To be honest, I find these correlation a bit unsettling. Clearly, there is more to intelligence than brain size, or classic geniuses like Albert Einstein, who had an average-sized brain, would have been out of luck! It is important think about how we should actually define intelligence, and to keep in mind that the studies cited above only show a correlation between brain size and a person’s score on an intelligence quotient test. Although IQ is historically the most widely used intelligence measure, by no means does it account for all aspects of human intelligence, nor is it an entirely consistent readout of cognitive ability between individuals. Furthermore, a closer look at the results of the gene-association study reveal that most of the relationship the authors found between HMGA2 gene variations and cranial size could be accounted for by the fact that the gene is also correlated with human height. Correlational studies have only established a weak to moderate linear relationship between brain size an intelligence, which is enough fuel to ensure that the brain size and intelligence hypothesis doesn’t burn out, but does little to explain the true basis of human cognitive capacity.
You might also want to look at the paper Decreases in Brain Size and Encephalization in Anatomically Modern Humans i have linked here - https://news.ycombinator.com/item?id=36833133