We have talked about greater male variability before, http://drjamesthompson.blogspot.co.uk/2013/09/are-girls-too-normal-sex-differences-in.html and now there is a new paper with a new result on the vexed question of the male/female ratio at the highest levels of mathematical ability. The particular interest in mathematics is that maths is based on symbolic logic, proceeds by means of logical proofs, is classifiable by broad level of difficulty, is very hard to do well, and is thus a good test of high intelligence. Whether you can get a proper solution to a mathematical problem is a matter of proofs, not just opinions. A solution to a maths problem can be wrong, but with work you might eventually get it right. As such, it has pride of place in human thought. According to Bertrand Russell “Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry”.

xkcd agrees, (Fields arranged by purity http://xkcd.com/435/) so it must be true (in the non-mathematical sense of true, meaning probably correct, though subject to revision, and who knows anything anyway).

Some recent publications suggested that the male/female maths ratio had fallen from 7 to 1 down to 3 to 1. This change certainly made it into the psychology textbooks, and suggested that cultural factors and educational advances were closing the “sex gap”. The new paper looks back to 1980 and finds a male ratio advantage which is greater than 3 to 1, so we seem to be back to the previous state of affairs.

Why the differing results? First, because different samples differ. Second, because there were some selection effects in the previous paper which may have accounted for the reduction in the gap. Third, because the male/female ratio always becomes higher the higher you set the level for mathematical achievement, so some of these fluctuating results may depend on how high the bar is set. That last result may tell you all you need to know. Being very, very good at mathematics is a man thing.

But, hold on, let’s look at the paper.

Joni M. Lakin “Sex differences in reasoning abilities: Surprising evidence that male–female ratios in the tails of the quantitative reasoning distribution have increased” Intelligence . Volume 41, Issue 4, July–August 2013, Pages 263–274. http://www.sciencedirect.com.libproxy.ucl.ac.uk/science/article/pii/S0160289613000457

Lakin highlighted the following points: Sex differences in quantitative reasoning help understand STEM engagement. (That is, if you don’t have the maths, then science, technology and engineering jobs may be beyond you, and this will account for a good part of the sex difference in such occupations). Prior work found secular decreases in male–female ratios at high math ability. Her study found small mean advantages: female in verbal, and male in the quantitative domain. As expected, observed greater male variability was present on almost all tests. Contrary to prior work, the male–female ratio increased for high math ability over time.

Lakin reviewed data from the Cognitive Abilities Test (CogAT; Lohman, 2011, Lohman and Hagen, 2001, Thorndike and Hagen, 1984 and Thorndike and Hagen, 1992) which measures verbal, quantitative, and nonverbal reasoning abilities for students in grades K–12 in the United States. The normative samples for each edition of the test were large and nationally representative, making the data appropriate for investigations of both means and variances. Lakin examined male–female variance ratios and mean differences across grades 3–11 and three forms of the test administered in 1984, 1992, 2000 and 2011. This study focused primarily on changes in the ability distributions over time both in the overall sample and in the proportions of males and females in the highest and lowest levels of ability.

Wai et al. (2010) had previously found a sharp decline in the ratio of males to females at the highest levels of mathematical ability (as measured by the SAT) among seventh grade students. In the early 1980s, the male–female ratio among the top 1 in 10,000 performers (0.01%) was an astounding 13.5:1 (13.5 boys for every 1 girl in the top 0.01%), but declined rapidly through the decade to remain stable at about 4:1 during the 1990s and 2000s. Wai et al. found that the ratio rapidly declined with less stringent cutoffs as well: In the top 1%, the ratio started at 1.4 in the early 1980s and declined to only 1.1 in the most recent cohort (2006–2010). For Wai et al.'s measures of verbal ability (the reading battery from the SAT), the ratio for the top 5 in 10,000 (.05%) appeared to decline modestly as well, from 1.2:1 in the early 1980s to 1:1 in the 2006–2010 cohort. For other measures of verbal and writing ability from the SAT and the ACT, the ratios (initially showing greater proportions of girls) appeared to decrease slightly (closer to parity in boys and girls) during the last 20 years. ACT-Science did not show any clear trends.

Lakin draws attention to two problems with the Wai study. Those authors used the top 5% in any subject, not just in mathematics. That could have diluted the “mathematics excellence” measure such that the student were only in the top 10% of ability. Second, and perhaps more importantly, their sample was based on students who volunteered to participate in additional testing for the opportunity to be selected for a summer enrichment program. This could have had a number of effects on the type of students who volunteer and their motivation levels relative to a random sample studied in the ordinary school context (Hedges & Nowell, 1995).

Incidentally, Lakin finds, as others have done, that white children have fallen from 80.6% of the 1984 US population, to 68.1% in 1992, to 65.0% in 2000 and currently to 55.7% in 2010. However, Lakin argues that this is unlikely to affect the sex ratios, and although this makes sense from a biological point of view, it might cause a problem from the strong social conditioning standpoint because it might be argued that “macho” Hispanic attitudes (Spanish speakers, mostly from Mexico, having risen from 6.4 to 17.6% over the same period) had affected the variability of the sexes in some way. I don’t know in what way, but if you can think of a way, let me know.

“All of the studies confirmed that, unlike the verbal domain, the differences in male–female ratios in the quantitative domain are magnified as increasingly stringent cutoffs are used. For example, on CogAT 7, the male–female ratio for the top 5% of quantitative scores was 2.02 while at the top 1% it was 2.77. Wai et al. (2010) found even more striking differences, especially in earlier years (surging up to 13.5:1 with the most stringent cutoffs in the early 1980s).^{7}Hedges and Nowell (1995) found in the 1960s Project Talent data (the only dataset in their study with sufficient score ceilings to support such estimates) that male–female ratios were 1.3 in the top 10%, 1.5 in the top 5%, and 7.0 in the top 1%. Although the magnitude of changes in the male–female ratios varied considerably across studies, such a trend would have direct implications for understanding the low number of women observed in elite mathematics fields.”

Lakin points out that the sex ratios increase with age. Boys mature more slowly than girls. Even more importantly, the maths test have to have plenty of upper range to reveal exceptional talent. The CogAT test, whilst reasonable for normal populations does not have a sufficient range of difficult items to challenge exceptional mathematicians, who are most usually men not women. The figures in this paper might be underestimate.

That men excel in mathematics is illustrated by the results observed at Cambridge University, where all Senior Wranglers have been men, with two exceptions, Philippa Fawcett in 1890 who was not accorded her proper title because women were not allowed to graduate till 1948, and one woman thereafter in 1992. There it is in a snapshot: the awful history of women being denied their rightful place in intellectual life, and the strong likelihood that, on a level playing field the very best mathematicians are male. Lest it be thought that this is just a fenland phenomenon, since it began in 1936 no woman has ever won a Fields Medal, considered the Nobel for mathematicians.

Mind you, mathematics is hardly a normal pastime.

* Author Prof Joni Lakin comments: It’s difficult to educate the public on probability vs. categorical thinking. It’s not the way most people think or speak about gender issues, but I try to be careful in my paper about it. In other words, although overall I agree with much of what you’re saying, I would want to rewrite your claim: “Being very, very good at mathematics is DISPROPORTIONATELY, BUT NOT ALWAYS, a man thing.” People also forget that the variability hypothesis also means that being very, very bad at mathematics is also a man thing.”

Agreed. It is part of gender disputes to selectively attend to one end of the ability curve and ignore the other.

Fawcett was a cousin of Littlewood. Just in case anyone should doubt that maths ability might run in families.

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ReplyDelete"According to Bertrand Russell 'Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry'.

xkcd agrees, (Fields arranged by purity http://xkcd.com/435/) so it must be true"

That would be because, as Max Tegmark argues, math is the fundamental truth of nature; that is, the universe is inherently mathematical. And I agree with this.

"math is the fundamental truth of nature": more like, it's only the parts of nature that are susceptible to mathematical analysis that we understand much about.

ReplyDeleteJeez,

Deletenope, partially correct but math (how you define it) is a human tool (and of other possible extraterrestrial creatures) to understand the experience to see reality based on quantitative symbols. The real nature of reality are the patterns, that made our vision coerent because patterns are fluidly regular like a creation of old movies.

No exactly ''math'' but ''logical-deductive thinking'' (pragmatic/logical recognition of patterns) that seems proportionally prevalent (and testosteronically too) among men than women.

Emmy Noether was the daughter of Max Noether. She had a very masculine personality apparently. Edmund Landau was once asked what he thought of her as a women mathematician. He replied that he thought she was a very fine mathematician but as to her being a women he had his doubts.

ReplyDeleteJim, she looks fine to me, and had to put up with insufferable treatment most of her life. A triumph of the intellect over crass attitudes. Edmund Landau has a receding hairline and a funny mustache. Can't speak about his mathematics, though.

ReplyDeleteI think Landau was remarking on her personality not her physical attractiveness.

ReplyDeleteJim, in that case I am unable to make any comment at all, other than to give all mathematicians the Masculine-Feminine scale from the MMPI, and see if we can get some alluring results.

DeleteAn update on: "Lest it be thought that this is just a fenland phenomenon, since it began in 1936 no woman has ever won a Fields Medal, considered the Nobel for mathematicians." Maryam Mirzakhani, who was born and raised in Iran, has been awarded the highest honour a mathematician can attain. http://www.theguardian.com/science/2014/aug/13/fields-medal-mathematics-prize-woman-maryam-mirzakhani

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