Thursday, 10 January 2013

Facts, Lies and Statistics


Facts matter, and most of us will know the phrase Fact Checkers, which came up quite a bit during the recent US presidential election.  But Facts are only part of the story.  The Choice of Facts matter just as much as the facts themselves, and nowhere is this seen more than wherever statistics and data are discussed.  Western mathematics education doesn't serve most people well in this regard, and I could explain to you why, or you could watch this TED lecture by Arthur Benjamin.

The lecture is only 3min long, but for those time-short readers I can summarise by saying: we should teach less algebra, and more statistics at school.  Going to be an engineer?  You need algebra.  The other 99% of the population, you really, really need statistics!

You really, really need statistics

Why, I hear you ask?  I'm glad you asked!  Below is an poster of the Incredible Shrinking Doctor, an image commonly used in high school maths classes to explain distortions caused by the misuse of statistics:
The image is linked from this page, which has a great discussion on the ambiguity of data.  Ambiguity?  How?  The image is meant to show the shrinking number of doctors in California between 1964 and 1990.  The reduction in doctors was, in actual fact, approximately half.  But, because the images were shrunk by half in both height and width, it appears as if the number of doctors actually shrunk to a quarter of what they where (the small doctor is about 1/4 the size of the original doctor).  The Facts are right, but they are presented in such a way so that the loss of doctors to family practice is much worse than it actually is. 



Facts matter.  In fact, Facts matter so much, that some people are willing to choose which Facts they use very carefully to make sure they give the right impression to people who don't know any better (like voters and investors).

Here's an example from a post on twitter today from Stephen Koukoulas (@thekouk), an experienced economist (you can read his Bio here).
Is it a Fact?  Absolutely!  Perfectly correct.  Doesn't look good for the profligate Howard government, does it! As far as I can tell, it comes from here, the 2012 MYEFO documents, table D1 (see screenshot below).

In fact here is the table partially reproduced below (with the relevant data I believe used by @thekouk highlighted).

The 'last 8 Howard Budgets'

Why did he choose the 'last 8 Howard Budgets'?  Is 8 some magic figure, or some standard Economic rule of thumb?  Not as far as I know, but I do know that by choosing the last 8 years, he maximises the point he is trying to make, that the Howard government was a wasteful spender.

Note the first figure in the list - a 10.7 increase in real spending over the previous year.  What happened?  To be honest, I'm not really sure, but I do know that the inclusion of that one, large value significantly biases the average over those 8 years. 


The last 7 Howard Budgets

What if 7 was the magical economic rule of thumb?  Then the average increase in spending under the Howard government in its last 7 budgets was less than 2.3% per year, much less than under the current Rudd/Gillard government. So much for the 'profligate' Howard government!

(@thekouk could have used 9 years, and arrived at the figure of 3.6% increase in real spending per annum, still worse than under the current government, but not as usefully 'bad' as using 8 years of data.)


Teaching Stats and the Choice of Facts

Don't get me wrong, I follow @thekouk on twitter, and I have learnt quite a bit from doing so.  He has a broad range of experience in both the private and public sector. 

He always uses Facts.

And Facts matter, but our students also need to know that the Choice of Facts also matters. For this reason, Statistics should matter more than algebra when it comes to maths education, and we should always, always question the Choice of Facts that are presented to us, and teach our students to do the same.