Nutty clusters

'But surely,' said my friend, 'you would expect something like leukemia cases to be spread evenly across the country. Where there's a cluster of cases, there must be a cause. Like a phone mast.' No, no, no.

First you've got to realize that clusters are natural in something that's random. You wouldn't expect a coin toss to go heads, tails, heads, tails... repeatedly or the results on a roulette wheel to flip between red and black, time after time, all nice and evenly spaced out. You get clusters. Similarly if you drop a whole tray full of ball bearings on the floor, it would be really strange if they all lined themselves up nice and evenly spaced. You will get clusters and gaps. That's just the nature of something random. Yes, on average, across a huge sample, it will kind of even out, but in any particular place there's likely to be either a cluster or a gap.

So we can't make the leap in logic from 'there's a cluster' to 'it has a cause'. Many clusters don't have causes.

We also have to be careful when saying about something common like phone masts 'Look, lots of clusters are near phone masts, so phone masts must cause them.' It would be strange if lots of clusters weren't near phone masts. They'll also be near lots of other things that occur pretty evenly across the country. There will be lots near pubs and churches too. But those who seek to blame phone masts for the ills of the world don't think it through, they just jump in.

I'm not saying that no cluster has a cause. The cluster of asbestosis cases near the Turner & Newall asbestos factory in Rochdale was no coincidence, for example. But most clusters are simple statistical artefacts, arising from the nature of random numbers. There are good tests to see if a cluster is likely to be random or causal - but these are rarely employed by those who panic about clusters.

So next time there's a cluster of cases of something locally, don't fall for the same mistake as the medieval types who decided this must be down to their version of a phone mast, the local witch. Make sure you understand the numbers before using them in anger.

(The picture (from Wikipedia), by the way, is a star cluster. And, no, it wasn't caused by a phone mast.)