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I have a philosophical question about causal relationships inference. Suppose we have UCBAdmission data, where different gender and different department have different admission rates.

> d=as.data.frame(UCBAdmissions)
> d
      Admit Gender Dept Freq
1  Admitted   Male    A  512
2  Rejected   Male    A  313
3  Admitted Female    A   89
4  Rejected Female    A   19
...
...
21 Admitted   Male    F   22
22 Rejected   Male    F  351
23 Admitted Female    F   24
24 Rejected Female    F  317

My question is can we do any causal relationships inference on this data? I would say both gender and department would case difference on admission, but how can I know it is gender cause department or the other way around?

In other words, how can I do Bayesian network structure learning on this data? Is it even possible?

Haitao Du
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    You can't do anything causal on this data. No amount of statistical acrobatics will do in this case. – Aksakal Dec 14 '16 at 18:51
  • @Aksakal could you clarify "No amount of statistical acrobatics"? what else if we have, we can do causal analysis? – Haitao Du Dec 14 '16 at 18:52
  • The first and foremost: you dont have data on qualifications of female applicants vis-a-vis male. You can come up with endless number of factors that may throw off any kind of causal analysis you attempt. – Aksakal Dec 14 '16 at 18:55
  • you need a control group. get the same applicant applying as a man and a woman and see what happens to their chances of admission. these things are done in discrimination studies, e.g. the resumes were sent under African sounding names vs. Caucasian sounding names, and the interview requests were analyzes – Aksakal Dec 14 '16 at 18:57
  • @Aksakal While like your 1st comment very much, it is not 100% true: Because gender is almost completely random (ignoring trans people and confounders on both - department choice and survival [a.g. sic parents killing all their boys whose daughters would then maybe more likely apply for psychology]), you could infer the total causal effect of gender on department choice. (That would, however, tell you if that is biologically or through society/education) – jan-glx Dec 20 '16 at 09:24
  • @YAK, gender is random but picking a department by people of different genders may not be random, also the qualification level by gender may not be random too. you can't control for these given his data set. it's very difficult or impossible to control for this effect at all in observational study, in my opinion – Aksakal Dec 20 '16 at 13:57
  • @Aksakal I totally agree. I was just nitpicking on the "anything causal" as you can infer sth. causal - just not what OP wanted to infer. – jan-glx Dec 20 '16 at 14:48

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