What conclusions would it offer? Among the top 100 chess players I think there are three women. Most people seem to think it's due to some cultural factors or gender discrimination. This could be applied to any asymmetries you might find.
I can ask follow up questions if the answer is known.
But mainly, I want to know if the ratios from my questions don't match the gender ratio in the general population, at which point does the ratio start to diverge?
Was it when a student needs to choose a major? Or when a professor interviews a PhD candidate? Or when assigning tasks and someone getting a less impactful part? Or when deciding the ordering of the authors based on (very subjectively) the contribution?
I suspect you will need to do the research to answer these questions yourself. Sadly you can't even just run a name join because humans don't have primary key uniqueness.
1. What's the gender ratio of scientists with h-index >100? >50? >10?
2. What's the ratio of scientists with missing wikipedia pages breakdown by gender, with h-index>100? >50? >10?
3. What's the gender ratio of scientists of first/second/third authors, on papers with citation >500, >200, >100.