Our analysis challenges the idea that free schools will save money or improve standards

Francis Gilbert's picture
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Exclusive analysis conducted by the LSN shows the free schools project is going to be a very inefficient use of resources and will not, in all probability, raise standards. This is because the vast majority of free schools that are going to be set up will be small in size and our analysis of the Department for Education's own spending data shows small schools (fewer than 700 pupils) are much more expensive to run and less successful academically than their bigger counter-parts. While a major selling point about the free schools scheme is that they are small, our analysis reveals that this is actually something that counts significantly against them, particularly in terms of being an efficient use of resources. For example, the average cost per pupil in Toby Young’s West London Free School during its first year will be £7000 more than the average cost per pupil in secondary state schools  and this figure does not include the costs of actually setting up the school.  Furthermore, our analysis reveals that smaller schools achieve worse results than their larger counter-parts. We can also show that the most economical solution to stop this waste and under-achievement would be to close a small school immediately if there were spare places in schools nearby; this would be the most fiscally prudent and best academic solution all round. Thus, this analysis is important for any new government to consider.

The truth is that small is not beautiful where cost is concerned. Our calculations show (spelt out in detail below) that many free schools are liable to cost thousands of pounds more than their larger maintained counterparts. Even this is a conservative estimate because this calculation does not "factor in" the costs of setting up school, which runs into millions (we have put a Freedom of Information request to the DfE for these figures). In other words, the total costs per pupil for our free schools are astronomical; the taxpayer will, in effect, be paying tens of thousands pounds more per pupil in free schools, compared with the costs per pupil in the maintained sector. It is a shocking and needless waste of money at a time when the government is claiming that it’s being fiscally prudent.

Let’s explain these points in more detail. Our number-crunching of the 2009-2010 data about schools shows that that smaller schools tend to be more expensive to run and attain worse results compared with larger schools. If you plot a graph of cost per pupil against school size, it shows a very interesting story. From the largest schools down to a size of about 700, the most efficient schools have similar costs per pupil. Even for these sizes, as the schools get smaller the range of costs increases (thus, the smaller the size the higher the average cost). But below a school size of about 700 – which most free schools will be -- even the minimum cost increases, and it is of course there that you see the highest costs per pupil.

It also tends to be the biggest schools that do best in exams. A graph of FTE pupils against exam results (% achieving 5 GCSEs or better including Maths and English) shows two main groups: (a) a general mass of schools who have tend to have better results the bigger the school; (b) a smaller group of schools with outstanding results (90-100% success). Closer examination shows that this latter group is essentially made up of the selective schools, and that they tend to have 700-1400 FTE pupils and fewer than 10% free school meals; but that it makes little difference whether they are community, voluntary aided, voluntary controlled, or foundation.

If you run a linear regression (the process of fitting the best possible straight line through a series of points) of the cost of a school against its size, it provides a simple estimate which illustrates how much more expensive a small school is to run. A simple linear regression shows that 77% of the variance in the cost of a secondary school is accounted for by the number of pupils. The regression line follows the formula: Total gross revenue expenditure = 957,798 + (4435 times the number of pupils).

Thus, in round figures to the accuracy of the regression, the average running cost of a school per year is £1m, plus another £4,400 per pupil. This obviously means that the smallest schools are the most expensive per pupil. The DfE’s data base includes 2,960,878.5 FTE secondary pupils, educated at a total cost of £15.9 billion pounds. The average school size is 1,032 FTE pupils and the average cost of educating a child is £5,353 per year. According to the regression, a school with 400 pupils would cost £2.732m to run per year, an average cost of £6,829 per year. If in its first year it had only 60 pupils, as many free schools will do, it would in theory cost £1.224 million, a cost of £20,000 per pupil – nearly fifteen thousand pounds more than the average cost of a pupil. And that of course is before considering setting-up costs.

According to Toby Young, Year 1 of his West London Free School will have 120 pupils, which will cost the taxpayer £12,416 per pupil for next year -- £7064 more than the average cost per pupil in maintained state schools. This cost per pupil does not include the cost of setting up the school, which will no doubt run into millions. Since we do not have the figures yet from the DfE we can’t calculate this fully. But judging by the costs of the Bolingbroke Academy, which is costing £14m to set up, this means that the cost per pupil in total in free schools will be astronomical in their first five years -- at the end of which, of course, they could be closed down by a new government! Toby’s school will in the end be one of the more “economical” free schools because he is envisaging it admitting 840 pupils when it is full, which will be in seven years time. Most free schools will be considerably smaller and thus much less economical than his.

In other words, most secondary free schools will cost the taxpayer thousands of pounds more per pupil than their bigger maintained counterparts. Our calculations show that the most cost-effective way of solving this waste of money would be to shut down the school immediately (thus saving £1million straightaway) and allocating the pupils to the nearest school with places. This would, also in the long run, probably boost the results of the school with extra pupils because as we have seen bigger schools do gain better results on the whole.
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Andrew Nadin's picture
Thu, 27/01/2011 - 22:30

The fact that Free Schools don't have to break even for the first 5 yrs says it all.

At the Bedford Free School debate, I asked Mark Lehain how much money he's budgeted to get from Stg3 Feasibility to the launch (we're not even talking about the on-going running costs, just the initial set up costs). His response? He said he didn't know, as it would depend.
Considering he's about to submit his Stg3 Feasibility to the DfE I was amazed he said he didn't know. If Lehain's project was being run by a commercial organisation (something I have experience of), the project would be cancelled or postponed due to insufficient planning and unacceptably high ambiguity and variability - esp when it comes to the cost/benefit.
And here's the rub. Putting a project as complex & expensive as opening a school (even a small school) into the hands of enthusiastic amateurs is tantamount to negligence. It would NEVER happen in a commercial environment. Ironically, introducing commercial principles into our education system is exactly what Gove is promoting....but without the rigour, agility or experience that commerce demands.
So forget the poltical dogma for a second, free schools are unsound from a common sense economic perspective - and your research proves just that.
In the local paper tonight, Richard Fuller (MP, Cons) is 'grandstanding' about a meeting he managed to organise for Bedford Borough Heads, Governors and LA with Gove at the DfE. Following this mtng, his vision for the future? Become an "all-academy borough". Nowhere in his vision does he allude to how this will be paid for. Just last week, Cllr Michael Headley (Borough Finance Portfolio holder) said that £1m would need to be trimmed across local services to pay for the Lehain-led Free School. Considering Lehain is a maths teacher, he still needs to learn to 'do the math'.

Francis Gilbert's picture
Thu, 27/01/2011 - 23:10

Using the regression line formula generated from my analysis, I can work out the costs per pupil for the Bedford and Kempston school in its first year, Andrew: their website site says they are admitting no more than a 100 pupils in the first year. The calculation is quite simple, it's (100x4435) + 957,798 divided by a 100 = £14013 per pupil, compared with the state average of £5353. When the school is at capacity it will have 500 pupils, costing £6350.596 per head, over a thousand pounds more than the state average per pupil. This will only happen after 5 years and this figure does not include setting up costs. These results show that the borough would be far better off closing the school and sending pupils to the nearest bigger one with places as soon as they can (or are allowed to); this would be more efficient and improve results.

Andrew Nadin's picture
Thu, 27/01/2011 - 23:20

This is brilliant, I'll send to Lehain.....await barrage of mathematical denials.

Andrew Nadin's picture
Thu, 27/01/2011 - 23:28

The big issue here is not that smaller schools cost more (stands to reason, but now we have the evidence), but why no one at the DfE told Gove before he embarked on this madcap ideology. I don't really understand how/why the treasury has let this through whilst we scrimping & saving like mad to get the deficit down. There are so many more cost effective ways of raising standards in schools. Not least of which would be to give ambitious teachers like Mark the opportunity to run a failing school and prove he can raise the standards.

Francis Gilbert's picture
Thu, 27/01/2011 - 23:33

Yes, and as my linear regression shows, somewhat counter-intuitively, bigger schools get better results. This analysis completely blows a hole in government policy!!

Toby Young's picture
Fri, 28/01/2011 - 06:24

This is complete balls Francis, from top to bottom. Maths isn't your strong suit, is it? Stick to Media Studies.

Alan's picture
Fri, 28/01/2011 - 07:14

"It also tends to be the biggest schools that do best in exams. A graph of FTE pupils against exam results (% achieving 5 GCSEs or better including Maths and English) shows two main groups: (a) a general mass of schools who have tend to have better results the bigger the school; (b) a smaller group of schools with outstanding results (90-100% success). Closer examination shows that this latter group is essentially made up of the selective schools..."

I wouldn’t question the latter part of this statement. However, in our rural locality our technology college does well to hold its own against its neighbouring grammar - they both have approximately 600 pupils. Pupils and teachers work exceptionally hard to keep up standards, but there's no sixth form in our college, and to take A levels means travelling at least 50 miles. So surely, in this instance, a non-selective free school could provide a solution.

Gerry Newton's picture
Fri, 28/01/2011 - 07:41

It really is pretty thin stuff as 'analysis', and given the fetish on this site for calling Gove a Stalinist your calls for collectiviization are pretty ironic.

Francis Gilbert's picture
Fri, 28/01/2011 - 09:01

In response to both Gerry and Toby, I would like to point out that I have completed a Quantitative Methods course for my PhD in Education which requires passing a number of exams in order to upgrade. I passed them last year and am due to upgrade. This is a fairly simple but valid statistical exercise which the DfE no doubt have done but kept hidden from the public because of the light it throws upon public policy. I will take you through the "maths" again when I have a spare moment!

Alan's picture
Fri, 28/01/2011 - 09:05

Question to Toby Young: Would you select pupils on ability at 10-years-of-age if you could?

Andrew Nadin's picture
Fri, 28/01/2011 - 09:05

Toby Young's usual 1,000 word diatribe reduced to 2 words - "complete balls". Speaks volumes.

Janet Downs's picture
Fri, 28/01/2011 - 09:07

To say that there is a 'fetish' on this site for calling Mr Gove a 'Stalinist' is a distortion. I made it quite clear at the time that the quote "Gove: Libertarian or Stalinist?" was the introductory question put to Mr Gove on the BBC Today programme. You could equally argue that in using this quotation we had a 'fetish' for describing Mr Gove as a libertarian.

Charles Baily's picture
Fri, 28/01/2011 - 09:15

First, thanks to Toby for raising the debate to a more appropriate level of numeracy. A splendid exemplum of rational debate.
Alan, it's probably me, but I can't follow your reasoning. Presumably the 'neighbouring' grammar school has a sixth form. Why is it not open access? Or is it actually an independent school? If there is insufficient local demand for sixth form education to support post-16 provision at the technology college, why should an (additional) free school fare any better, once it's transformed local provision into two 300-strong schools? Or are you expecting that the extravagant generosity of Fort Gove towards free schools will allow individual A-level tuition, much as Francis' article indicates? The reason why many communities have opted for a 11-16 plus sixth form/FE college solution is that with a non-selective intake you need at least 1500 students on roll to provide a minimal range of GCE subjects taught in economically viable groups.
Your suggestion seems to me like the faith-based 'God of the Gaps' argument being touted here in Bedford - if you've got any issue at all with current provision, a free school must be the answer. Got a problem? Poke it with a stick. And if it's gold-plated, so much the better.

Francis Gilbert's picture
Fri, 28/01/2011 - 12:08

I suppose the main policy implication of this data is that the free schools project is doomed to be extremely costly because most of the schools will have fewer than 700 pupils. I am certainly not advocating "collectivisation" but pointing out that where appropriate amalgamation would reduce costs and raise standards in all probability. That said, as Alan illustrates, there will always be exceptions. That's why good local governance is so important; LAs are best placed to make these decisions. What certainly doesn't work is central govt opening small schools without proper consultation and at huge and needless expense for the taxpayer.

Alan's picture
Fri, 28/01/2011 - 13:01

Charles, thanks for your reply. I’m sorry you can’t follow my reasoning. Yes, the neighbouring grammar school has a sixth form which is ‘open access.’ However, there’s a risk of a double whammy for pupils who failed the 11+, they may not gain admission even if they achieve 8 good GCSEs (inc. Maths and English) due to limited places. Do you think this is fair, or worth the risk to self-esteem?
I didn’t say there is insufficient demand for a sixth form. And yes, I’m thinking in terms of a specialist college that would serve more than one school. As far as funding is concerned, I think if anything needs poking then it’s the conscience of bankers. It’s about time they coughed up. After all they are in the top 25% ability group. Aren’t they?

Andy Smithers's picture
Fri, 28/01/2011 - 13:46

With the increase in birthrate we are going to need more schools. New schools are obviously more expensive than a current functioning school and always cost more to run in their first 5 years as they come up to full size.

I do not follow your logic Francis - are you saying that any new schools should be as big as possible or that we should not be building any new schools ?

Francis Gilbert's picture
Fri, 28/01/2011 - 14:59

In response to Andy, the analysis I've done obviously isn't "trying to say" anything. The most obvious and cost-effective solution to a rising birth-rate would be for a Local Authority to plan provision where appropriate; if this meant they need to open a new school then that's fine. My analysis suggests though that they would do well to consider making schools bigger if there's room because this would save costs and actually improves results. The analysis is there to inform, not dictate, public policy.

Francis Gilbert's picture
Fri, 28/01/2011 - 15:05

I believe Canary Wharf College (a free school opening in my borough Tower Hamlets) is proposing a one form entry for Sept 11, with 20 pupils being the maximum. My regression formula suggests this will cost the taxpayer £52324 per pupil!! Two form entry would cost £28,380 per pupil. Both figures excluding set-up costs.

Francis, if somebody asked you how much it would cost to run a school for one pupil do you think £962,233 would be realistic? Does this answer pass the common sense test?

You have extrapolated from your linear regression. This means you have extended the model beyond the range of the data used to generate it. You have assumed that the model, that perhaps is collected on data ranging from 500 to 1500 pupils, will follow a pattern extendable to schools with fewer than 200 pupils.

You also assume a linear model is valid. Did you do any significance testing beforehand to check this? There are perhaps reasons why the total cost might be reasonably modelled as fixed cost plus per pupil cost, but this isn’t necessarily the case – your ‘fixed’ costs might not vary much for a school increasing in size from 1000 to 1200, but for 100 to 300? Who knows? Do you have the data to support this?

In terms of the link between school size and results did you test for all the possible independent variables that might affect results and then decide that school size was the most significant? In your linear regression what were the value of the parameters for FSM, level of education of female carers, number of students with English as an additional language etc?

"Thus, in round figures to the accuracy of the regression, " What is this supposed to mean? I understand each word individually.

If I were your statistics teacher I would be upbraiding you, not upgrading you. But, perhaps you can prove me wrong and submit your analysis (that the government is trying to supress) to a statistical journal for peer review.

Sorry to be so negative but this has to be one of the worst abuse of statistics that I have ever seen.

Alan's picture
Fri, 28/01/2011 - 16:39

Sorry Francis, I didn’t mean to speak over you, just didn’t spot your comment.
I agree, good local governance is essential from a monetary perspective as well as an ethical one i.e. education is a profession not to be taken lightly. I guess our geographies are quite different, and then there are other arguments over the personal benefits of small schools versus large ones. Travelling to school over large distances is another factor. From a wellbeing perspective, it’s not uncommon in rural areas for children to travel for 2 hours by bus to get to school. By the time they get home homework can be a challenge.

Andrew Nadin's picture
Fri, 28/01/2011 - 17:00

Charlie - I'm no statistician, so no comment on your critique of methodology. However, seen as no one in Govt or the NSN has bothered to look at overall cost of opening lots of small schools, I think Francis' analysis bears some credibility. It passes the common sense test from the pov that duplication of numerous fixed & variable capital functions across a high number of small schools MUST be highly cost intensive.

Your example of a single pupil's education costing £960k proves this. It may not cost £960k to educate one child, but if every single child was taught individually the sum of the parts would exceed the current whole. Cost efficiency is derived from eradication of duplication. A small free school in every neighbourhood sounds wonderful....how about 80% income tax to pay for it?

Anyway, the wider issue here is not Francis' mathematics, it's the lack of planning & thought from Gove concerning the funding & practicalities of what he's doing. A commercial organisation would never allow employees this amount of freedom without a robust business model to support it, but maybe Gove has one and he's not saying - private companies run schools for profit? Now that would fit with current policy.

Step 1. Mass deregulation
Step 2. High attrition rate due to lack of management capability
Step 3. Hand failing free schools & acads over to big business
Step 4. Parents evening P&L review instead of test scores

Francis Gilbert's picture
Fri, 28/01/2011 - 17:24

I have only just in got in after a rather long day! I will attempt to respond in Charlie's points in more depth when I have some proper time.

Basically, he's asking me to produce some substantive academic research for peer review. I certainly think this is worth doing because the linear regression does suggest an interesting relationship between size of school and cost. Obviously, all the calculations I've done are estimates, but I believe to be fairly accurate ones because they are based on the DfE's own figures. But I don't have the full figures at my fingertips in the way the DfE do. I've put Freedom of Information requests for their budget projections for spend per pupil and am awaiting their reply, but as yet they are not publicly available in the way costs for LA schools are.

As Andrew points out, the bottom line is though that small schools are very expensive to run compared with bigger ones. A basic, common sense point which Gove & co have ignored.

Gerry Newton's picture
Fri, 28/01/2011 - 17:44

Francis, I'm afraid that no amount of excuses about a 'long day' can alter the fact that you have simply dug yourself into a very deep hole with this. The final sentence from Charlie sums it iii perfectly. The idea that government are trying to 'suppress' this information is preposterous.

Francis Gilbert's picture
Fri, 28/01/2011 - 18:10

Gerry, I will return to Charlie's points in due course. I don't feel I've dug myself into a hole at all, but raised a very important point: whichever way you look at it the costs of the free schools are going to be exorbitant at a time when we need fiscal prudence.

Small schools are not necessarily more expensive. Yes, there may be some indivisibles that every school must have exactly one of - e.g. a headteacher - and so these costs, when spread over more pupils will decline (although I imagine as the new schools start-up the headteachers will teach). The majority of a school's costs will be staff who will be employed in proportion to the number of pupils. So far it sounds like bigger is better. But independent academies will have the ability to hunt around for better deals. They may be able to source from small local suppliers who wouldn't have the scale or scope to supply through the LEA. So those other costs, that are not staff related, may be lower per pupil for a small school than for a big one. It depends how good and how cost conscious your procurement is.

Consider this, though. If we take your argument of large indivisibles at face value and say that average cost per pupil will decline markedly as pupil numbers rise, then why aren't you campaigning for super schools of 5,000+ pupils? Does everybody here accept that at that scale quality of provision might decline? So, ignoring the proposition that small schools might not be more expensive, we have a cost / quality trade-off. So on where do you draw the line? In my opinion you can't, it is an individual matter of opinion. Small schools allow certain management facets to be achieved more easily, but robust management can ensure effective quality control in much larger schools. You might argue that a smaller school in itself adds a positive element to the experience of pupils, in which case pupils and parents can express a preference for the experience that they want.

There seems to be an underlying assumption that because smaller schools cost more to run their funding formula will be different. Where has that assumption come from? If I am mistaken, and nobody believes that, then isn't it the case that smaller schools will have to make concessions in their provision somehow (assuming they can't bring costs down elsewhere)? That being the case it is up to the DfE to ensure that new schools will provide adequately and up to pupils and parents to choose to go to the school. If neither of these things happen then you will all be vindicated.

Andrew Nadin's picture
Fri, 28/01/2011 - 20:08

Charlie - i think you're being rather too literal. No one is saying (well I can't speak for Francis!) that small schools are not desirable, or that 5000+ schools are a brilliant idea. The point is that in the real world, Gove's plan to open a shed load of new small schools is going to cost a fortune.

Initially the biggest cost will be start-up budget, not staff / labour (that comes later). Premises, refits etc will be very expensive & wasteful compared with investing the same money in existing schools to raise standards.

Schools expansion programs are already undertaken by LAs who project population changes, birth rates and existing demand, in order to ensure sufficient provision, but only at the right time.

The problem with Gove's plan, and the point I take from Francis' maths, is that this has all been ignored in favour of pursuing a political ideology which has no root in existing reality. The manifestation of the pursuit of the Govian dream will be schools which will costs many thousands of pounds per pupil, not least because there will also be a nearby school which is half full because the free school has poached some of the intake. I'm not asking you to concede all your points about the maths, but there is a semblance of reality & real world that needs to be injected into this plan before a whole load of schools run into management & financial difficulties to the detriment of all of our kids.

Francis Gilbert's picture
Fri, 28/01/2011 - 23:53

I would like to endorse what Andrew says here, and also point out that while we know that free schools will be small, certainly with pupils fewer than 700 pupils, we don't know exactly how many pupils there will be per school with any degree of certainty. Toby Young has told me his figures but other websites for free schools are very coy indeed about pupil numbers.

Charles Baily's picture
Sat, 29/01/2011 - 10:58

It isn't just cost that is the issue, it's cost/benefit. Benefit must be measured as effective delivery of appropriate curriculum. A grammar school can operate on a roll of about 600 because of the homogeneity of its ability range. A non-selective secondary school can't. To provide an adequate curricular choice, taught in groups sufficiently homogeneous to be manageable without teacher burn-out, needs twice that. Is the aim of the 'English Baccalaureate' actually designed to restrict the curriculum and give small free schools a competitive edge? Perish the thought!
Yes, above a certain size, say 2000, little significant further advantage is gained; and yes, in rural areas population density makes optimum size expensive to achieve in terms of travel costs. But these are factors that need to be planned for, not left to the vagaries of random self-selected providers to pop up with institutionally shallow projects that are instantly and uncritically embraced by the DfE, for purely ideological reasons - you can see how ideological by reflecting that if a demographically-driven need for a new school is identified, the one kind of school automatically disqualified will be a community school run by the LA.
As children mature and their aptitudes and aspirations come into focus, choice within school becomes far more important than choice between schools. And if the effect of mushroom free schools is the shrinkage of non-selective community schools, to the inevitable detriment of their curricular provision, all children become the losers.
Finally, all credit to the World at One interviewer yesterday who, faced with Gove accusing 'vested interests' of opposing free school proposals, asked if parents of children at schools adversely affected by a neighbouring free school also counted as 'vested interests.' No very clear answer to that, I'm afraid.

Francis Gilbert's picture
Sat, 29/01/2011 - 12:19

I've started to think about Charlie Ben-Nathan's points (see above) and would like to make these points:

It is true that the data is only correlational. It is furthermore true that a regression analysis of the data can only be regarded as indicative;
perhaps a more valid impression can be got from the scatterplots. To the extent that the regression is valid, school size explains 16% of variance in the cost per pupil. The model is statistically significant at p <.001, but this is hardly surprising given the enormous sample size (over 3000 schools). The remaining variance is presumably explained by factors such as the ones you mention Charlie, for most of which the data are not available. It is possible they could affect the validity of the model to the extent that they correlate with school size.

The data does go down to quite small school sizes, including 150 schools with 500 or fewer FTE pupils. Ten are listed as smaller than 200,
although it is of course possible that for the very smallest schools there is something unusual about them or that there is some problem with the data. However as I've said, the scatterplot does appear to show that as schools get smaller, the average cost per pupil increases, as does the range of costs.

Again, it has to be admitted that these are only correlational data, but it might be interesting to ask whether the new kinds of schools have any characteristics that would allow them to buck the trend that appears to be seen on the scatterplot.

Charlie, I can email you the scatterplots and the relevant Excel spreadsheets if you wish to look at them, but I can't publish them because of copyright issues connected with SPSS and I would only email them on the condition that you did not publish them either because of the copyright issues involved. I'm sure you'll appreciate this.

Alan's picture
Sat, 29/01/2011 - 16:03

“A grammar school can operate on a roll of about 600 because of the homogeneity of its ability range. A non-selective secondary school can’t. To provide an adequate curricular choice, taught in groups sufficiently homogeneous to be manageable without teacher burn-out, needs twice that.”

A non-selective secondary with a roll of 600 can function just fine. We have 5 ability groups, 1 teacher per set, no burn-out and few problems. I know this brings no solace, but homogeneity of ability is an elitist concept, nothing more.

Francis Gilbert's picture
Sat, 29/01/2011 - 21:57

Simon has contacted me through our email system asking for my Scatterplots which show the linear regression. Unfortunately, I don't have his email or know who he is. I am happy to email this to anyone who wants my Scatterplots etc on condition they won't publish publicly because of copyright issues. The email system for LSN is playing up at the moment so it's best to email me at francisgilbert10@gmail.com until it's fixed, which will be soon.

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