Since August 2007, eleven detached feet have been found in the borderland of British Columbia, Canada, and Washington, United States. They had been disarticulated and no bodies have been found, despite the even more bizarre fact that all of them were wearing sneakers. Some of them even sported socks.
Asked by the press, experts called the series of discoveries “astounding” and “almost beyond explanation”. Unusual theories were brought to surface, ranging from a shipwreck or an airplane crash, from which the corpses have never been recovered, to the one claiming that the feet could have come from the 2004 Tsunami in the distant island of Indonesia. In fact, one of the feet was wearing a sneaker sold mainly in India, and almost all of the sneakers had been manufactured before 2004.
There was also the Hollywood inspired fear of a psychopath in action, one obsessed with cutting off feet in sneakers. The explanation, however, lies somewhere in the story of the crazy Statistician.
Abraham Wald was a peculiar Jewish mathematician born in Europe who migrated to the USA to escape from the Nazis. Wald applied his brains to a seemingly simple task: evaluating airplanes’ vulnerability. To do so, he observed the aircrafts full of holes that came back from the front. Quite simple, right? One should reinforce the more damaged patches to give them better chances of a successful return.
However, after elaborating sophisticated analysis techniques, his unique recommendation may sound insane. Wald suggested that the patches that had not been damaged were actually the most vulnerable, and they were the ones where armour should be added first. Something like wearing a band-aid where there is no wound. What for?
The answer is in the aircraft he analysed – they were the ones that had actually returned from the front. Wald’s insight was taking took into consideration that the airplanes that had returned were the ones that had made it through all the misadventures. The holes were a tell-tale sign of the strongest spots, the ones which could resist the mishaps, not the weakest areas. It was the other way round: the pristine spots pinpointed the places that could not be hit, otherwise the planes would have been lost in combat and would never be analysed by him back at home. The ones that did return with intact weakest areas had been lucky.
Wald’s analysis considered what is called selection bias: the data set has already been selected somehow, and a proper analysis must consider that. Here is another example: have you ever wondered why the line is never busy when when you call a wrong number?
Actually, we only realize we dialled the wrong number when someone on the other end answers the phone. We keep on our minds a very peculiar data selection. If the call is left unanswered, we hear the busy line tone without ever realizing we dialled the wrong number. An appalling mystery arises if we do not take into account that the data we are considering has been selected already by some process.
Which brings us back to the severed feet mystery. The solution to this conundrum does not involve any huge accident, nor any Tsunami dragging feet along for millions of miles away, and thankfully it doesn’t involve an electric saw psychopath either.
The simple answer is that the feet belong to people that committed suicide jumping into the waters nearby the area. Those that could be identified were linked to depressed individuals who had been reported as missing. There was no sign whatsoever that the limbs had been separated with the use of any tool. On the contrary, those extremities detaches as part of the natural body decay process and the most recent foot found was still connected to the leg bones.
But why were all of them wearing sneakers? It cannot be just by accident, and indeed it wasn’t. The truth is, sneakers are designed to be light, and so they usually float in water. The suicide victims who wear heavier shoes end up having their feet sunk to the bottom of the waters, despite being separated from the rest of the body. On the other hand, the ones who were wearing sneakers had their feet floating for a while until some of them reached the coast. The one to blame for picking the feet in sneakers is not a psychopath; it is the natural water buoyancy.
Exactly like the hit airplanes, exactly like the busy line, the cut off feet mystery is the result of a peculiar and a rather morbid selection bias. It could sound quite depressing, because it means there are many more feet out there to be found that belonged to suicidal people. Those who wear shoes will hardly ever be found.
In order not to end it on such a dark remark, it is worth pinpointing that even this article displays a biased selection. Only a story with a title that draws attention end up getting a post that you, dear curious reader, have followed so far. It worked, didn’t it? Since you are reading this far, since you have been selected, I can assure you I know it did. Like all the other news, it is easier to sell tragic stories, but that does not mean that the world is a more and more terrifying place.
There is a whole lot of good news, of small gestures of kindness that will never show up on the breaking news. Any analysis, even if not quite rigorously statistical, must take those into account, and I hope that getting to know what selection bias is and its importance helps you face things in a different way. [via Marginal Revolution, BoingBoing]
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