Understanding spurious correlation in data-mining

Last May, Dave at Euri.ca took at crack at expanding Gabriel Rossman's excellent post on spurious correlation in data. It's an important read for anyone wondering whether the core hypothesis of the Big Data movement is that every sufficiently large pile of horseshit must have a pony in it somewhere. As O'Reilly's Nat Torkington says, "Anyone who thinks it’s possible to draw truthful conclusions from data analysis without really learning statistics needs to read this."

* If good looks and smarts are distributed normally, and

* If good looks and smarts have nothing to do with each other, and

* If movie producers want both smarts and looks

* Then, by observing employed actors we’ll assume that looks and smarts have a negative correlation

* Even though we constructed this experiment with no correlation

Here’s a graph of 250 randomly generated points (with no correlation). With the red circles representing “actors who are smart and good looking enough to get a job (looks+smarts>2), and lighter blue x’s representing “people who wanted to be actors”

Clearly if we only look at actors with jobs, we’ll see a clearly negative correlation between smarts and good looks. In fact, some brilliant actors are less attractive than an average person, and some gorgeous actors are dumber than an average person. Even more interesting though, is that if we try to rule out bias by looking at aspiring but unsuccessful actors as well, we’ll find that they exhibit a similar correlation...

You’re probably polluting your statistics more than you think (via O'Reilly Radar)