Thursday 19 April 2007

Correlation does not always imply causation, as any even slightly good statistician knows.

I was thinking about it because some right-wing idiots are proposing that the Virginia Tech massacre can be attributed to porn. There have been more school shootings in the States recently, and porn is more readily available than it was in the seventies. Therefore porn implies mass homicide.

Presumably efficiency of motor cars, number of Disney films and anything else which has gone up in the last thirty years also causes murders. Oh, unless those things aren’t stuff your particular lobby is already against.

But, as I muttered under my breath “correlation–causation, guys…” I wondered what would happen if you plotted a graph of correlation against causation.

For example, cigarettes smoked per day and lung cancer exhibits a strong correlation. It also has a strong causation, so it would go in the top right of the graph, with a lot of both. Height versus weight in people has a moderate correlation and a moderate causation, because obviously how fat you are is a pretty important factor, so that goes somewhere in the middle of both axes. And depth of ocean versus latitude, intelligence against love of gazelles and number of blue Smarties in a tube versus time of purchase probably exhibit bugger all of either, so they’re pretty much at the origin.

There is almost certainly a correlation between correlation and causation; there are plenty of things where there is a correlation but no causation (porn and gun crime, for example), but far more with none of each. It’s also impossible for something without a correlation to be caused by the factor you’re plotting it against, because otherwise there would be a correlation.

So, correlation correlates with causation. So, does correlation cause causation, given that it correlates with it?

Even better, can we plot the amount of causation and correlation of the correlation against causation graph on itself? And then do we have to re-draw the graph because it will change the correlation?

Of course, this is a load of silly crap; it’s a daft word game. Correlation versus causation has a high correlation, but a low causation, so it’s going to be in the same place as porn and gun crime on the graph. But I quite enjoyed the train of thought that got me there.

So, why did ol’ Cho go on his killing spree? Well, surprise surprise, it seems he was a bit of a crazy. He wrote mad, angsty plays and weirded the Hell out of his classmates and teachers. And, for the morbidly voyeuristic amongst you, the World’s media have seen it fit to release the videos he made of himself in the two hours between his two bouts of death-dealing, during which he goes on slightly mental rants and points his gun at things and generally reinforces the image of being a nutter.

I’d like to propose a correlation–causation thing: ‘nutters and widely-available guns’ are both correlated with and a factor which causes people to get shot. And, possibly the more worrying one, that giving exactly the widespread publicity they wanted to those who martyr themselves in this way might be a bit correlation–causation-tastic too…

1. wifey says:

fresh from my thesis: people often say violent films and video games have a strong correlation (and causation?) with violent crime – but studies have been done showing what most people probably realise anyway – that in japan there is much more violent tv, films and games available, and the violence is, well, more violent, than in europe and america, but they have a much lower occurrence of violent crime than europe and america do. so maybe there’s an unexpected reverse correlation for you there. or maybe violent tv just isnt a very big factor in causing crime.

2. Tom says:

As part of the news frenzy surrounding 32 deaths (and ignoring the 200-odd per day in Iraq)…

There was a minister somewhere in McDonald’s when it happened. http://www.foxnews.com/story/0,2933,266511,00.html Don’t forget to check the bit below the ads… Yes, everybody, one student said “video games”. Quick, burn them all. Don’t put tighter controls on guns; we just need to stop showing people virtual violence. That’ll stop them being able to shoot people anymore.

I liked the idea of checking the correlation of correlation-causation. Thing is, logic shall never defeat mindless commitment to other people’s incorrect statements and opinions.