Despite what you may have been told, there is a positive correlation between brain size and IQ score. A recent paper in the journal Intelligence looks at the correlations between IQ and specific brain structures. Here are the study highlights:
“Brain size is known to correlate with general intelligence (g).
It is unclear which other neuroimaging variables contribute beyond total brain size.
We model multiple brain measures and g in a large sample aged around 73 years.
All brain variables together account for around 20% of variance in g.”
peakmemory 
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