Matching Conditional Independence Assumption

#1
Hello everyone,

I am a newbie in statistics and got stuck with an exercise.
I am not sure if I am in the right thread but I didn't know where to categorize Matching into. I've got data from Berkeley 1973: "Top 6 departments by enrollment".
Can somebody explain me why the independence condition makes sense in this case? The outcome is "total percent admitted", the treatment is "gender" and X is "field of study". In my opinion the independence condition should be violated because even if field of study is given gender isn't independent with admission rate. What are your thoughts about that? Is the independence condition plausible in this case?

Thank you very much
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
Can you define what you mean by independence condition? Independence between what or conditional on what. Different instructors may use varied terms and definitions.
 
#5
@hlsmith

Okay, so basically i have a dataset for major application with male and female applicants. They use gender as treatment. I need to explain why gender (the treatment) given the field of study is independent from the outcome ( Total Pct. Admitted). Outcome ⊥ Gender |Field of Study

Thank you in advance!
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
OK. Well, if you are assuming a confounding triangle, controlling for field of study closes the backdoor path from outcome through field of study back to gender. But wouldn't make the two variables independent.

However, if I am following what you wrote, you could have a mediated effect, Gender -> Field of Study -> Outcome. Given this set-up, controlling for Field of Study would make the outcome independent of gender given there are no other open paths between gender and outcome.