Extraordinary claims. Ordinary investigations.

Mysterious severed feet and the Crazy Statistician

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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.

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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.

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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.

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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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Posted in Fortean,Skepticism | 8 comments

8 Comments so far

  1. […] those severed human feet that were being reported last year? As it turns out, there’s a very simple, if somewhat gruesome, explanation for them. Filed under Amusing/Interesting/Appalling Comment (RSS)  |  Trackback […]

  2. Erik R. January 9th, 2012 12:14 pm

    Pure genius. Well done to tie such a nice bow at the end.

  3. Jake January 9th, 2012 7:11 pm

    I take this approach when reading reviews online for a product I’m considering buying. Let’s use Amazon as an example since they use a 1-to-5 grading scale. I generally only take into account the ones and the fives. Having worked in retail I know that a higher percentage of people who have a bad experience will tell some one else then someone who had an excellent experience. This is generally why so many companies are interested in getting you to take their customer satisfaction surveys. The folks who had a bad experience are going to search out the surveys or any means of spreading the word that their experience was bad. The folks that had a good experience don’t want to take the time to let other’s know because they’re happy with their experience and that’s all that matters. Most folks if they were looking at reviews and there were 10 five star reviews and 10 one star reviews would move along to another product. But I would also weigh the fact that the 10 bad reviews probably represent around 60% of the people who had a bad experience while the 10 good reviews statistically would only represent maybe 15-20% of the people who had a great experience. Based on that info even though the one star vs the 5 star reviews are equal you can surmised that far fewer people had a bad experience than those that had a great one.

  4. julianpenrod January 10th, 2012 3:32 pm

    A lot of doggerel description, intended to con the gullible and who are afraid to admit they don’t understand the world well enough to recognize when they’re being had.
    What about the issues the article carefully does not address?
    Why is this phenomenon only happening now?
    Big fish will swallow anything, even a foot in a sneaker.
    A sneaker may float, but, with a human foot in it, it is, at best, unlikely. Among other things, many sneakers have absorbent linings, and, filled with water, they would hold the sneaker down. And a foot wearing a sock should be even less buoyant. They float only if they have been set on the water like a toy boat.
    Why is this only happening there? There are many places, supposedly, where people are depressed enough to take their lives and supposedly where they had.
    his blog, basically, is devoted to trying to make at least the gullible and malleable less trusting of their correct innate senses and come running to the New World Order for instructions on how to think.
    If the blogger is so aware of deriving reliable proofs, what is their “evidence”, not counting things dutifully issued by government offices and “laboratories”, evidence people can assemble on their own, to double check what they are told to think, that Arab men belonging to al Qaeda crashed commercial jets into the Twin Towers and the Pentagon? It should be mentioned that a study recently suggested it was a chemical reaction, like a demolition explosion, and not the weight of the collapsing sections, that brought the Twin Towers down.
    Don’t expect any real address of these issues, though. The New World Order acts only by lies, trickery, unjustified dismissials, arrogance, contempt, mockery, vulgarity. But failing to actually address these matters, will be an admission of craven intent.

  5. Anthony Bragalia January 31st, 2012 7:57 pm

    I must concur with julianpenrod, why is this strange foot phenomena being reported only there and only recently?

    And just precisely where are these ‘waters nearby the area’ (as you say) into which all of these people are jumping that their feet would be found like this? Is there an abnormal incidence of suicide in that region? Are other suicide-prone areas of the world also experiencing recent outbreaks of detached floating feet?

  6. Mori February 1st, 2012 11:30 pm

    There are several bridges nearby, you can look up a map of the area. There’s also been an experiment with a sneaker with a GPS tracker inside which also showed that feet would indeed wash up ashore — I saw reference to it in a recent TV show, sorry for not presenting further reference to it.

    Granted, there could be a different factor responsible for those feet washing ashore, but it could also be an “invisible gorilla” (see http://forgetomori.com/2008/skepticism/attack-of-the-invisible-gorillas/ ), that is, a phenomenon that is not actually new but due to a confluence of reasons, usually media exposure, starts being more noticed. It’s common for “invisible gorilla” cases to have experts saying “they never saw anything like it before” when more thorough research shows this does not mean the phenomenon wasn’t actually happening before (such as animal “mutilations”, or the the guardrail shards mystery in Japan).

    Needless to say, this is only my take on the subject. One would only have a more definite evidence of the explanation advanced here (which, of course, isn’t originally mine) if one could actually track all the series of events leading from a confirmed suicide from a bridge nearby, to the subsequent find of a naturally detached feet washing up ashore. That would be unlikely for rather obvious reasons given that the missing piece is exactly the one of having a confirmed method of suicide, we actually know from the evidence the feet were naturally detached.

  7. Nema Tode February 2nd, 2012 1:46 pm

    A few years ago I was taking a walk on a remote beach in California with a friend. We climbed up on some boulders in the surf and settled on a large, flat boulder to have a picnic. We laid out a blanket, set out our nice picnic and quietly started eating and talking, when I saw something move out of the corner of my eye. It was a small, black crab peeking over the edge of the boulder. Then I saw something move across from me–it was a small black crab on the other side of the boulder. Then I noticed little jerky movements on all sides of us–dozens of small black crabs advancing, looking at us sideways as if they were plotting against us. It was like a horror movie. I had a moment of real panic but I knew deep inside that there were no human-killing crabs in California, so I tried to think of some reasonable explanation. Then it occurred to me that my friend and I had been jumping around on the rocks and talking really loudly as we approached our boulder. Before we arrived, every boulder on the beach probably had dozens of crabs on it, but as we approached they scurried into hiding before we saw them. Then after we sat down and stopped moving, they gradually came back to their stations on the rock, but each one stayed about 4 feet away from us. This created a circle of crabs around us, and the illusion that they were surrounding us, but really they were avoiding us. Was my initial fear a case of selection bias? Or was it a different logical fallacy?

  8. Thomas January 17th, 2013 11:12 pm

    The picture is from the tv serie lost

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