Are small schools better? No, just more variable

From Alex Tabarrock at MR:

 

"Did Bill Gates waste a billion dollars because he failed to understand the formula for the standard deviation of the mean?  Howard Wainer makes the case in the entertaining Picturing the Uncertain World "

 

http://www.marginalrevolution.com/marginalrevolution/2010/09/the-small-schools-myth.html#comments

 

This is such a common error it bears reminding ourselves of it.

 

Small schools, small countries, small companies invariably tend to show up at the top of lists -- AND AT THE BOTTOM. This is because small samples tend to be more variable.

 

It's for this reason that the list of the richest cities in the US (where the size cutoff for "city" is at least 25,000 people) tend to have just a bit over 25,000 people. Small cities can be homogeneously rich -- OR POOR. Chicago suburbs have plenty of both types.