At Extremes, the Standard Deviation Dominates Comparative Means
In a prior post, I talked about standard deviations in a theoretical model, that was somewhat bolstered by empirical info.
Well, guess what.
Here's a paper in Nature showing that standard deviation effect:
Gender differences in individual variation in
academic grades fail to fit expected patterns
for STEM
R.E. O’Dea 1,2, M. Lagisz1
, M.D. Jennions 2 & S. Nakagawa 1
Fewer women than men pursue careers in science, technology, engineering and mathematics
(STEM), despite girls outperforming boys at school in the relevant subjects. According to the
‘variability hypothesis’, this over-representation of males is driven by gender differences in
variance; greater male variability leads to greater numbers of men who exceed the performance
threshold. Here, we use recent meta-analytic advances to compare gender differences
in academic grades from over 1.6 million students. In line with previous studies we find strong
evidence for lower variation among girls than boys, and of higher average grades for girls.
However, the gender differences in both mean and variance of grades are smaller in STEM
than non-STEM subjects, suggesting that greater variability is insufficient to explain male
over-representation in STEM. Simulations of these differences suggest the top 10% of a class
contains equal numbers of girls and boys in STEM, but more girls in non-STEM subjects.
So they do show differential results -- you've got overlapping distributions with the female average being higher.
This is not based on real data, but model data:
And so this is what they inferred based on actual school grades:
The bottom graph is the female-to-male ratio at different percentile levels.
Basically, for the vast majority of levels of academic achievement, girls do better than boys, whether STEM or non-STEM. Indeed, the average achievement for girls was higher for both STEM and non-STEM subjects. But boys did have a greater standard deviation, so once you get into the right tails, you see more boys than girls. For STEM subjects, the crossover is at the top 10%, and for non-STEM it's for the top 2%.
This has obvious repercussions in professions where top academic performance is important... but also has repercussions when just being a bit above average is good enough. One would expect women could dominate those fields. Even most STEM-related professions really don't require being in the top 10%.
Anyway, I see this as an observation, not a problem. That women tend to be more close to their population average than men are is not something that can necessarily be fixed. Given that the averages are higher - can you really make them more variable, in terms of population distribution?
And why would you want that?
I mean, being a female weirdo myself, I may like it to be more socially acceptable for a woman to be a weirdo... but I'm not that sure it's all that socially acceptable for male weirdos.... So. I still don't see that males dominate the top 10% in STEM is a problem. Doesn't mean there's no women around. Just fewer than men.
Well, guess what.
Here's a paper in Nature showing that standard deviation effect:
Gender differences in individual variation in
academic grades fail to fit expected patterns
for STEM
R.E. O’Dea 1,2, M. Lagisz1
, M.D. Jennions 2 & S. Nakagawa 1
Fewer women than men pursue careers in science, technology, engineering and mathematics
(STEM), despite girls outperforming boys at school in the relevant subjects. According to the
‘variability hypothesis’, this over-representation of males is driven by gender differences in
variance; greater male variability leads to greater numbers of men who exceed the performance
threshold. Here, we use recent meta-analytic advances to compare gender differences
in academic grades from over 1.6 million students. In line with previous studies we find strong
evidence for lower variation among girls than boys, and of higher average grades for girls.
However, the gender differences in both mean and variance of grades are smaller in STEM
than non-STEM subjects, suggesting that greater variability is insufficient to explain male
over-representation in STEM. Simulations of these differences suggest the top 10% of a class
contains equal numbers of girls and boys in STEM, but more girls in non-STEM subjects.
So they do show differential results -- you've got overlapping distributions with the female average being higher.
This is not based on real data, but model data:
And so this is what they inferred based on actual school grades:
The bottom graph is the female-to-male ratio at different percentile levels.
Basically, for the vast majority of levels of academic achievement, girls do better than boys, whether STEM or non-STEM. Indeed, the average achievement for girls was higher for both STEM and non-STEM subjects. But boys did have a greater standard deviation, so once you get into the right tails, you see more boys than girls. For STEM subjects, the crossover is at the top 10%, and for non-STEM it's for the top 2%.
This has obvious repercussions in professions where top academic performance is important... but also has repercussions when just being a bit above average is good enough. One would expect women could dominate those fields. Even most STEM-related professions really don't require being in the top 10%.
Anyway, I see this as an observation, not a problem. That women tend to be more close to their population average than men are is not something that can necessarily be fixed. Given that the averages are higher - can you really make them more variable, in terms of population distribution?
And why would you want that?
I mean, being a female weirdo myself, I may like it to be more socially acceptable for a woman to be a weirdo... but I'm not that sure it's all that socially acceptable for male weirdos.... So. I still don't see that males dominate the top 10% in STEM is a problem. Doesn't mean there's no women around. Just fewer than men.