The two subjects that I like to teach most are those in which I’ve received the least formal education. My Economics, in theory, comes from a year’s evening course at Birkbeck College meant as an access course to a masters degree and no-one has ever taught me Statistics. Trying to figure them out is my big task.
I think I have an advantage here; I have had to learn very little for examinations and consequently have learnt little, if anything, “parrot fashion”. I still have to puzzle my way through ideas thinking, quite deeply, about what they mean. One of my favourite gripes about Economics is that textbooks, teachers and students don’t worry about the mechanics of an idea; for example, everyone knows that an expansion of the money supply causes inflation. Well, I don’t. The manner in which this happens is not obvious to me. I’ve figured it out now but textbooks have been of no help whatsoever in this.
Anyway, it was Statistics that I wanted to write about. If you don’t already, please listen to “More or Less“, a BBC radio programme about the use of numbers in public life. This is invariably excellent; accessible and intelligent. They have been exploring the idea of statistical significance recently. To me this is one of the most important ideas in the how we try to understand the world and, also, one of the hardest to get your head around. It is also badly taught at pre-university level, or generally not taught at all. I shall discuss at some future point what I think is wrong with Statistics at A level but, the principle is beautifully illustrated by Arthur Benjamin in a short TED talk.
The reason that I wanted to write here was that Tim Harford in More or Less made a logical error when talking about hypothesis testing, and, in particular, the idea of p-values. The error is beautifully explained by the bayesianbiologist in his/her blog, I couldn’t possibly do it as well.
Secondly, I was struck by this article on the BBC’s website. In which Matthew Syed writes about the dominance of black men in sprinting events. I probably misunderstood but thought that Mr Syed had missed the point. I wrote the following comment “Okay, at risk of my making a really dumb error, I had a difficulty with this article. The article says, sensibly I think, that because we see the 100m dominated by black athletes we incorrectly infer that black people in general are good at sprinting. Which is silly because there is no homogenous group of “black people” to which this could apply.
I think this is say that given that a runner is black, he is likely to be good at sprinting.
But, what about the reverse? Given that a man is good at sprinting, what’s the probability that he is black? And, if we knew, what would this tell us?”