Grasping Reality on TypePad, by Brad DeLong

Yes, it's time for our once-every-three months websurf over to Donald Luskin. Why? As a public service: somebody needs to lay down a marker that he simply does not know what he is talking about, and that anyone who believes anything he writes without very careful verification is asking for big trouble.

And it is unbelievable. You don't have to read a dozen paragraphs before you run across something so bats--- ignorant that it should cause every National Review editor and writer to resign in shame, move to Rwanda, and take up a life of anonymous service to others.

But I don't have the heart to surf over and read any more. So let me pull out a true turkey from the archives: the time Luskin denied the existence of the entire discipline of statistics:

The Conspiracy to Keep You Poor and Stupid: The Times and the Journal cite many authoritative-sounding studies.... But to get an accurate picture [of inequality]... you'd have to track hundreds of millions of individuals.... [N]one of this is reliable... the Panel Study of Income Dynamics... tracks only 8,000 families out of a U.S. population of 295 million individuals.

The whole science of statistics exists because Luskin is wrong. As long as you can take a random sample of your population, you can find out an enormous amount about the population from a relatively small number of observations. You can find out what proportion of rich people had poor paretns, or what proportion of twenty year olds think they will graduate from college, or pretty much any other average proportion that you want.

Now the "random sample" part of this is very important. But if your sample is random--if the fact that the yes-no pattern of observations so far makes it no more (or less) likely that you next observation will be a "yes"--then the law of large numbers tells us that the sample average you compute will converge to the true population average at a frighteningly rapid speed.

The standard demonstration of this is to repeatedly flip a coin and count the excess proportion of heads over tails. We know that--with a coin flipped and caught in the air by a human being at least--the population average taking all coins that have ever been flipped of the excess proportion of heads is zero. How many observations do we have to take--how many coin flips--before the sample average converges to this population average of 0% excess heads?

Let's see. Here's one run of 1,000 "flips" from Excel's internal random number generator:

Here are ten more:

Here are ten more:

Impressive, no?

Try some yourself.

You could have a population of 295 million flipped coins. Yet you don't need to look at "hundreds of millions" of them to determine what is going on. Looking at a couple of thousand will do.

This is the principal insight of the science of statistics. it is an important insight. It is a powerful insight. It is also not an obvious insight--that's what makes it powerful and important. Yet it is one that Donald Luskin has never managed to grasp.

That's really sad.