Sex Differences in the Distribution of Mental Ability

Kevin Langdon and David Seaborg

Published in Noesis #144, November 1999
Copyright 1999 by Kevin Langdon and David Seaborg

An earlier version of this article (by Kevin Langdon) was published in Vidya #155/156 (August 1996). This version appeared in Gift of Fire #100, October 1998 (a few further slight modifications were made for publication in Noesis and on the Web).


Dr. Arthur Jensen’s Bias in Mental Testing explores the question of male/female differences in ability in a very interesting section of Chapter 13. Jensen cited studies indicating a difference of approximately one IQ point in the standard deviation of males and females in general intelligence, with males having the greater variability.

Differences in general population means are less clear-cut. The following table is derived from Table 13.1 in Bias in Mental Testing:

Number of Studies Showing Significant (p<.05) Difference in Favor of:

Type of Test   Neither   Males   Females
General Intelligence   40   3   15
Verbal Ability   81   13   37
Quantitative Ability   15   16   4
Visual-Spatial Ability (nonanalytic)   24   9   2
Visual-Spatial Ability (analytic)   35   25   3

All the studies made use of tests published since 1966. Jensen defined “analytic” visual-spatial ability tests as those which “require analysis, that is, mentally breaking up a gestalt into smaller units in ways that facilitate spatial problem solving.”

According to Jensen:

[T]he sample sizes are generally adequate for even quite small differences, equivalent to a tenth of a standard deviation or less, to show up as statistically significant.

Jensen added a note of caution:

The most widely used standardized tests of general intelligence have explicitly tried to minimize sex differences in total score by discarding those items that show the largest sex differences in the normative sample and by counterbalancing the number of remaining items that favor either sex. This is true, for example, of the Stanford-Binet and Wechsler scales of intelligence. Such tests, therefore, obviously cannot be used to answer the question of whether there is in fact a true difference between males and females in general intelligence.

The table below is adapted from Table 2 of an article in the July 7, 1995 issue of Science, “Sex Differences in Mental Test Scores, Variability, and Numbers of High-Scoring Individuals,” by Larry V. Hedges and Amy Nowell, both in the Department of Education at the University of Chicago.

Subject Area Difference of Means Ratio of Variance Ratio of 90-Plus Scores Ratio of 95-Plus Scores


Reading Comprehension



-.15   1.16   0.90   1.00
-.05   1.03   0.94  
-.18   1.16   0.83  
.00   1.10   1.03   1.06
-.09   1.16   0.80   0.83



.25   1.05   1.57   1.50
-.06   1.00   0.89   0.87
-.03   1.08   0.87  
.07   1.05   1.06   1.06





.12   1.20   1.33   1.50
.24   1.05   1.76  
.26   1.25   1.90   2.20
.08   1.19   1.70   1.90
.22   1.16   1.67   2.06
.03   1.06   1.34   1.64

Nonverbal Reasoning


.04   1.04   1.09   1.00
-.22   1.15   0.74   0.67

Spatial Ability


.13   1.27   1.86   2.33
.25   1.27   1.90   2.39

Differences are male minus female means, in general population standard deviation units. All ratios are male/female; 90 and 95 refer to the 90th and 95th percentiles.

One striking pattern that appears here is the strong advantage of males over females in mathematical and (especially) spatial reasoning.

Among . . . mathematically gifted 13-year-olds, [sex] differences favour males in mathematical reasoning ability, but not in verbal reasoning, where there are no [sex] differences. Our gifted males score approximately one half of a standard deviation higher than females on the SAT-M, our measure of mathematical reasoning. Males’ SAT-M scores are also more dispersed, yielding an upwardly shifted distribution of male scores (Benbow, Behavioral & Brain Sci. 11, 1988). The resulting proportion of males and females at age 13 at various cut-off scores on SAT-M is approximately as follows: 500 (average score of college-bound 12th-grade [18-year-old] males): 2:1; 600: 4:1; 700 (top 1 in 10,000 for 7th graders [13-year-olds]): 13:1. These ratios have remained relatively stable over the past 20 years, and have now been observed among mathematically gifted students in the 3rd grade (8-year-olds), and cross-culturally (though they are smaller in Asian populations).
—Camilla P. Benbow and D. Lubinski, 1993, in Ciba Foundation Symposium 178,
“The Origins and Development of High Ability”

Although controversy exists about the magnitude of the sex difference in spatial ability under various testing conditions, reviews by Pool (Eve’s Rib, 1994) and Voyer et al. (Psychological Bulletin 117, 1995) show that on the “purest” spatial measures, such as rotating an imaginary object, or shooting at a moving rather than a stationary target, the sex difference approaches one standard deviation.
—J.P. Rushton and C.D. Ankney, Psychonomic Bulletin & Review, 1996

. . . it took five years of extensive nation-wide search to find 36 extremely mathematically talented girls.
—Camilla P. Benbow, Neuropsychologia 24, 1986

The mean variance ratio in the table is 1.13, indicating a difference of approximately two points of IQ in standard deviation between men and women, twice Jensen’s figure.

Norming data for the Langdon tests show an even greater difference in favor of males. In populations with average IQ’s of approximately 140 (sigma=16), the following differences were observed:

Test/Norming   LAIT (Norming #2)   LAIT (Omni Sample)   PIAS
N   553   20,000   1464
Male Mean   145.7   137.5   142.0
Female Mean   139.3   132.0   131.5
Difference   6.4   5.5   11.5

Calculations based on the above data give figures ranging from 2.2 to 4.6 for the difference in standard deviation between men and women. The PIAS data may be less reliable than that for the LAIT, which accords more closely with the lower figures mentioned above.

Data from Ronald K. Hoeflin’s Mega Test provides additional evidence for a high level of male/female difference in standard deviation, based on a far-right-tail population similar to those attempting the Langdon tests. According to data contained in a letter from Dr. Hoeflin to Kevin Langdon dated December 4, 1985, ten times as high a percentage of those scoring 5 or below (out of 48) on the Mega Test were women than of those scoring 30 or above.

One possible factor in the observed male/female differences on the Langdon and Hoeflin tests is that both include spatial elements, but neither is highly loaded on the spatial factor, which has to do specifically with visualizing the rotation of objects in two- and three-dimensional space.

At this point, we may ask why the observed differences in variance exist.

We are diploid organisms, like all higher animals. Unlike haploid organisms, which have only one set of chromosomes, we have two parallel sets, with 23 chromosomes in each set. Each chromosome has one or another allele (alternate form) for every gene it carries; our 23 chromosome pairs are the vehicle for the approximately 100,000 genes in the human genome. (Many plant species alternate between haploid and diploid generations; in social insects, males are haploid.)

Diploid organisms shuffle the alleles passed on to the next generation through sexual reproduction, in which genetic material is systematically varied. A further refinement is what geneticists call dominance. Certain alleles mask the effect of others, which are called recessive. The alleles of other genes are additive, resulting in an intermediate phenotypic expression in heterozygotes. (E.g., breeding a Manx cat with an ordinary, long-tailed cat produces stubby-tailed offspring.)

The following quotation is from a Web page entitled “Diploidy and Dominance,” by Deborah Stacey, Associate Professor of Computing and Information Science, University of Guelph. <>:

A famous biological example is that of the peppered moth in Great Britain. The original, dominant form of the moth had white wings with small black specks which functioned as camouflage against its habitat of lichen-covered trees. During the Industrial Revolution, black forms of the moth started to dominate the population. Industrial pollution had killed off the lichen covering the trees in the moth’s habitat. The new black form thus had a survival advantage over the speckled version. The colour was controlled by a single gene. And not only had the population percentage changed—dominance among alleles had changed also—the “black allele” was now dominant. When the population balance had shifted towards the dark form, it became dominant and the speckled form was held in abeyance. The black version of the moth was not “new”—it had been invented earlier and was only expressed when the environment had changed. This demonstrates that diploidy and dominance can permit alternative solutions to be shielded against overselection. It also demonstrates that dominance is not an absolute state of affairs—dominance can evolve as well.

When an organism carries identical alleles of a given gene, it is said to be homozygous for that gene; otherwise it is said to be heterozygous. The pattern of alleles for a given organism is its genotype. Its pattern of externally-expressed genetic factors is its phenotype. Recessive alleles are not expressed phenotypically unless they are homozygous. This permits organisms to retain alleles that are not favorable if expressed in existing conditions; this genetic material can be drawn on in adapting to changing conditions.

As most of the genes on the X chromosome do not have a corresponding locus on the Y chromosome, males are effectively haploid for the sex chromosome pair; recessive alleles of these genes, including nature’s more advanced experiments and (far more numerous) lethal and debilitating mutations, are much more likely to be expressed in males, giving rise to the observed greater variability in males on various measurable traits, including g. This is adaptive for the species, as males are expendable; the size of the next generation depends on the number of females that survive long enough to reproduce.

In every society, human and animal, males do the fighting. This is not only because of their greater physical strength, but it is due also to the most basic requirement of a species: survival of the next generation. In a population of ten males and ten females, if nine females died in battle, only two or three children could possibly be born to the group the next year. . . . So males are more expendable.  —Robert E. Ornstein, Psychology: The Study of Human Experience. San Diego: Harcourt Brace Jovanovich, 1985.

The vast majority of animal species are polygynous. In a polygynous species, it is greatly to the male’s advantage to be more variable in general, because only a few of the males—the most fit, the best competitors—get all (or substantially all) of the females, while the rest of the males are left out in the cold. Gambling on a long-shot mutation is a strategy with a high expected return under these circumstances, as a male of only average fitness will not mate and pass on his genes anyway. A successful mutant could become an alpha male and mate with many females. We recognize that there is another, “sneaky” mating strategy used by the males of some species. Although unable to compete as alpha males, lower-status males may still find opportunities to mate when the alphas aren’t looking. This may reduce the advantage of variability, but cannot eliminate it, in polygynous species.

Birds, for some reason, have evolved in the opposite direction; it is the male who has a matched pair of sex chromosomes and the female in whom one chromosome is incomplete.

Dinosaurs, from which birds are believed to have evolved, were ground-nesters, as are certain birds today. Many ground-nesting species are polyandrous; the cause of this may be that only the cooperative efforts of a group can protect their nests effectively. Male birds are locked into this evolutionary strategy, even though, as most are polygynous or monogamous, this isn’t the best adaptive stategy for them.

Butterflies and moths are another exception to the general rule, as are snakes and monitor lizards (from which snakes are believed to have evolved). The hetero-gametic sex in some fly families of the order Diptera is the male and in other families the female. This is also the case for some other orders of insects and also for frogs and toads. Also, within some families of insects and lizards there are differences between genera. The inconsistent pattern here does not support the more general conclusions suggested above, but there may still be some merit in our argument with respect to mammals and birds; other considerations may predominate in other cases.


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