Bacon Sandwich

I'm pretty busy writing up my work at the moment, hence the long break in posting this month. I'll try to fire out a few short but useful entries over the coming weeks rather than saving it all up for the monolithic posts I usually make.

Every week, some newspaper or another makes us frightened or happy by covering the latest risk data regarding "causes" or "cures" for cancer, stroke, heart disease and the like. Apparently they won't be happy until they've fully catalogued all Things at least once over, and preferably twice with flatly contradictory information. They present us with statements such as "Bacon Sandwiches raise cancer risk by 20%". That would probably put quite a few people off eating bacon sandwiches, but it's not a statistic you'll ever find in a peer-reviewed scientific paper. And there's a good reason for that. This sort of figure is what is called a "relative risk increase". It's calculated by taking the dividing the new risk (with bacon sanswiches) by the normal risk (sans sandwich) and multiplying by 100. We can see the weakness of that way of representing the numbers with an illustration such as this:

The risk of killing yourself with a revolver loaded with only a single bullet in a random chamber is 1 in 6. Put two bullets into two random chambers and the risk is 2 in 6 (or 1 in 3). These are absolute risks as opposed to relative risks. In percentages, the absolute risk is just over 16% with one bullet, but twice that (32%) with two bullets. Now let's do a Daily Mail on it and express this as a relative risk increase. That's a 16% increase over 16%. So by putting in the extra bullet you've just increased your risk of killing yourself when you pull the trigger by 100%. That last number is certainly the scariest, although we must admit that none of these numbers is particularly fun.

But here's where it gets interesting (stop rolling your eyes please). Imagine the risk of catching a fatal dose of the flu is 1 in 10,000,000 for each time you go to work on the train, but is 2 in 10,000,000 if you take the bus. These odds are very much lower than the absolute risks relating to the gun. In percentage terms they sound comfortingly low too (0.00001% increasing to 0.00002%). You're probably not going to base your public transport decision making on these numbers. However when we convert these numbers into a relative risk increase, we get... 100%. A headline that says "Buses Raise Flu Death Risk by 100%" is certainly going to either make you think twice about using the bus, or is going to make you think that those silly boffins are just spoofing (didn't they say buses were better for some reason last week?). You get exactly the same punch in a Daily Mail headline as the gun risk, and yet in reality they're not even vaguely similar.

This week a nice site caught my eye which puts all of that statistical wonder into a fun little web program that allows you to see the various ways in which scientific data can be made more scary. There's all sorts of ways to make a scare story out of a non story, and you can rest assured that most of the newspapers are quite prepared to use them.

Image from Wikipedia released under the terms of the GNU Free Documentation License.