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A classic example of "selection bias" involves looking at the performance of professional basketball players. The example goes, among NBA players there is no correlation between height and performance.
Obviously that cannot be generalized to "height has no relationship with being good at basketball for all players", it is just that by the time you are selected to play for the NBA, other features are more important.

What I can't seem to do is to explain this through a DAG. I've come up more or less with this structure:

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But it seems clear to me that here fixing the value "Plays for NBA" to TRUE would not make height independent from performance. Does it mean that the structure of the DAG is wrong? Or is there a better way to show this kind of selection bias?

CarrKnight
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    What's the difference between Playing Skill and Performance? – Adrian Keister Jul 12 '21 at 16:31
  • ah, yes! Performance is observable (say, points scored per game) , skill is not – CarrKnight Jul 12 '21 at 23:18
  • Why not just make it $$\text{player height} \leftarrow \text{plays for NBA} \rightarrow \text{performance}$$ this way, given that someone plays for the NBA, their height is independent from their performance. I am guessing this is what you mean by "The example goes, among NBA players there is no correlation between height and performance." – mhdadk Aug 31 '21 at 13:10

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