§ How to fairly compare groups
Why is this a key argument? 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!