: How much of the difference in brain size is attributable to gender, not physical size? I've been reading a paper regarding the effects of gender on grey matter and white matter, and one passage not directly related to the

This is an excellent question. In my attempt to answer it I'll cite sources from the best research on the subject to date, and we'll conduct our own investigation.

Body size vs. Head size vs. Brain volume

In your question, you asked how body size (weight and height) relates to brain volume by gender. Body size is related to brain volume through another measure, head size. Larger body, larger head, larger brain.a Men and women have different body sizes, and different head sizes as well.

Conducting our own investigation

Sample

In the paper you referenced, Gur et. al. looked at 80 healthy (40 male and 40 female) volunteers aged 18-45 years. They used an automated parcellation approach, meaning they used automated image processing on the brain images to derive their measurements.

In our investigation, we'll use data frome the publicly available Human Connectome Project, or HCP. We'll look at 896 healthy (393 Male and 503 female) volunteers aged 22-36 years. HCP also used an automated parcellation software, called FreeSurfer.b We'll use IntraCranial Volume - the volume inside the cranium - to represent head size.

Total Brain Volume - Males vs Females

We see here that men have larger brains than women. We can also see from the linear model results that the estimated mean difference from our sample is a substantial 153.9 milliliters (as compared to ~200 milliliters in Gur et. al. 2001). For reference, this is about 2/3 one of those half pint boxes of milk you used to get at school lunch.

But how much is total brain volume related to head size?

TBV vs ICV

We can see right away that these two measures are highly correlated. It makes sense. Typically, bigger animals -- with corresponding bigger heads -- have bigger brains:

But what you want to know is whether the difference remains after accounting for head size. In other words, is the difference disproportionate to head size?

Adjusting TBV by ICV

Here we use a method called residualizing to remove the effect of ICV on TBV we observed above. You can find the code we're using here, and a reference describing the procedure in detail here.

Let's check the graph of TBV vs ICV again, to make sure the effect is removed.

Revisiting TBV in Males vs Females

Here we'll reexamine the difference between Male and Female brain sizes using the adjusted values.

The difference is still statistically significant, but smaller. The linear model estimates the adjusted average difference to be 23.6 milliliters (compared to 153.9 before). Going back to the milk reference, this is about 1/10 the box, or one sip.

Conclusions

We found that the difference in brain volumes between men and women is partially, but not completely explained by their difference in head sizes.

The difference is smaller, but still there after adjusting. Now your next question may be, so what? Do these differences in brain volume explain anything about behavior or ability? That's where papers like the one you referenced come in.

Gur et. al. suggest in their paper that females compensate for smaller total brain volume by having increased gray matter, and therefore more tissue available for computation. Other studies conclude that in order to understand gender differences in cognitive ability, you have to look closer at the parts of the brain that are activated during different tasks.c

The HCP data could help us test these ideas too, but that's outside the scope of your question.

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