Well, I think the standard explanation for this case was something this: Being male (X) causes you psychologically to prefer STEM departments, which are more e

Well, I think the standard explanation for this case was something this: Being male (X) causes you psychologically to prefer STEM departments, which are more economically useful, which means they are better funded, which means they are larger, which means they can admit more people, which means you are more likely to be admitted (Y). So X is positively correlated with Y. However, being male (X) also causes you to be less likely to be admitted in each individual department (parts of Y), e.g. because people in admissions offices have some degree of anti-male bias, known in psychology as women-are-wonderful effect [1]. So X is negatively correlated with the parts of Y (being admitted to individual departments). So in this case, X does cause both Y, via the male psychological preference for STEM, and not-y_n (for {y_1, y_2, ..., y_n} = Y, for an n-partition of Y), via anti-male admissions bias like women-are-wonderful. So the previously most plausible initial explanation for why X causes Y (university being biased again women) is indeed false. I guess the lesson is that detecting a case of Simpson's paradox (when partitions of a variable like Y have different direction of correlation with some other variable X than the entire variable Y) can point to causal explanations being different than what they would naively seem to be. [1] https://en.wikipedia.org/wiki/Women-are-wonderful_effect https://en.wikipedia.org/wiki/Women-are-wonderful_effect