lomiller
Penultimate Amazing
- Joined
- Jul 31, 2007
- Messages
- 13,208
The weakness of the correlation between brain size and the male/female dichotomy places a limit on how well you can distinguish male from female by looking at nothing other than brain size, but it most definitely does not mean you cannot do better than chance.
As noted in my previous post, it is possible to quantify this.
Start with the following facts.
Using those facts, we can design the following crude algorithm that, given the size of a brain belonging to some person drawn at random from the world's population, guesses whether the brain belongs to a man or to a woman:
- About 50% of the world's population is men, and 50% women.
- The distribution of brain sizes in men is approximated by a normal distribution.
- The distribution of brain sizes in women is approximated by a normal distribution.
- The mean brain size for men is approximately one standard deviation (of either distribution) greater than the mean brain size for women.
Despite the obvious crudity (some might even say stupidity) of that algorithm, it performs better than chance. Roughly 16% of men's brains are no larger than the mean for women's brains, whereas 50% of women's brains are no larger than that threshold, so case 1 guesses right about 75% of the time (50/66). Roughly 84% of men's brains are larger than the mean for women's brains, whereas 50% of women's brains are larger than that threshold, so case 2 guesses right over 60% of the time (84/134). For brains drawn at random from the world's population, about 1/3 are handled by case 1 (half of (16% plus 50%)) and 2/3 by case 2, so the algorithm guesses right about
- If the brain size is no greater than the mean brain size for women, guess that the brain belongs to a woman.
- Otherwise guess that the brain belongs to a man.
(75%/3 + (2 * 60%)/3) ≈ 65%of the time, which is better than chance. Despite its crudity, the algorithm is almost twice as likely to guess right as to guess wrong.
(An algorithm that splits the two cases at the intersection of the probability density functions for the two normal distributions would do slightly better, but its performance would be harder to explain to this audience.)
Ok but could the brain type identified by this technique be used to accurately predict:
a) the existence of feminine personality traits?
b) whether someone self identifies as transgender?
My guess is that it would not. If so this would mean that all you have is statistically expected error margins and not a tool that could help identify someone's gender.