This statement becomes evident when comparing different species. Our intelligence is not uniquely related to the volume of our brains, although there is evidence that somehow they both are related. When considering absolute volume, Homo Sapiens never appear at the top of the list. Differences in brain structure appear to be mainly responsible for differences in cognitive performance, not the size of our brain.
For instance, differences in brain size between men and women are well-established, resulting to larger brains for men than for women. However, there are no differences in IQ scores between them.
Structural aspects of our brain are the most important variables for the performance and success than just the size of our brain.