Selection Effects

An article on the BBC website just now regarding the London riots has caught my attention with the headline:

One in four riot suspects had 10 previous offences

And it goes onto say that:

Three-quarters had a previous caution or conviction

Is it really true that 75% of those committing crimes on those evenings had previous convictions, or is it that those with previous convictions have their details on a police database and it was therefore possible to identify (and find) those people based on images from photographs and recordings made last month?

Many people fail to notice when a selection effect (selection bias) is occurring, and in many situations. I remember many weekend nights out in my youth with my good friend John where he would observe that all the girls were going in the opposite direction to us and should we not go somewhere else. I stuck to the line that we were only ever going to pass people going in the opposite direction. It certainly wasn’t anything to do with us being uncool.

And here’s a good article on World War 2, regarding selection bias and aircraft design. An engineer was asked to inspect aircraft returning from battle over a period of time, and to come up with a recommendation on where to add armour. After building up a statistical model of where the aircraft he inspected has sustained damage, he recommended reinforcing armour in the parts that were generally not damaged. Can you think why? Answer under the fold.

Well, the clue is in the post title. The engineer, Abraham Wald, realised there was a selection effect going on. The aircraft he got to see were the ones that were not shot down. Therefore he surmised that the places that were not hit on the aircraft he had analysed were precisely the parts that were more likely to down the aircraft if they did sustain a direct hit. Clever that.