mechanical Engineering

Social Sciences

Economics; Geography; Law; Politics; Psychology; Sociology

Arts, Creative Arts and Humanities

Art and Design; English; History; Media Studies; Languages; Performing Arts

Business and Administrative Studies

Accountancy; Business and Management; Marketing

So let's start with employment, surely a perfectly good benchmark of how 'good' a degree is. The AGCAS report splits graduates into those in UK employment, overseas employment, as well as those working and studying. We add these three together to give us our employment figures:

Top 5 for Employment:

Civil Engineering (78.3% employed)
Marketing (74.6%)
Business and Management (73.6%)
Architecture and Building (73.4%)
Accountancy (73.0%)

Bottom 5 for Employment:

Law (35.2%)
Physics (37.9%)
Chemistry (44.0%)
Biology (58.0%)
History (58.7%)

I think it's fair to say there are some surprises here. Marketing, and Business and Management two subject areas often cited as housing archetypal 'Mickey Mouse' degrees make the top 5, whilst historically 'tough' subjects like chemistry and physics are at the opposite end. Are people really better off studying business over biology? Or is there something wrong with our metric?

Naturally, I'm inclined to believe the latter, and with good reason. As is so often the case, one statistic does not tell the whole story; whilst these numbers tell us what proportion of graduates were employed six months after graduation, it is not simply the case that everyone else was unemployed. AGCAS reports a number of 'studying' statistics as well, such as those studying for a higher degree, a PGCE, or professional qualifications. Perhaps then, unemployment is a better way of assessing degrees, as this takes people who are 'employed' with study into accout. Let's see what happens:

Top 5 for Unemployment:

Law (5.5% unemployed)
Sports Science (5.6%)
Geography (6.4%)
Civil Engineering (7.0%)
Psychology (7.4%)

Bottom 5 for Unemployment

Computer Science and Information Technology (13.7%)
Media Studies (12.3%)
Art and Design (12.2%)
Electrical and Electronic Engineering (11%)
Accountancy (10.9%)

Quite a big change. Law jumps from worst for employment to best for unemployment (as you might expect, they're all studying), and accountancy has done the opposite. There are still some surprises, such as Computer Science and IT having the highest rate of unemployment, and another 'Mickey Mouse' course in the form of Sports Science being second best. However, this seems a much less debatable statistic than employment, and so it seems reasonable to take these figures at face value.

There is, of course, an issue we have yet to discuss, which will be a rather pressing one for many new graduates: money. What good is being employed if you're only getting paid £5 an hour for those fancy letters after your name?

The salary data in the AGCAS report are a little harder to find, let alone digest. Whilst we get nice pie charts and percentage breakdowns for destinations, discussion of salaries is restricted to an introductory paragraph. If we trawl through these, however, we do get some numbers, and merging them all together we can do another top and bottom 5, this time based on the average salary of respondents.

Top 5 for Salary

Economics (£24065)
Civil Engineering (£24006)
Architecture and Building (£23689)
Mechanical Engineering (£23683)
Electrical and Electronic Engineering (£22372)

Bottom 5 for Salary

Art and Design (£15656)
Media Studies (£16295)
Psychology (£16500)
Sports Science (£16627)
English (£16642)

Once again, a rather marked change. Media Studies keeps the bottom 5 place it enjoyed under the unemployment stats, but it is joined by Sports Science, which was second best for unemployment. There are no real surprises in our top 5, however, all these subjects having a fairly substantial pedigree.

For the sake of argument, then, let's suppose that you are most interested in average salary. As I mentioned, the AGCAS report makes it much easier to find the employment/unemployment figures for a subject than it does to find average salaries. Do these provide an adequate indicator of average salary? Our top/bottom 5s above would suggest not, but these only cover 10 of 26 subjects. Let's plot some graphs!

First up, average salary against employment, is there a strong link between the two?



Hmm, no obvious pattern there, then. How about unemployment, does that give us a better fit?



There doesn't seem to be any sort of pattern there either.

We can in fact calculate a number that gives us an idea of how closely related two sets of numbers are. The correlation coefficient between two sets of (x,y) points (like our (employment %, salary) points on our graph) varies from -1 to 1. If it's close to 0 that means our numbers are not closely related, whilst if it is close to +1 or -1 it suggests a strong relationship. For example, if in our plot of employment against salary above all our points seemed to be on a straight line, this would suggest a correlation of around 1 or -1. The sign indicates the direction of the correlation. If it's positive this means as salary increases, so does employment. If it's negative, then as salary increases, employment decreases. This doesn't mean the two are related - "correlation does not imply causation" is one of a statistician's many mantras - it just shows that these data happen to have an association (which we may go on to convince ourselves is a causal one).

So that diversion aside, what correlations do we get in our two plots above? Looking at them, we'd expect it to be close to zero; there doesn't seem to be much of a pattern in either of them. For the first plot, of employment against salary, we find a correlation coefficient of 0.12 - so not much of a surprise there. For unemployment it's even worse: 0.06. In short, neither employment nor unemployment is a good indicator of average salary.

There is one area of the AGCAS report we haven't discussed, however, which might prove useful. Whilst each subject has a page of percentages of those in employment, studying, and so on, it also has a page showing what types of jobs are held by those who are employed. These range from a variety of 'Professionals' down to 'Numerical Clerks and Cashiers', and 'Retail, Catering, Waiting and Bar Staff'. This last one doesn't sound too glamarous; you've just spent 3 years earning a degree and you're still working in a bar? More to the point, these jobs are going to be low paying, so hopefully they're a better indicator of average salary. Let's see:



There definitely seems to be a pattern there, and the correlation between the two variables is -0.88 - that's a pretty strong negative correlation. The higher the proportion of those employed in retail, the lower the average salary. Not a surprising result, but it's always worth checking these things.

Is this at all useful, though? The salary data are in the document, you just have to dig for them a bit more. There is, however, one thing we've not mentioned. Because the report doesn't give average salaries the same prominent treatment as the employment data, some numbers are, in fact, missing. Whilst we can see what proportion of history graduates are studying in the UK for a teaching qualification, we can't find their average salary six months after graduation (and the same goes for performing arts). However, because we've identified the percentage of those working in retail as a useful indicator of average salary, we can use this knowledge to predict the average salaries of history and performing arts graduates. (In statistics, we'd call our retail statistic an 'instrument' for salary.)

So how do we turn our retail employment data into a prediction of salary? If you read my previous post about the times goals are scored in football matches, you should already know where I'm going with this. If not, then go and read it now, and come back when you're ready to apologise for such an oversight.

So anyway, it's time for some more linear regression. We're looking to fit the model S = a + bR, where S is salary, and R is the percentage of those employed who are employed in retail. If we can estimate a and b, then we can use this equation to estimate S when we only know R, as is the case for history and performing arts degrees. We can also plot a cool line on our graph to show the trend. Running the numbers, we find a = 25014 and b = -468, and plotting the line this generates onto our graph gives us:



We can now either use our equation S = a + bR with a and b replaced with 25014 and -468, or read straight off the line on our graph. For both history and performing arts, retail employment was 17.4%, so plugging R = 17.4 into this equation gives S = 25014 - 468*17.4 = £16,870.40. Our model suggests that both subjects seem to lead to (relatively) low average salaries, something which would not have been easy to discern from the report alone.

Alas, this all assumes our model is accurate, and with a relatively small number of observations I wouldn't be inclined to place too much confidence in these conclusions. Here I've taken a single report to base rather a lot of analysis on. However, it does illustrate a couple of interesting points. Firstly, mere 'employability' figures seem a rather dubious metric on which to base the value of a degree. Perhaps more surprisingly, unemployment doesn't seem to be a particularly good one either, at least in terms of indicating average salary. Whilst this report did have salary data in it, they weren't as clearly laid out as the other data, and were in fact missing for some subjects. This has allowed us to demonstrate how you can use another variable (if you think it's a good enough surrogate) to estimate missing data. Whilst for this particular problem you're probably better off just trying to hunt down the data you want in another report, our way is clearly much more fun.