Department of Awful Statistics: Small Schools Edition

It seems even Bill Gates can be taken in by poor understanding of statistics.  Specifically, this one:

The chart at left, for example, shows by size the percentSchools1age of schools in North Carolina which were ever ranked in the top 25 of schools for performance.  Notice that nearly 30% of the smallest decile (10%) of schools were in the top 25 at some point during 1997-2000 but only 1.2% of the schools in the largest decile ever made the top 25.

Seeing this data many people concluded that small schools were better and so they began to push to build smaller schools and break up larger schools. Can you see the problem?

The problem is that because small school don't have a lot of students, scores are much more variable.  If for random reasons a few geniuses happen to enroll one year in a small school scores jump up and if a few extra dullards enroll the next year scores fall.   

Thus, for purely random reasons we would expect small schools to be among the best performing schools in any givenyear.  Of course we would also expect small schools to be among the worst performing schools in any given year!  And in fact, once we look at all the data this is exactly what we see.  The figure below shows changes in fourth grade math scores against school size.  Note that small schools have more variable scores but there is no evidence at all that scores on average increase with school size. 

The Gates foundation, which pushed for smaller schools on the basis of this finding, has apparently now acknowledged the mistake.  Victory: math!


Presented by

Megan McArdle is a columnist at Bloomberg View and a former senior editor at The Atlantic. Her new book is The Up Side of Down.

How to Cook Spaghetti Squash (and Why)

Cooking for yourself is one of the surest ways to eat well. Bestselling author Mark Bittman teaches James Hamblin the recipe that everyone is Googling.

Join the Discussion

After you comment, click Post. If you’re not already logged in you will be asked to log in or register.

blog comments powered by Disqus

Video

How to Cook Spaghetti Squash (and Why)

Cooking for yourself is one of the surest ways to eat well.

Video

Before Tinder, a Tree

Looking for your soulmate? Write a letter to the "Bridegroom's Oak" in Germany.

Video

The Health Benefits of Going Outside

People spend too much time indoors. One solution: ecotherapy.

Video

Where High Tech Meets the 1950s

Why did Green Bank, West Virginia, ban wireless signals? For science.

Video

Yes, Quidditch Is Real

How J.K. Rowling's magical sport spread from Hogwarts to college campuses

Video

Would You Live in a Treehouse?

A treehouse can be an ideal office space, vacation rental, and way of reconnecting with your youth.

More in Business

Just In