Tuesday, August 20, 2013

Perfectly Normal, Statistically Speaking.

Who, exactly, is normal. Bee has a meditation on this point and concludes that everybody is above average, in some respect at least. If you consider a few hundred parameters, nearly everybody is going to be an outlier in some respect. But is that the right metric? Shouldn't the real question be whether some total deviation from the mean is significantly larger than the deviation expected on the basis of chance?

The classic (but totally arbitrary) test for statistical significance is a result which would be expected purely by chance less than 5% of the time. Suppose that you have a couple of independent, random, normally distributed variables. Then almost 10% of the time (1-(.95)^2), at least one of them will be in the 5% zone. Similarly, with ten such variables, 40 % of the time at least one is in the zone, and for 100 variables, more than 99% of the time.

So if you were to assemble a bunch of the relevant variables (height, weight, strength, agility, vision, leaping ability, etc.) Lebron James is still exceptional - a veritable freak of nature - and you aren't.

Of course I'm a pretty lousy statistician, so somebody ought to check my work. Though I already know my variables aren't statistically independent.