3 ms·

Well it depends on context I would say. Like first you have to consider sample size. The more you break something down the lower the sample size becomes, and th

by im3w1l 2y ago

Well it depends on context I would say. Like first you have to consider sample size. The more you break something down the lower the sample size becomes, and the more breakdowns you try, the more likely you will find some kind of spurious pattern. But let's say the effect is real. Then you have to start considering what is causing why, which is highly context dependant. To take the example of gender bias in the grad school admissions, men were more likely to be admitted but the effect reversed when breaking down by department. Hypotheses come to mind: A department being easy to get into causes a higher male ratio. (Subhypotheses: Maybe men want to take it easy? Maybe women seek out prestige?) High male ratio of applicants to a department causes it to become easier to get into. (Maybe funding flows to male departments?) There is some kind of unknown factor that both causes a high male ratio and a high rate of admissions (Maybe a booming sector attracts men and leads to easy admissions?) With all these possibilities I think it should become clear that there can't be a general solution to your question, you have to consider the context and dig deeper.

cubefox 2y ago
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

by im3w1l 2y ago

cubefox 2y ago

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