Whenever we observe a relationship between two variables (discrete or continuous), there is always the question whether this relationship is a Cause-Effect relationship or whether it is due to a latent (unobserved) variable:
Can we understand this in the Berkeley Admissions case?
Majors A and B are very popular with the men - 1385 men applied vs. 133 women. Majors A and B are also easy to get in - about 2/3rd's of the applicants (men or women) get accepted. So although men and women have the same acceptance rate, 10 times as many men are accepted because 10 times as many applied.
Majors C-F are more popular with the women - 1346 men applied vs. 1702 women. Majors C-F are hard to get in - about 1/4th of the applicants (men or women) get accepted.
If in an observational study (as opposed to a clinical trial with random assignments to "treatment" and "control") we find an relationship (association) between two variables it is usually very hard (impossible?) to decide whether it is due to a cause-effect relationship or whether there is a latent variable responsible for the relationship. In the Berkeley case it turned out that Major was a latent variable. A list of other potential latent variables includes:
1) Prior educational achievements
2) Age
3) Financial situation of parents
and so on
Note that we could determine here that Majors is a latent variable explaining the relationship between Gender and Acceptance because we had the data to do so! So generally in a study you want to "measure" as many variables as possible because you won't know ahead of time which of them might turn out to be important.