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I'm not making any conclusions myself but I will present whatever evidence I find and let you make a conclusion -
Brain size is irrelevant to intelligence, females have other features in their brains that could make them smarter:
Females > males in school:Although men have bigger brain size which is partly explained by their bigger bodies, women have greater cortical thickness, cortical complexity and cortical surface area (controlling for body size) which compensates for smaller brain size.[68] Meta-analysis and studies have found that brain size explains 6–12% of variance among individual intelligence and cortical thickness explains 5%.[69][70]
A 2012 study published in Intelligence by researchers Miguel Burgaleta and Richard Haier dispelled previous claims that bigger brain size indicates greater male g factor than females. They found greater male brain size was instead associated with greater visuospatial abilities but not with g factor or general intelligence.[73] The study also found no sex differences in g factor among the 100 participants.[73]
https://en.wikipedia.org/wiki/Sex_di...n_intelligenceA 2014 meta-analysis of sex differences in scholastic achievement published in the journal of Psychological Bulletin found females outperformed males in teacher-assigned school marks throughout elementary, junior/middle, high school and at both undergraduate and graduate university level.[121] The meta-analysis, done by researchers Daniel Voyer and Susan D. Voyer from the University of New Brunswick, drew from 97 years of 502 effect sizes and 369 samples stemming from the year 1914 to 2011, and found that higher female performance was not affected by publication year and thereby contradicted recent complaints of "boy crisis" in academic achievement.[121] Another 2015 study by researchers Gijsbert Stoet and David C. Geary in Intelligence found that girl's overall education achievement is better in 70 percent of all the 47–75 countries that participated in PISA.[122] The study consisting of 1.5 million 15-year-olds found higher overall female achievement across reading, mathematics, and science literacy and better performance across 70% of participating countries including many with negative gaps in socioeconomic and gender equality, and they fell behind in only 4% of countries.[122] Stoet and Geary concluded that sex differences in educational achievement are not reliably linked to gender equality.[122]
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Women with mild cognitive impairment progressed at a faster rate than men did:
http://www.sciencedirect.com/science...52873715000190
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Cognitive function in the oldest old: women perform better than men:
http://jnnp.bmj.com/content/71/1/29
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Men are more likely to have cognitive impairment:
http://www.mdedge.com/neurologyrevie...mild-cognitive
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Women have a smaller amygdala which plays a role in them being less sexual and violent (I guess making women more "self-controlling"):
https://www.npr.org/sections/13.7/20...uperior-to-men"Recent brain imaging studies show that a part of the brain that helps produce violence, called the amygdala, is larger in men than in women. Also, the frontal cortex (frontal lobes), which help to regulate impulses coming from the amygdala, is (are) more active in women. Mounting evidence supports the claim that male and female brains are different in many species, including us, partly because of androgenizing (masculinizing) influences of testosterone on the (anterior) hypothalamus, amygdala, and other parts of the brain involved in sex and violence.
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