I want to briefly go over this garbage study claiming to prove that brain size "causes" a difference in IQ between men and women. I plan on writing something more in depth, but I haven't seen any good discussion of this study's huge flaws yet.
First, it needs to be said that its consensus that theres no difference in average IQ (I'm ignoring the fact that IQ is meaningless here btw) between men and women. Any observed differences are due to specific subtests that are biased in some way.
Second, the idea that a larger brain size "causes" IQ is one of the most absurd ideas of IQ "researchers." Theres no actual proposed causal mechanism, no hypothesis as to *how* this happens, beyond tautology like "more neurons = smarter!!!"
Now, that said, this study is incredibly flawed. First, it didn't rely on raw tests but rather the "g factor," a reified construct with no empirical evidence to support it (see Mismeasure of Man). To compare it across gender, it used the Method of Correlated Vectors
For one, the authors, when they match participants on IQ scores, they find that the gender differences in brain size are not at all attenuated, nor within participants at large. This, obviously, goes against any causal hypothesis. However...
...the authors dismiss this because of the fact that...

Brain size correlates with IQ. Nevermind mediating factors, apparently correlation = causation!

The other reason is that the authors point out the correlation is weak, so other variables are at play
Which...

Yeah, no shit, but if this is causal we should expect significant attenuation of results! Mediating variables be damned to these authors!
Now, how do they claim they found mediation?

Well, they didn't; they ran a series of correlations with MCV and found that they were related to the "sex difference effect size."
Updating this thread because I used the wrong graph-

The authors use a variety of tests to compute their "g factor." However, upon closer examination theres a problem here
For one, three out of ten of the tasks aren't related to IQ but are executive function - tasks of day to day functioning.

Specifically, "card sorting," "list sorting," and the "flanker task." I'll go over these one by one.
I'm also not aware of many investigations into gender differences, so the results available are odd and unique for this.
As such, a third of the measures are unrelated to the task at hand and shouldn't have been included!

Brief note, authors try to justify this by citing Kane et al saying they're related; but this is just an overview of these measures correlating to a brain region!
On to the two vocabulary tasks - vocabulary size & oral reading recognition test.

The fact that these find a difference favoring men is odd, when it's well known that women outscore men in verbal areas (again due to socialization) https://psycnet.apa.org/doiLanding?doi=10.1037/a0036620
The vocabulary test is the Peabody Picture Vocab Test IV. Previous versions of this in representative samples (Add Health) found no substantial differences. I wasn't able to find the normative data, but the fact that this is observed is contrary to what's known
As such, it can be seen that the data used here is either unrelated to IQ, or highly biased by the sample! This is supported when viewing their table of partialling out "g." This comes from a mix of bias from each of these subtests
The authors also derive a "restricted" g based on four of the tests - Ravens, PPVT, oral reading, and the working memory executive function one. As it uses a measure of executive function & measures on a likely biased sample, the criticisms still apply.
The authors also do claim to do an independent mediation analysis, but this rests on the MCV correlations. As such, these same issues apply to their analysis
To conclude, this study is horrifically bad and contradictory in nature, and its amazing that the authors were even able to gain access to the data. The fact that this was published reflects the sorry state of "IQ" research in publishing complete hogwash
I'd also like to add that, as per the HCP data acquisition, the authors had to submit an overview of how they planned to use the data. This means that, unless the authors lied, the HCP *APPROVED* this study design!
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