Clemens et al. skewer their numbers in their "Enrollments" paper.

Let's dissect the Fraser Institutes "Study" on "Enrolments and Education Spending in Public Schools in Canada". This fine piece of work was written by some guy named "Jason Clemens", who, it turns out, seems to write quite a few pieces on the costs, numbers of students and other various factors surrounding public education in Canada. Pressprogress has a clip of his philosophy of manufacturing consent in the public to steer Canada towards private schools. Pretty sure he's an advocate for charter schools in Canada; see Washington State's issues with charter schools.

I have to say that Jason Clemens looks like the type of guy that would go to a strip-club, grab a plate from the buffet, and pull up a seat in perv-row to chow down.

But I digress.

Let's get into their 'document': This thing is supposed to be about "Enrolments (turns out they didn't even spell 'Enrollments' correctly) and Education Spending in Public Schools in Canada". I know that because that's what the title says. When you find a typo in the title generally the chances are slim that you're dealing with a winning document.

It doesn't take long to find some more errors.

Ok lets have a look at that. On the surface this looks correct, (12,070 - 9,231) / 9,231 = 0.3076. However, the actual numbers themselves are wrong. The data in the image is a result of calculations they made from data from the Statistics Canada cansim tables, specifically table 478-0014. Clemens et al. never actually say which row that they get their data from. There's something that resembles an explanation in the first few pages, but it's not clear what they mean. The closest row that I could find for spending, in Canada, on public education, was found in the row labelled "Public school board and direct government expenditures". Clemens et al. quote the total amount of spending on public education in 2003 to be $41.6B, which does not match the cansim data of $41.4B. Their 2013 number does not match the cansim tables either, it's off from the $60.5B value by the same 0.2 amount (60.7 is their number); somewhere 2 billions dollars disappeared. 

In any case, this isn't really the error. The error is in the consumer price index calculations (CPI) they used. Clemens et al. link another cansim table with Canada's CPI values from 2003-2013. Again, it's impossible to tell exactly how they applied this table in their paper. It's clear that they did it incorrectly, however. To be sure of my calculations, I used two different sources of CPI conversions; the same table as linked in the FI piece and the Bank of Canada converter. If you convert 41.6B in 2003 dollars to 2012 you get $49.1B using the BoC converter, if you use the cansim tables for "All of Canada" you get a CPI difference of 19.5%, which converts to $49.5B in 2013 dollars. Clemens et al. list the 2003 values of total spending in Canada as 46.9B in 2013 dollars, a 2.5B difference, or a 5.5% difference right off the bat.

Now the actual value they are quoting in the image is cost PER student in 2003/2004 vs the cost per student in 2012-2013. So this means that they've used the 60.7B divided by the number of students enrolled in 2013, as well as the 46.9B divided by the number of students enrolled in 2003. Their table 2 in the document, which is referenced by the cansim table with a hyperlink in the references section, claims that there are 5,286,949 in the public education system in Canada, the cansim tables claims there are 5,081,703 students. 

So which is it? 

Well, let's look at the quote above again: 

It's really easy to back calculate their numbers, all we have to do is multiply the cost / student, $9,231, by the number of students, 5,286,949 and we get: $48.8B dollars spent in 2003/2004. A quick search of their document produces no such number, "48" is nowhere to be found. How is this possible? 

There is simply no possible way you can get the $9,231 quoted in the document. Even if I fiddle with my CPI calculations, I can't realistically reproduce that figure. That's unreal.

Let's tally up the errors so far. 

1. Typo in the Title
2. Incorrect amount of students enrolled in 2003/04 and in 2012/13
3. Unclear use of CPI tables to convert values into 2013$. 
4. Unclear where they got their 2003/04 totals for $ spent

And this is after the 1st bullet that contains data. I really tried to reproduce their number of  $9,231 of "adjusted" spending in Canada. I tried weighting the amount of money spent in Canada per province; that didn't help. I fiddled with the CPI calculations, but there was no justifiable way that I could reproduce that figure. Not to mention, their total of numbers of students in each year do not match any of the cansim tables; they're overestimating the number of students by about 200,000, with the bulk of those in Quebec, which may or may not be adults. Have a look:

As you can see, their total in Quebec in 2003/2004 of 1,241,143 is a good 250,000 students higher than the highest enrollment year ever in Quebec, according to their referenced cansim table, of 983,709 students in 2003/2004. Fraser Institute even has another document that disagrees with the numbers of students used in this study. Explainable, perhaps, except they were published almost a month apart, written by the same people. These facts are neither here nor there when you consider the  clusterfuck application of the CPI tables.

It's pretty clear that dissecting this document in any real sense is going to be a quagmire, so I'll zoom out from the details and focus on the broader message. 

Their first main section of the document blathers on about how spending on public education has increased nominally by about 45% over the 10 years from 2003-2013. While this is well and good, not considering for inflation and talking about money is pretty much useless. Money is representation of value; a social interaction that changes over time due to various factors. Not accounting for the change in monetary value during any analytical period is going to introduce a number of biases and distortions. Obviously the cost of education has risen, but not by 45% as they claim. Depending on which values you use for CPI, you get a range from of 22-23.5% which is about 5% above an inflationary value of about 17-18% (22-17 = 5, 23.5 - 18 = 5.5) from 2003-2012. All told, the real cost of spending on public education has increased by about 5% above inflation.

Not to get stuck in the weeds of the errors of Clemens' calculations, this document offers absolutely no reason as for the increases. Are there extra downloaded costs onto the school boards? What extraneous contract obligations do the school boards have to deal with? What administrative red tape are staff dealing with when asked to do more work than they can handle? It completely forgets to mention that spending of public funds on private schools has increased a similar rate in the decade considered in the 'paper'. Why would the public fund private schools; makes no sense. The public is on the hook for over 4$B in spending on PRIVATE schools in Canada in 2012/2013 year; unless I'm reading the table wrong and that is the extent of private school spending, by private entities themselves, in Canada.

What the Fraser document misses: 

The Fraser Institute's paper misses the obvious point. We're ONLY spending about $12,000 PER child in Canada? That's it? Let's unpack that; we get schools, teachers, desks, books, gymnasiums, playgrounds, areas in cities or towns for kids to play, learn and interact together. We get all of that, and more, and it only costs about 12 thousand dollars per year?

I spent about $12,000 last year on my 3 year old's daycare service. I got... a babysitter. In a house. With 6 or 7 other snotty nosed kids. They went to the mall for their activities. I can't afford to pay $1500 / month for adequate, stimulating, child care, so I get the discount version. 

$12,000 a year for our children to go to school, for good quality public education, is the deal of a lifetime. $12,000 per year gets you mid-grade daycare services in several cities in Canada. Educating the future members of our society is not a "cost", rather it's an investment. An investment that's guaranteed to pay off if only given enough time, attention, stimulation and challenge.