Tag Archive: statistics

Three Wiki Sixes

(Submitted by friend of the blog, Susan Gerbic of  Guerrilla Skepticism on Wikipedia)

I was preparing for an upcoming Wikipedia workshop.  I chose November 2011 at random to retrieve stats for pages.

The Amityville Horror Wikipedia page had 66,633 views that month.

No way could someone have messed with the numbers because you can’t see how many hits a page receives until 36 hours after the fact.

[EDITOR: Numbers and how we perceive them always make for an interesting subject because they’re a perfect example of of searching with uncertain goals in mind. In the case above, the number was significant because it contained “666,” which some consider the number of the beast reference in a well-known holy text. Combining this with the Amityville Horror, which is a story of a supposedly real haunted house, is what makes the number’s appearance spooky. But it’s not as though this combination is uncommon.

In the example given, the number has 5 digits in total. 666 could have appeared in three possible places (66,6xx, x6,66x, or xx,666) and still caught someone’s eye. Presumably an especially observant person might have caught it spread out, as well (6x,6×6). And that’s sticking ONLY with 666. There are other numbers with classic occult meaning behind them, including 3 (although that does add to the spook factor of the above number ending with 33), 7, 9 (999 being the flip of 666), 11, and of course 13 (reference link).

So presumably any of those sets of numbers showing up in the hits could also grab the attention of someone predisposed to think of them. Some even pay attention to multiples or divisions of those numbers (although that does cover the 33 and 999 already discussed).

And that speaks only to occult numbers. People find significance in all sorts of other numbers, whether they be birthdays, anniversaries, favorite/lucky numbers, or all sorts of unusual examples. Had the number above been any different SOMEONE who looked at it was virtually guaranteed to find a number string that was, to them, meaningful. And small strings of combinations of only 10 digits are ripe for common reuse throughout everything we see. So unlike many of the stories we run on this site, numerical coincidences are probably the easiest to find on a regular basis. And yet… having said that, sometimes they still manage to surprise the heck out of you. And if you happen to be superstitious, I imagine some can be downright scary. But they’re still just coincidences. – Jarrett]

Monty Hall

Monty Hall

I have always been amused and intrigued by responses to “The Monty Hall Problem”, especially when I talk about it to audiences with a high concentration of engineers and mathematicians. If you are familiar with it, but you’ve always struggled with an unsettled feeling of “this can’t be right”, read further and let me know if my explanation of the solution helps to alleviate the discomfort. If you are not familiar, I guarantee you will give your brain a workout by reading on.

First posed to statisticians in 1975, “The Monty Hall Problem” is well-known among academics because it still sparks debate. Many seem to think that disagreements about its solution stem from issues in the clarity of the problem, but I contend that it really stems from human flaws in the way that we process information.

I often discuss this problem in statistics and cognitive psychology courses for several reasons. It is a great exercise in probability calculation and it can be used to teach basic mathematical modeling (and its purpose). An added benefit, since almost all of my students were psychology majors, is that it also illustrates a flaw in human cognition as well as a pattern of problem solving.  Even a knowledgeable statistician feels the need to run simulations to see the solution in action. Even then, fully grasping the mechanisms behind the answer often requires brute force cognition.

In general, human beings have a very difficult time wrapping their brains around concepts of probability. It is much like a visual illusion; we know that the lines are parallel/the circles are the same size/there is no motion, but we can’t make our brains process it in a way that represents that reality. It’s just not how our visual system works. I hypothesize that one of the reasons that probability is such a difficult field for most people is that it involves theory and models, which are distinct from observations and we must represent them differently in our minds to properly deal with them. Applications of probability often involve switching gears from the realm of models to data or vice versa and this is where I think most mathematicians get side-swiped in The Monty Hall Problem.

The Poser

In essence, here’s the problem:

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