Sex differences in intelligence

Introduction

In this discussion of sex differences I rely mostly on chapter 13, "Sex differences in g", from Arthur Jensen's book "The g factor", and a little bit on chapter 4, "Conditions for excellence", from Hans Eysenck's book "Genius - The natural history of creativity". Also on Richard Lynn's home page, and on my own experience with high-range tests.

Mean I.Q.

When it comes to the question whether or not there is difference in mean I.Q. between males and females, Jensen basically says no, after having considered a large amount of evidence. Eysenck is a little bit more skeptical and points out that the usual assumption of equal I.Q. of the sexes may be flawed. Based on data also mentioned by Jensen (R. Lynn, 1994, Sex differences in intelligence and brain size: a paradox resolved), Eysenck suggests 4 I.Q. points as a conservative estimate of the difference (favouring males). Lynn, on his home page, simple states in adults the difference is about 4 points.

Both Jensen and Eysenck indicate that the question is hard to answer, as I.Q. tests like Stanford-Binet and W.A.I.S. have traditionally been constructed to show no sex difference in total score, by leaving out or counterbalancing items that show sex differences. Such tests therefore are not capable of measuring a possible difference between the sexes.

I myself cannot observe a mean difference directly as I only deal with high-range tests. I will return to this point further on with regard to the variance difference.

Variance

The male variance in I.Q. is greater than that for females; Jensen says this difference is greatest in math and spatial ability. In math the male variance is 1.1 to 1.3 times greater (He does not give the difference for I.Q. or g).

In the high range, my own observation to date is that at or above the 98^th percentile there are about twice more males than females, while at or above the 99.9^th percentile there are about 15 times more males. These estimates are based on the male/female ratios in certain high I.Q. societies and on analysis of male and female performance on my tests. Trying to make this fit in terms of standard deviation ("variance" is, incidentally, the square of the standard deviation), I find that when the male and female mean are both I.Q. 100, the male standard deviation (S.D.) must be about 33% greater than the female S.D. However, if a mean difference of 5 points in favour of males existed, the male S.D. would only need to be about 11% greater. I do not yet know which is true (or if the truth lies in between). I must say though that an SD difference of 33% seems unlikely.

A remark sometimes made regarding the male/female ratio in I.Q. societies and among high-range candidates is that females may be so lowly represented because they simply do not like taking intelligence tests, or even because they attach less value to intelligence than males do as a result of having been raised and socialized to value other traits higher in women. In other words, that their representation is not proportional to their actual presence at high intelligence levels. The following facts however speak against this:

In general, people enjoy (like, tend to, are inclined to) doing what they are good at, so the fact that fewer women than men take high-range tests is in full accordance with their lower occurrence frequency at high intelligence levels. It is unlikely that people in large numbers are kept from doing what they are naturally good at merely by not liking or not valuing it. It is much more likely that the "not liking" is a result of being less good at it.
It is well known that females are far more interested in (enjoying, liking) taking all sorts of psychological tests than are males, so their strong underpresence among high-range test candidates must have a compelling reason other than "not liking".
A factual observation about high-range tests is that the harder a test is (as measured by the proportion of the test's problems that is on average missed), the fewer people choose to take it, the higher their median score, and the smaller their internal spread. It follows logically, is apparent, that people are avoiding tests that are too hard for them (rather than just avoiding tests they do not like), and are taking tests they can handle (rather than just taking tests they like).
It is also a factual observation about high-range tests that the harder a test is, the greater the male/female ratio among that test's candidates is. It follows logically that females are avoiding tests that are too hard for them (rather than just avoiding tests they do not like), and are taking tests they can handle (rather than just taking tests they like).
The distribution of female scores on high-range tests looks roughly similar to that of males, shifted downward by about ten I.Q. points.
In professions that require high intelligence, such as those in exact science and technology, there are still fewer to far fewer females than males working, despite decades of emancipation, affirmative action, government-prescribed minimum quota for females in certain professions, and lowering educational standards. Clearly, there is a force that keeps females away from these professions, and the longer the positive discrimination goes on and fails, the more painfully clear it gets that this force is mainly the ability requirement of the work itself, which is at least partly an intelligence requirement, while other aspects of creativity may also play a role.

These facts make it almost inescapable to conclude that the male/female ratio among high-range candidates and in I.Q. societies is roughly representative of the actual male/female ratio at high intelligence levels. Sometimes one has to leave a prejudice (equality) behind and accept the facts, even if one would like them to be otherwise. That I say "roughly representative" is not because I believe that "liking tests" or social or socialization factors may still contribute, but to leave open the possibility that yet other personality features are at play next to intelligence, like associative horizon.

Childhood and growing up

Girls mature earlier verbally, and after puberty boys catch up. The male advantage on spatial and numerical ability (discussed further on) is not yet present in young children, and develops slowly during childhood and puberty. Important to realize here is that the sex differences in mental abilities are caused by hormonal differences (estrogen/testosterone balance), which work partly prenatally and partly after puberty.

If there is a mean difference in I.Q. between the sexes, this will be fully expressed only in adults, and not yet in children. In any case, it seems that when testing children, e.g. for giftedness, one should be aware of these developments and differences, the risk being that one would select too many girls and too few boys as "gifted".

Ability types at which females are better than males

Females are slightly better than males at straight-forward arithmetic (not at more complex math). On short-term memory the difference is greater; They score .3 S.D. higher than males, and one may suppose that this disposes them for multi-tasking.

A verbal ability type that consistently favours females is "fluency"; Such tests require the candidate to name as many as possible words starting with a given letter within a limited time. Females are also better at reading, writing, grammar and spelling. The popular notion that females are better than males at verbal ability on the whole is not true; They are only better at these specific tasks, while there is no or as good as no sex difference in verbal ability on the whole.

Other tasks at which females outscore males are those involving perceptual speed (e.g. matching figures) and clerical checking, both speed and accuracy (e.g. underlining certain letters in a text, or digit/symbol coding). Their advantage on such tasks varies from .2 to .4 S.D. Females are also better at motor coordination and finger and manual dexterity, but those are not mental abilities in a strict sense, although they do occur in the "performance" sections of some individual tests.

Ability types at which males are better

The largest difference is that in spatial ability; the mental manipulation of figures in two or more dimensions. The difference varies from .3 to .5 S.D.

Then there is a difference in numerical ability (except for simple arithmetic) of .1 to .25 S.D. And as already said, in both spatial and numerical ability there is also a large difference in variance, favouring males.

As for verbal ability, males are better at tests of general knowledge. In verbal reasoning there is as good as no difference.

Conclusion

Most important to realize is that because of the difference in variance (regardless if there is a mean difference), in any above-average sample it is normal to find males scoring higher than females. It would in fact be suspect to find this not to be the case; That would indicate possible problems with test ceiling (too low) or test construction (items selected to be sex-balanced instead of for psychometric soundness), or fraud with statistics.

Also important to know is that the state of affairs among children, regarding mental abilities, is not representative of how it will be when they have become adults.

Dilemmas that come forth from these facts: Should test scores in the high range be expressed within-sex rather than sex-combined, given the difference? And: Should "giftedness" be defined within children, or within adults? I am inclined to say "Yes" to the first, and "Beyond doubt within adults" to the latter question.