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 (first chapter with the Gates story free here). The Gates Foundation certainly spent a lot of money, along with many others, pushing for smaller schools and a lot of the push came because people jumped to the wrong conclusion when they discovered that the smallest schools were consistently among the best performing schools.
States like North Carolina which reward schools for big performance gains without correcting for size end up rewarding small schools for random reasons. Worst yet, the focus on small schools may actually be counter-productive because large schools do have important advantages such as being able to offer more advanced classes and better facilities.
Schools2 All of this was laid out in 2002 in a wonderful paper I teach my students every year, Thomas Kane and Douglas Staiger’s The Promise and Pitfalls of Using Imprecise School Accountability Measures.
In recent years Bill Gates and the Gates Foundation have acknowledged that their earlier emphasis on small schools was misplaced. Perhaps not coincidentally the Foundation recently hired Thomas Kane to be deputy director of its education programs.