Cohen's d - how many standard deviations difference there are between mean values of two distributions

Course
#1

Cohen’s d is how many standard deviations difference there are between mean values of two distributions.

Here’s an excellent interactive resource for visualising what that means.

I wonder when we say there is a one standard deviation difference what standard deviation are we referring to? If we say there is a two standard deviation difference between women’s and men’s heights for example?

Does this matter for height for example? The variability of height in each population differs, so when we say the mean differs by one standard deviation what do we mean, the two populations have different standard deviations? Is it one standard deviation of the female population or the male, or one standard deviation of the whole population?

#2

Cohen’s D is the number of standard deviation between the means of the two distributions using the standard deviation of the combined distributions.

With respect to height, male and female within-sex variability is pretty similar, although males do have a bit more variability (as they do for most traits).