What we're seeing is that female students at Stanford are less concentrated on a single major than the male ones. As a result, their top pick isn't as high as the male top pick. I'd guess that the distribution of female majors is higher entropy than the male one.
Simpson's paradox would be if there was some second confounding variable that corelated to gender which was causing these results. There might be, but I'm not seeing it.
Pick any subject where men are under-represented and you can find, if you look for it, groups who are (rightly) trying to fix it.
Men do face discrimination in nursing. However, men are still paid more on average than female nurses[1]. Make of that what you will. The thing I find most striking is that before the 20th century, most nurses were men and in the early days of computing there was a much higher number of women in the field.
[1] http://medcitynews.com/2015/03/male-nurses-earn-maybe-gender...
https://www.reddit.com/r/nursing/comments/1l1k75/any_male_nu...
http://www.jacksonvilleu.com/resources/career/men-in-nursing...
There is a gender gap even within specific nursing professions but it's not nearly as extreme as that.
Only ~10% of registered nurses in the United States are men[1].
> According to the Census Bureau, men made up about 9 percent of registered nurses in 2011, roughly a three-fold increase from 1970.
[1] https://www.census.gov/newsroom/releases/pdf/cb13-32_men_in_...
Computing and IT started to come of age during the post WW2 boom so there would have been a lot of women with the math background to make programming and working with computers somewhat of a logical next step in ones career.
Coincidentally, these woman who had math backgrounds were also some of the fist to have their jobs automated out of existence (the woman who calculates someone's insurance premium is replaced with a box of punch cards).
Just speculating but it wouldn't be a stretch to see how when choosing between going home or switching careers the woman who didn't become the stereotypical 50s-60s housewives as their jobs were automated found new jobs writing punch cards (programming) and operating computers.
(i'm in a hurry, probably lots of grammar mistakes in that)
Correct, that was the case with a number of the roles. Those roles were sort of like the modern day CRUD development and things that (mostly) get automated away.
However, Grace Hopper[1], Betty Holberton[2], Frances Spence[3], along with around a half dozen of the original programmers of the ENIAC[4] would disagree that they were only filling a secretary like position.
In reference to my previous comment, I mostly found it surprising that these pioneers didn't lead to more women pursuing CS early on. I suppose it has more to do with the cultural trends that came after the war as you said yourself.
[1] https://en.wikipedia.org/wiki/Grace_Hopper
[2] https://en.wikipedia.org/wiki/Betty_Holberton
I suggest you reflect on this and what people say and mean when they talk about topics relating to privilege, power, gender, race, wealth, patriarchy, etc., and you'll get it, too.