I suck at weekends. I’ve done nothing useful today. But something earlier reminded me about this, and for lack of anything else worth saying I’m going to talk about maths some more. I say bug humbah to your Hallowe’en malarkey. If you want spooky monsters and candy, go bother someone else. At my house, you get a lecture on algebra.
Simpson’s paradox is one of those really weird quirks of mathematics, which more people could do with understanding. It’s not even enormously complicated – the deep maths behind it can get pretty weird, but it’s really easy to appreciate how bizarrely counter-intuitive this stuff can be.
So, the paradox, and an example lifted straight from Wikipedia.
Some medical research happened a while back, into treatment for kidney stones. They took 700 people, split them into two groups, and tested a different treatment on each group. Treatment A worked on 273 out of 350 people in the first group, a success rate of 78%. Treatment B worked on 289 out of 350, or 83%.
So Treatment B works better, right?
Well, it turns out there are two different types of kidney stones. Broadly speaking, you can divide them into the “small” kind, and the “large” kind. So, even though Treatment B works better overall, maybe Treatment A is better for either small or large ones specifically. Right?
Well, half-right.
In fact, they found that Treatment A worked 93% of the time on small stones, while Treatment B worked 87% of the time. Meanwhile, with large stones, Treatment A hits 73% to Treatment B’s 69%.
So, for small kidney stones, Treatment A works demonstrably better than Treatment B. And for large kidney stones, A is still more successful than B. Treatment A actually works better in both individual cases.
But for kidney stones in general, Treatment B has a better overall success rate.
I’m a pretty intelligent person who studied mathematics more than anything else in life until I was 22, and I still don’t know how the fuck that works.
I mean, I understand all the maths behind it, it just still hurts my head. So now I’m going to go lie down. (This may also be related to the fact that it’s midnight now.)
