statistics · traps · cause
Berkson's paradox
The group you kept can invent a link.
Two traits can look negatively related inside a selected group even when they are unrelated, or positively related, in the whole population. The selection itself creates the apparent link.
Students are admitted if they are strong in either math or sports. What do you see inside the admitted group?
In the full population, math skill and sports skill are independent.
The school admits anyone who is high on at least one.
Students who are low on math must have been high on sports to get in, and students who are low on sports must have been high on math.
Inside the admitted group the two skills look negatively related.
The link is created by the way the sample was selected.