October 19, 2020 2:27 PM

An "Achievement Gap" Is Usually A Participation Gap

People often look at the difference between the highest-rated male chess player in a group and the highest-rated female chess player in the same group and conclude that there is a difference between the abilities of men and women to play chess, despite the fact that there are usually many, many more men in the group than women. But that's not even good evidence that there is an achievement gap. From What Gender Gap in Chess?:

It's really quite simple. Let's say I have two groups, A and B. Group A has 10 people, group B has 2. Each of the 12 people gets randomly assigned a number between 1 and 100 (with replacement). Then I use the highest number in Group A as the score for Group A and the highest number in Group B as the score for Group B. On average, Group A will score 91.4 and Group B 67.2. The only difference between Groups A and B is the number of people. The larger group has more shots at a high score, so will on average get a higher score. The fair way to compare these unequally sized groups is by comparing their means (averages), not their top values. Of course, in this example, that would be 50 for both groups -- no difference!

I love this paragraph. It's succinct and uses only the simplest ideas from probability and statistics. It's the sort of statistics that I would hope our university students learn in their general education stats course. While learning a little math, students can also learn about an application that helps us understand something important in the world.

The experiment described is also simple enough for beginning programmers to code up. Over the years, I've used problems like this with intro programming students in Pascal, Java, and Python, and with students learning Scheme or Racket who need some problems to practice on. I don't know whether learning science supports my goal, but I hope that this sort of problem (with suitable discussion) can do double duty for learners: learn a little programming, and learn something important about the world.

With educational opportunities like this available to us, we really should be able to turn graduates who have a decent understanding of why so many of our naive conclusions about the world are wrong. Are we putting these opportunities to good use?

Posted by Eugene Wallingford | Permalink | Categories: Computing, Personal, Teaching and Learning