The paradox of sex differences in intelligence: Part I – Psychometric evidence

Few questions have generated fiercer discussions in the scientific community than those related to intelligence and intelligence testing (see blog: Increasing IQ: Why Bother?). The present blog which will appear in two parts (I: Psychometric and II: Neurobiological evidence) is about gender differences in general intelligence. As stressed by Nyborg (1994), this topic has been characterized by a minefield of methodological and theoretical problems. It is also a sensitive subject matter, packed with ideology and concern over political correctness. As a result, test constructors have calibrated their instruments to conform to gender equality views. Certain test items were removed, so that the test no longer showed a gender difference in overall intelligence  (Wechsler, 1981; Vogel, 1990). Some recent findings, indicating that males outscore females by about 3.8 IQ points (Lynn et al., 2004; Irwing & Lynn, 2005; Jackson & Rushton, 2006; Nyborg 2015), are therefore puzzling and difficult to explain. Is the difference even greater? Have the test constructors done a bad job?

Nyborg (2005, p.507) concluded that: “Proper methodology identifies a male advantage in g that increases exponentially at higher levels, relates to brain size, and explains, at least in part, the universal male dominance in society”. 

We are aware that this is just a limited view of sex differences. As stressed by de Vries and Forger (2015), sex differences in the brain are not separable from sex differences in other body parts. Women may see things differently, but they are also perceived and differently treated by the world creating different knowledge and experiences which might have profound consequences for the brain.

Psychometric evidence  –  g 

As stressed in the brief introduction, it is unlikely that psychometric evidence could ever provide a definitive answer to the question of the present blog. Ackerman (2006, p.722) noted: “... whether males or females have higher mean general intelligence depends on the operationalization of the content of the tests selected to assess cognitive ability.”

Even more numerous are methodological problems related to sample selection and the methods used to establish sex differences. In particular the method of correlated vectors has been criticized suggesting that multi-group confirmatory factor analysis is a better option (Irwing, 2012). A detailed review of the literature is beyond the scope of this blog, therefore we will provide just two examples of more recent findings related to sex differences in intelligence exemplifying the aforementioned problems.

Lynn (1999) proposed a developmental theory in order to explain sex differences in mean performance on measures of general intelligence. Briefly, the theory states that girls mature more rapidly in brain size and neurological development than boys up to the age of 15 years. Faster maturation of girls up to this age compensates for their smaller brain size resulting in little or no sex differences in intelligence. From the age of 16 years onwards, the growth rate of girls decelerates, which may explain a male advantage of about 4 IQ points that is consistent with larger average male brain size.

To test this hypothesis, Savage-McGlynn (2012) used multi-group confirmatory factor analysis to assess mean differences in younger (7–14 years) and older (15–18 years) groups of individuals. The groups were taken from a nationally representative sample of children from 85 schools and colleges across the UK with a sample of 663 younger (323 male) and 263 (114 male) older participants. The participants were invited to participate in the standardization of Raven’s Standard Progressive Matrices Plus. The analysis led Savage-McGlynn (2012, p. 139) to conclude: “…the current investigation failed to find significant mean sex differences between groups of male and female participants younger than 15 or older than 15 years of age”.

Another study that investigated sex differences in g was performed by Irwing in 2012. Multi-group factor analyses were used to analyze the American standardization sample of the WAIS-III, which consists of 2450 individuals aged from 16 to 89 years.  Sample sizes differed for full-scale IQ scores (603 males; 696 females), and for specific factors of Verbal Comprehension, Perceptual Organization, Working Memory, and Processing Speed (1174 males; 1303 females). The analyses performed by Irwing (2012) showed a sex difference favoring men in g (0.19 – 0.22d), Information (0.40d), Arithmetic (0.37–0.39d), Symbol Search (0.40 – 0.30d), and a sex difference favoring women in Processing Speed (0.72 – 1.30d). These differences were only significant for main effects of sex but not for age nor for interaction effects. Irwing’s conclusion (2012, p. 131) involved the statement: “…our findings provide further support for Lynn’s developmental theory of sex differences, and suggest that the consensus view that there is greater male variability in cognitive abilities requires further investigation.”  

Although both studies used similar methodology, they provided contradictory findings. At first glance, the most obvious reason might be the different tests used to determine g. Irwin’s (2012) study used WAIS-III whereas Savage-McGlynn’s (2012) study used SPM+. One might expect different outcomes particularly because WAIS-III lacks 3-D mental rotation tasks, and because items that showed excessive sex differences were eliminated in the construction process. Yet another explanation was put forward  by Irwing (2012). Because sex differences were most attenuated between the ages 28 to 60 years (even showing a reverse pattern at age 40, female IQ > male IQ), and because this age span corresponds with the time period that is crucial for professional success, therefore it could be speculated that successful males (being more engaged with their professional career than females) might have been less inclined to participate in standardization studies than intelligent women. All these factors could have led to an underestimation of sex differences in g. One could also argue that research on intelligence-related sex differences is limited by its exclusive reliance on IQ tests. 

Psychometric evidence  –  specific abilities

Similar methodological issues have been reported for studies focusing on sex differences in spatial, mathematical, and verbal abilities. A meta-analysis of studies published before 1973 found an average difference of about half a standard deviation in favor of males on tests of visuo-spatial ability (Hyde, 1981). Most pronounced gender differences of nearly one standard deviation have been reported for mental rotation tasks (Mackintosh & Bennett, 2005). These findings were confirmed in a more recent large scale study including 90,000 females and 111,000 males from 53 nations (Lippa et al., 2010). The results showed significant male advantages in mental rotation (d = .47) and line angle judgment (d = .49). A meta-analysis of mental rotation tasks showed that sex differences increased when the tasks were presented under time constraints (Voyer, 2011). The duration of time limits did not influence the results; the difference was only observed between test conditions with a time limit of any duration and those without a time limit.

Due to their relevance for education, sex differences in mathematical and verbal abilities have recently received a great deal of attention. A comparison of  students’ mathematical and reading abilities in different time periods led to the conclusion that the gap between boys and girls has disappeared (Hyde, 2014; p. 381): “Overall, then, it appears that girls have reached parity with boys in mathematics performance, at least in the United States”.  Based on the same scientific evidence it was further concluded (Hyde, 2014; p. 382): “If there is a female advantage in reading comprehension and other verbal skills, it is a small one.”

The question is whether such conclusions can be made based on the evidence provided?  

The most commonly reported evidence for the diminishing gender gap in mathematical ability stems from the study by Wai et al. (2010). The study analyzed male/female ratios in mathematical reasoning based on SAT-Math and ACT-Math test batteries in 5 years intervals from 1981 till 2010 (SAT) and from 1990 till 2010 (ACT). The most striking finding was a drop from a 13.5:1 ratio (13.5 boys for every 1 girl) in the top 0.01% level of SAT-Math performance observed in 1981 to a 3.55 ratio observed in 2001, which remained unchanged for the last 10 years of the studied interval. However, what has been most often ignored is the fact that the ratio of perfect SAT-math scorers increased from 1996 onwards, while no obvious trend can be seen in the perfect scorer data for the ACT-Math (see figure below).

Another problem suggested by Lakin (2013) was that the selection procedures used in the Wai et al. (2010) study might have been biased. The sample was based on volunteers who participated in additional testing for the opportunity to be selected for a summer enrichment program. This might have had an unforeseen influence on the motivation of the respondents.

Yet another problem that is common to all psychometric approaches is test selection. Using a different test often changes the study outcome, although both tests are assumed to measure the same trait.  For instance, Lakin (2013) examined sex differences in verbal, quantitative, and nonverbal reasoning abilities in US students as measured by the Cognitive Abilities Test and reported: “The most surprising finding was that, contrary to related research, the ratio of males to females in the upper tail of the quantitative reasoning distribution seemed to increase over time” (p. 263).

The difficulty with task selection was further highlighted by Hyde and colleagues (2008), who attempted to gain better insight into gender differences in mathematical ability by classifying task items into four levels. Level 1 only required recall of facts and performing easy algorithms whereas level 4 contained items that required complex reasoning over extended time periods (i.e. the students were required to connect ideas to develop alternate approaches). The analysis could be performed only partially because none of the test items could be classified as a level 4 item.

Perhaps one of the first written accounts of female superiority in verbal ability is found in an ancient Sanskrit book, suggesting that nine shares of speech were given to women and one to men (Nyborg, 1994). Systematic analyses have shown that females surpass males in some, but not necessarily all areas of verbal ability (Halpern, 2004). Specifically, females seem to have an advantage in episodic memory tasks where verbal processing is required or can be used, as well as in verbal fluency (Maitland et al. 2004). A recent study analyzed data collected by PISA (10 years of data collection), which included mathematic and reading performance of nearly 1.5 million 15 year olds in 75 countries, showed that: “the average sex difference in reading was three times larger than the sex difference in mathematics. Not only was the sex difference in reading relatively large, the overall average difference increased from 32.0 points in 2000 to 38.8 points in 2009” (Stoet and Geary, 2013; p. 2). Ten points are approximately 1/10^th of a standard deviation.

Therefore, the assumptions based on the psychometric-trait approach represent a more or less successful balance between “scientific rigor” and “political correctness” as exemplified in the concluding remarks of two recent review papers tackling sex difference in cognitive ability:

“The gender similarities hypothesis states that males and females are similar on most, but not all, psychological variables. The current review found much evidence in support of gender similarities” (Hyde, 2014; p. 393).

“Importantly, these findings describe group averages and therefore often have limited relevance to understanding individual men and women. Many men excel in writing tasks and many women excel in mental rotation tasks, even if group averages exist” (Miller and Halperen, 2014;  p.42).

Real-world intellectual success

Alternatively, data based on ecologically validated measures of intellectual success in arts and sciences may provide insight into sex differences in cognitive ability. The most prestigious award in science, medicine and literature is the Nobel prize, followed by the Wolf prize granted in Israel for Physics, Chemistry, Medicine, Mathematics, Agriculture and Art (music, architecture, painting and sculpture). 

Domain	Year			Female  S	Male  S	%
	1901 – 1940	1941 – 2000	2001 – 2015
Nobel Prize Laureates
Physics	1	1	0	2	199	1.0
Chemistry	2	1	1	4	168	2.3
Medicine	0	6	6	12	198	5.7
Economy	0	0	1	1	76	1.3
Literature	4	5	5	14	94	13.0
Wolf Prize Laureates
Physics		0	0	0	56	0
Chemistry		0	0	0	46	0
Medicine		4	1	5	49	10.2

The table above summarizes female laureates for both prizes in physics, chemistry, medicine, and literature and economy (only for the Nobel prize) from the first time it was awarded till 2015. Two assumptions can be deduced. First, there is a clear difference in the number of female Nobel laureates in literature compared to other domains, especially physics and chemistry, which roughly corresponds with the reported male advantage in mathematical reasoning and the female advantage in verbal ability. Second, the data does not indicate that this difference decreased or has changed over the last 100 years, since the first Nobel prize was awarded. A similar trend can also be observed for the Wolf prize. Can all these be attributed to sociocultural influence and male chauvinism? Probably not. The first female Nobel prize in physics was awarded to Marie Curie Sklodowska in 1903, and the second to Maria Goeppert Mayer in 1963. One can speculate that in 1903 and even in 1963 there was much more gender inequality and “male chauvinism” and much less pressure for “gender similarity” than today. Thus it seems that scientific excellence was always recognized being male or female.

In the mathematical field, the three most prestigious prizes are the Fields medal awarded since 1936 every four years to mathematicians under 40 years of age at the International Congress of the International Mathematical Union, the Wolf prize, and the Abel prize awarded since 2003 annually by the Government of Norway. The only woman laureate is Maryam Mirzakhani, who was awarded the Fields gold medal in 2014 (55 male laureates). The Abel prize was awarded to 16 male mathematicians and the Wolf prize also exclusively to 55 male mathematicians.

Some insight into sex difference in mathematical ability can further be obtained from the number of female mathematicians holding a full or emeritus professor position at prestigious universities. The table below shows the number of female/male full or emeritus professors at the 3 top Universities in the US and Europe. The rankings are based on ARWU (Academic Ranking of  World Universities by subject mathematics = M; and total = T; http://www.shanghairanking.com/ARWU2015.html).

US									Europe and UK
Princeton University M = 1   T = 6			Stanford University M = 2   T = 2			Harvard University M = 3   T = 1			UPMC – Sorbonne M = 5   T = 36			University of Oxford M = 7   T = 10			ETH     Zürich M = 14 T = 20
♂	♀	%	♂	♀	%	♂	♀	%	♂	♀	%	♂	♀	%	♂	♀	%
34	3	8.1	35	3	7.9	23	1	4.2	54	7	11.5	27	6	18.2	23	0	0

The male to female ratios range from 4.5 for Oxford to 23.0 for Harvard, whereas ETH Zürich has no females in the highest academic rank. These frequencies confirm the trends observed in the right tale of the normal distribution pointing to a male advantage in mathematical ability.

References

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