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Sex Differences in IQ

Conventional wisdom overturned

The conventional wisdom about sex differences in IQ is that males and females have the same average IQ.  The conventional wisdom also stipulates that males are more variable than females, meaning that there are more mentally deficient and gifted males than females. 

Presented here is information from two good papers on sex differences in IQ that disagree yet end up having the same conclusion with regard to the high extreme of IQs.  Additionally, data from Mensa Canada is given that agrees with both those papers on that point.

Before continuing, it might be prudent to tackle one of the first objections that will be raised to a finding that the sexes are not equal in terms of IQ: that IQ tests are biased. Test bias is an intricate subject, and if you are interested in the details, the book Bias in Mental Testing by Arthur R. Jensen is suggested.  (He started out believing that IQ tests were biased and through careful research ended up concluding that they generally were not).

Let it suffice to point out the analogy of height differences: Men are taller on average than women. If one does not like the situation, one cannot seriously accuse the height-measuring device of being biased. Many people have been influenced by anti-IQ reporting in the media, and politically correct writings by authors such as Stephen J. Gould to think that if IQ tests show an inequality it is obvious evidence that they are biased.  There are ways of measuring test bias and merely showing that there is a difference between groups is not enough.

WISC-R

The paper that supports the conventional wisdom is Jensen, A. R., & Reynolds, C. R. (1983).  It finds that females have a 101.41 mean IQ with a 13.55 standard deviation versus males that have a 103.08 mean IQ with a 14.54 standard deviation.  You may want to read the IQ Basics page first if you are unfamiliar with IQ and standard deviations.  By just looking at those figures, it seems to corroborate the conventional wisdom that has been known for decades: the average IQs are about the same and males are a bit more variable.  However, if the summary data is used to generate a graph, a different picture emerges:

 
Graphs drawn in Excel using the NORMDIST function.

Note that due to the seemingly unimportant slightly higher male average IQ, the extra male variability does not mean that there are many more mentally deficient males. Instead, the areas under the curve show that at the high extreme, such as the Mensa or gifted cut-off IQ of 130 (indicated by the red arrow) and above, there are significantly more males than females who qualify.

Raven Progressive Matrices

The situation is even more pronounced if one looks at the other paper: Lynn, R., & Irwing, P. (2004). In this paper, which looked at adult IQs, a five point higher IQ was found for males over females and the standard deviations were found to be equal. Graphed, it looks like this:

Looking at the graph produced from this meta-analysis, beyond the 130 cut-off, the ratio of the areas under the curve for males and females is about 2:1.

Real world effects in Mensa

This 2:1 ratio corresponds best with what is found empirically in Mensa Canada even though the tests usually given have material more like the WISC instead of the progressive matrices.  Toronto was picked as the sample population because the Toronto Proctor had reported that females are 33% of entrance exam takers. Note that Mensa aspirants in Canada need to be at least 14 years old to be tested.

In June of 2007, the Mensa Canada member directory was used to get the names for every Mensan listed from Toronto. Using the first names and the website http://www.gpeters.com/names/baby-names.php to decide whether some doubtful names were given more to boys or girls, the number of male and female Mensans in Toronto was tallied. Results: 150 males, 83 females, out of 233 total, giving 35.6% females. So the ratio is 2:1 males to females, the same as attempt to get in.

Notes on the papers

The first paper, Jensen, A. R., & Reynolds, C. R. (1983), is based on the WISC-R, the Wechsler Intelligence Scale for Children - Revised. The Wechsler tests are the most widely used IQ tests because of their great psychometric properties. The paper took a stratified, random subsample of the WISC-R standardization sample, based on 1970 US Census. The sample sizes were: N=944 for males and N=924 for females. The mean significance was p<0.0001. The standard deviation (strictly variance) significance: p<0.05.

The second paper, Lynn, R., & Irwing, P. (2004), is based on the Raven Progressive Matrices. The Ravens tests are considered the most pure measure of g (the general factor of intelligence).  That is, they have very little contamination of the measurement of general intelligence by specific mental abilities.   The meta-analysis looked at the data from 57 studies (some that showed higher IQs for females, and some that showed higher IQs for males), to come up with a weighted effect size.

The main differences between the two papers are that the WISC has verbal (educationally dependent) and performance (non-educationally dependent) components and it was given to children. The Raven is a pure performance type test, and the paper only looked at scores from adult samples. The second paper is the more trustworthy one for two reasons. First, it is based on 57 samples instead of one large one. Second, it includes a statement that might actually explain the disagreement between the two papers: "Results showed that there is no difference among children aged 6–14 years, but that males obtain higher means from the age of 15 through to old age."

Conclusion

Male and female mean IQs are about equal below the age of 15 but males have a higher mean IQ from age 15 on.  The effect of sex differences in IQ is largest at the high extreme of intelligence.  Since many of the more prestigious roles in society are associated with high IQ, the lack of female representation in these roles may be partially due to fewer females being competitive at the highest levels.  This does not mean that females should not be given equal opportunity to demonstrate their abilities as this would create an worsened artificial 'glass ceiling'.

 

If you have formal arguments to present (based on scientific sources, not what is reported in the media), please email them to .   Especially appreciated would be references to any better papers on the subject or graphs of raw sex difference data.  Because the graphs here were created using summary statistics, they might turn out to be misleading if the actual distribution curves turn out to be skewed or otherwise aberrant.

If you have informal arguments to present, then you are encouraged you to comment on this web page at the following sites:

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Posted September 23, 2007

References

Jensen, A.R. (1980). Bias in mental testing. New York: Free Press.

Jensen, A. R., & Reynolds, C. R. (1983), Sex differences on the WISC-R. Personality and Individual Differences, 4, 223-226.

Lynn, R., & Irwing, P. (2004). Sex differences on the progressive matrices: A meta-analysis. Intelligence, 32(5), 481-498.

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