Irony of the Day: Newspaper Fails at Math, Gets A Plus

One of the basic problems in interpreting/comparing anything is confusing rates of change with the levels of what you are comparing.  If you go from having one shoe to having two shoes, your shoe improvement rate is 100% but you only have two shoes.

What is the latest example of this basic error? Ironically enough, it relates to education.  One of the big local stories here is that there is much grade inflation at Carleton University.  That the average grade has increased over time, so that there is heaps of inflation.  So far, ok.  Whatever.  In today's Ottawa Citizen, it was reported that the University of Ottawa (Carleton's direct competitor),* has much less grade inflation as its grades have not changed as much over the years.

*To be clear, I would be making the same argument if it is the other way around--I care more about the innumeracy here more than the Carleton/U of O rivalry

So, this must mean that U of O has more strict marking, giving students lower grades, right?  Nay:

But while grades may be steadier at the University of Ottawa, they tend to be higher overall. About 38 per cent of grades assigned in 2010 were in the A range — A+, A or A- — compared to 33 per cent at Carleton the same year.
Fewer failing grades were assigned at UOttawa, too, with 4.5 per cent rating an F or an E (between 40 and 49 per cent score in the class), versus 5.2 per cent who failed at Carleton in 2010. 

So, grades have always been inflated at Ottawa and Carleton is now getting closer to the same rates.  This is not great news for anyone, but it is especially bad news for the Ottawa Citizen, which apparently sucks at math.

If grades are already inflated, we ought not to expect much more grade inflation.  It is like comparing the growth rates of advanced economies with those of less advanced countries.  After all:
change = (value now - value at last relevant time point)/value at last relevant time point.
The smaller the value was at the previous time point, the bigger the change will be in percentage terms.   So,   (100-90)/90 < (10-5)/5 as 1/9 or 11%  < than 5/5 or 100%.  But would I prefer to be in former or the latter?  Depends on what we are measuring.  If it is chocolate chip cookies, I would prefer the former situation as more CCC's is better than less, even if the rate of change is smaller. 

So, the lesson, as always, is to consider what the hell is being measured and whether the absolute change is what is most important or the relative change is the most important.