Posts tagged “large numbers”
James B. Stewart wrote a piece about Apple and the Law of Large Numbers. Maybe the article was okay as a whole, but he entirely misrepresented the Law of Large Numbers, which has ab-sa-toot-ly nothing to do with individual corporations and their future growth projections.
How does this slip by the NYT? How does it get by their legions of fact-checkers, statisticians, and Nate Silver? Shouldn't any mention of statistical theory or mathematical theorems be properly represented by a paper that continually pushes the need for better science and math education?
I digress. A fun piece from Dr. Drang has popped up on the blogosphere about this blunder.
Let's start with what the Law of Large Numbers really states. Put simply, it says that the sample mean of a random variable will tend toward the underlying population mean as the number of samples grows larger. For example, Wolfram Alpha says the average height of an adult male is 5′ 9″. If you measured the height of a few randomly selected men, you might get an average for your sample that's quite far from 5′ 9″. But if you increased the size of the sample, the tendency would be for your sample average to move closer to 5′ 9″.
The law does not state that "a variable will revert to a mean over a large sample of results." The Law of Large Numbers says nothing about individual measurements; it's all about averages. And it certainly doesn't "suggest" anything about the future growth of large companies.
If the Law of Large Numbers worked the way Stewart says, you could repeatedly measure the height of Dirk Nowitzki and he'd eventually shrink down to 5′ 9″. I'm surprised the Mavericks' opponents haven't thought of this.
Read the full article here.