Sunday, 8 September 2013

Are girls too normal? Sex differences in intelligence


Here is a snapshot from Ian Deary’s lecture  “Ten Quite Interesting Things About Intelligence Test Scores” (Teaching Intelligence which aims to show the difference in the distribution of boy’s and girl’s intelligence scores. The point of interest is that even when boys and girls have exactly the same levels of intellect, differences in the standard deviations have considerable impact at the extremes of intelligence. Girls are more normal, boys are more extreme, so there are more boys at extremes, and the more extreme the extremes, the more boys. This finding at age 11 may go some way to explaining the sex ratios observed in later life occupations, or perhaps only partially so.


If, like me, you find the graphic a little difficult to understand, look at the new version below.



Starting from the left, you can see that those children who have an average IQ of 60 (very low) are 58% boys and 42% girls. At average IQ 100 there are 48% boys and 52% girls. At IQ 140 there are 58% boys and 42% girls. I have also increased the size of the Y axis, so that you can see a 40 point range of percentages from 30% to 70% rather than the 20 point range in the original, which made things look too dramatic. Both figures deliberately use zero suppression (don’t show the full 0 to 100 percentage range) to exaggerate the visual effect, which is legitimate, because otherwise the effect would be very difficult to see. If you just stick one IQ distribution over the other it is hard to see the difference.

In both figures you must remember that there are many more children in the middle ranges (perhaps we should show very wide bars here), and very few at the extremes (perhaps we should show very thin bars). Girls are normal, boys somewhat less so. Very bright children are more likely to be boys in the ratio 58:42.

This shows that girls predominate over boys at the centre of the intelligence range, but there are fewer at the extremes, which is where boys are slightly more likely to be found.  Assuming that the boy/girl difference is sustained in adulthood, then if men and women are promoted to jobs entirely on merit, and work equal hours, there will be 58 men to 42 women in the elite occupations.

Of course, this finding is also germane to the genetic versus social conditioning debate. It is easy to argue that restrictions in society affect all women, and that these barriers push mean abilities downwards. However, it turns out that there were no sex differences in average intelligence even in 1932, and not thereafter, despite many fears to the contrary. Girls and boys have the same average intelligence, but not the same standard deviation. (Whether men and women have the same average intelligence we can debate later).

However, it is less easy to give a social conditioning account of why girls’ standard deviations would be more narrow, because it would involve proposing a force capable of simultaneously stopping girls from being very bright and stopping them from being very dull, and being able to do so in such a way that it showed up in a test taken by children working on their own without teacher or class input. How would one simultaneously hold back a bright girl from giving a bright answer and stop a dull girl from giving a dull answer? Furthermore, how would one do this so subtly as to narrow the girls’ distribution of abilities only very slightly?

It is also difficult to explain how social conditioning could affect the standard deviation of brain volume. The sample size of 89 normal subjects is too small, but total brain volume as measured by MRI reveals suggestive results. The 42 males have a total brain volume ml of 1354 ± 111 and 47 females a total brain volume ml of 1215 ± 105.  Reite et al. BMC Psychiatry 2010 10:79   doi:10.1186/1471-244X-10-79. By the way, I am not making a brain/intelligence association here (though there is a significant positive correlation) just a link with the common findings of sexual dimorphism.

Darwin regarded greater male variability as a fact, though of unknown cause. Greater variability suggests, but does not prove, a genetic cause. However, since the effect is only visible at the extremes it is important to ensure representativeness of the the study samples. The most representative sample is an entire population to make sure that neither dull nor bright children have been lost to the testing procedure. Wendy Johnson, Andrew Carothers and Ian Deary have the full population samples from Scotland in 1932 and 1946.  “Sex Differences in Variability in General Intelligence: A New Look at the Old Question.” Perspectives on Psychological Science 2008 3: 518 . I have used their data in this posting. They also have a good discussion about whether this finding is sufficient to explain observed difference in men and women’s occupations and achievements.

The male to female ratio in intellectual demanding occupations is higher than the ratio observed at age 11. Part of that is down to the fact that measurements at age 21 may be more representative of adult levels. There is some suggestion that girls develop faster than boys, and the relative advantage reverses in favour of men as they reach maturity.  Girls have an early advantage in height, which then reverses in later development. Part of the occupational difference in later life is that many men are much more likely to put in long hours, and to value their careers and their status above other interests. Matched for time invested, the differences are smaller, and sometimes favour women. Importantly, the sexes have different interests. We shall return to all that later.

Of course, the great Dr Heim knew all about this 40 years ago, based on undergraduate intelligence tests. The title of the relevant chapter may be judged too inflammatory for current sensibilities, but it was said in jest.


  1. excellent post - males are more variable on almost every characteristic - this is a psychometric fact inexplicably unknown to the general population. superb graphs - more creative depiction than overlapping normal curves with males having more area on the extremes. this fact of higher male variability is what got Larry Summers in trouble, even tho he merely suggested it as 1 of 3 hypotheses for why fewer females were in science. it's almost as forbidden a fact (yet equally indisputable) as racial group mean differences in ability. well-done, bringing this to the fore!

  2. I think this graph makes a case for nurturism. At the highest IQ bucket, the ratio of boys to girls is less than 3:2. The ratio of boys to girls at the top of any intellectually demanding field is much, much greater than 3:2. The differing standard deviations between girls and boys in IQ goes the right way for a naturist explanation for differing achievement, but the difference is too small.

    Now, I personally incline to a naturist explanation for the differences in achievement between males and females, but this evidence is actually pretty disturbing to me on that score.

  3. Picture may look different at age 21. Will post about this later

  4. Given the rates of violence in society, shouldn't we consider whether boys are too abnormal?

    In the highest IQ bucket shown on this graph . . . the ratio is much less than 3:2. From what I've seen elsewhere, SD for boys, considered the norm, is 15, for girls that is 13. While we a talking a tiny fraction of the overall population, a male with 160 is 4 SD, a female is approaching 5 SD, and so on.

    I would like to see this controlled for verbal and non-verbal IQ. Is this all non-verbal? Is there a difference between males and females on the verbal portion, like there is on SAT and GRE tests?

    While human development is complex enough that it requires the input of more than just a mother, after conception it is the mother who is most vital. In many hunter-gatherer groups, a woman's brother played the role Westerners associate with father, providing the 10% or so of calories from meat, protection, etc. People tended to have many children, so women would likely have more than one brother. Survival required stability in women for children to grow to an age at which they were self-sustaining. Unstable, not-normal women were not suitable mothers, but potential shamans, priestesses, and vestal virgins. Women's role in maintaining society made them keenly aware of "normal". Evolution's experiments on men didn't necessarily prevent them from making their brief contributions to conception. Once in a great while, the genetic variation brought in would benefit reproductive and survival rates of descendents.

    Less than a year ago, a study was released directly correlating intelligence with mental illness, , although that has been known for some time. There's no indication that IQ over 120 benefits earning power, achievement, etc. It greatly increases the odds of having a first degree relative with a serious mental illness, however.

  5. Thanks for your comments. Men are about 10 times more violent than women. I don't think this is directly related to differences in the standard deviation of intelligence. It is more likely to be due to greater upper body strength and testosterone. However, lower intelligence is related to crime generally, so part of the preponderance of crime could be accounted for in that way, but not the major part.
    There is certainly a hypothesis that in our evolutionary past our sudden increase in creativity may have been linked to a mutation which increases vulnerability to mental illness. However, the implication that having an IQ above 120 confers no benefit in earning power or achievement is wrong.

    1. Not a valid point. Neither of the three posts presents good argument against the statement that "having an IQ above 120 confers no benefit in earning power or achievement". Earning power is not discussed in either of the three posts. Neither of the three has any pointers to the IQ of 120 threshold. The only unambiguous thing in the three posts is that the "achievement" (understood very narrowly as bachelors vs masters vs PhD) does seem to increase with the increase of IQ.

    2. See the following for earnings and wealth and achievement. But the way, nothing special about the IQ 120 cutoff. Same argument holds throughout the IQ range, even into the highest reaches.

  6. "How would one simultaneously hold back a bright girl from giving a bright answer and stop a dull girl from giving a dull answer? Furthermore, how would one do this so subtly as to narrow the girls’ distribution of abilities only very slightly?"

    1) Heavy loading on crystallized factors. I've heard it said that, on average, girls are more prone to adapting to scholastic expectations (that could be better stated).

    2) Don't make the loading too heavy, and have some other confounding expectations.

  7. Don't quite understand what is being proposed here.

  8. Sex differences puzzle me. They don't seem to be present among some groups (such as Asians). Moreover, I can cite one case of a highly selective organization that shows no sex differences. One group of gifted children that I know of (they are very restrictive about their privacy, so I won't say what it is) has about 2000 members, who are about evenly divided between boys and girls. This organization has an IQ cutoff of 145 and requires corroboration of a +3 SD score on achievement test results.

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  10. Instead of asking why females are more normal, maybe ask why societies select - or at least tolerate - men who chart where the bell gets rung.

    The civilized world has always needed ditch diggers, and they are always men. (Since brains are expensive to run by size, and calories were expensive prior to, say, 1900) Men in heavy labor had no use for larger brains(most societies had rigid classes, especially at the bottom), so the left lip of the bell found a place in society, for men.

    And the civilized world has always found a place for exceptionally clever men - iconoclasts, artists, visionaries, merchants, etc. An exceptionally bright women.... well, she might be accused of witchcraft!

    Also, high variability in the male population could be much more useful with the tasks men have done, socially speaking. Take a major event requiring complex social organization - like exploring the New World. It would require financiers, visionaries - and exceptionally strong, brave underlings who don't hatch mutinous plots.

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  12. Could the higher variance for men be related to being xy instead of xx? An abnormal x (high or low IQ, both of which are abnormal) would be suppressed by a normal one in a girl, but not in a boy. This relates to the higher miscarriage rate for boys too. IQ is more complicated than hemophilia, though, no doubt involving many genes, so all we get is some correlation out of the xy phenomenon.
    Note that this is a physiological explanation rather than an evolutionary one. The xy vs. xx chromosome difference might be the result of evolutionary pressure, but once it's there, it has implications like more hemophilia in males which are not the result of hemophilia being helpful for males.

  13. I like that you included the explanation for why you don't use the 0-100 range, but I still think you should---it's good to show that the difference isn't really very big (tho very significiant nonetheless).
    Both diagrams should only include the percentages for one sex, though with horizontal lines at 0 and 100%, since the second sex's percentage is just the residual. You can convey the same information with half the ink, and convey it more clearly since you can put the key in the title and the reader isn't distracted by redundant lines.

  14. How is a 58-42 ratio at the extremes "slightly more likely"?

  15. Yep, "slightly" too cautious at the extremes and "more likely" would be better. On these numbers a chi square would be significant.

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