Monday, May 14, 2007

Statistics - Yawn!

Is yawning contagious? From my experiences I would have to say "yes", but this is "anecdotal" (maybe it is just me?). So a more scientific examination is required. Luckily this question was put to the test on Mythbusters, a TV-show that tries to debunk (or prove) popular myths with scientific experimentation. They had done an experiment, which had "proven" that yawning was contagious, because there was a clear difference in % of people who yawned after they were "yawned at"; 29% yawned vs. 25% who were not yawned at.

To my surprise, Mythbusters were wrong: A clever nerd calculated the correlation of the data, (if the difference is significant or just chance), and showed it to be chance (or more scientifically put: the correlation coefficient was smaller than 0.1). This was surprising to me, because I believed that the 29-vs-25% was proof for my experiences. When I read an article in a dutch newspaper about yawning, (sent by my father who miraculously knew what I had been reading about online), I felt a strong urge to yawn...

A few days later, I read about something called Benford's law.
It says that numbers in everyday life seem to follow a surprising "law of digits". As a result, many things around us tend to be numbered much more often with "1" (33%) than with any other number. For example, house-numbers are most likely to start with a "1", but also stock-quotes, the size of files on computers, number of headlines etc. I had never heard of this law. Even stronger: I had never had the experience of noticing that numbers occur irregularly.

Science (or more specific math) is often used to quantify our suspicions (or Benford's suspicions in the second case). As with the "the show with 3 doors" problem, the results sometimes seem counter-intuitive. For me this shows that on many occasions, our mental abilities cannot grasp certain facts of life just from observation.
We can only grasp them by applying a method (math) to them, after which they are shown to be "true". We then choose to accept these things as "the truth", and become foolish to believe otherwise.

In the first case, I had observed that yawning makes me want to yawn, and I correlated it. That this is wrong, I still find hard to believe (which makes me, in effect, more "foolish"). In the second case, I had never correlated the frequency of occurrence of the number one to an uneven distribution of numbers, but I have no problem believing this.

And how about you, did you yawn reading this?