Monday 17 October 2016

Differences in sex differences: US trends and India


Sex differences fascinate, but would be easier to understand if only they would stand still for a moment! Reported sex differences vary in magnitude, 3 to 1, or 4 to 1, or 7 to 1.

As usual, it depends on the representativeness of samples, the abilities being measured, and also how far out on the right hand side of the bell curve you go when you measure the man/woman ratio of high achievers. In the early 1980s on the SAT-Math the sex ratio was approximately 2 to 1 for scores ≥500 (top 0.5%) and roughly 13 to 1 for students scoring ≥700 (top 0.01%).

As Gigerenzer keeps pointing out, most people misunderstand the combination of decimal points and percentage signs. 0.5% means 1 in 200, or 5 in a thousand, or 50 in ten thousand.  0.01% is even more tricky: it is not a fifth but a fiftieth of 0.5%. It is 1 in 10,000. In sum, males are 2 to 1 at a level of ability reached by 50 out of 10,000 students, but at the very high levels achieved by 1 out of 10,000 students the male advantage is 13 to 1. At least, that was the picture in the 1980s. What are things like now?

Before that, here is some background:

Maths is a man thing. September 2013

Advice to men caught unawares. November 2014

The historical record is clear: eminent men predominate by at least 7 to 1 or, in Charles Murray’s “Human Accomplishment” 30 to 0 for the very top thinkers, people like Aristotle, Darwin, Galileo, Newton, Einstein (page 143) .  Women have the perfect alibi of motherhood, and as Larkin noted, sexual liberation did not come till after the Beatles’ first LP.

Sexual intercourse began.

In nineteen sixty-three

(which was rather late for me) -

Between the end of the "Chatterley" ban.

And the Beatles' first LP.

In fact, some liberation began in 1870 with the Education Act, more in 1914 with the First World War, more after the contraceptive pill in the early 1960s and more and more thereafter.  Although that is true about our own age, perhaps this story is wrong, a mere blip of epoch-centric bias, and denies the rights and the impact women had made centuries before.  Thirty wills survive today from the late Anglo-Saxon period and ten of those are the wills of women, each of whom was a significant property owner , with the same rights of ownership and bequeathal as any man.  Women were highly significant figures in Saxon history, and were admired for their power and nepotism, even if it involved the occasional murder. Interestingly, royal succession was not by primogeniture, but by classifying royal progeny as aethelings (throne-worthy) and from this gene pool the royal family would select the one who seemed best qualified for the job. Meritocracy within aristocracy. So, when pressure groups today want to force employers to appoint women to high offices, they should recall that, as a rule of thumb, in the year 1000 it  was already the case that about a third of the richest Saxons were women.

However, given the clamour for equality in modern times, surely the speed of women’s advance should be quickening?

The sex ratio in accomplishment depends on the skills being measured (harder subjects increase sex differences) and how accomplished you have to be to be judged accomplished (harder standards increase sex differences). So, if we go for Fields Medallists, the score is 55 to 1. Coming down slightly from those sorts of levels, how are young American men and women doing in Maths?

Matthew C. Makel, Jonathan Wai, Kristen Peairs, Martha PutallazSex differences in the right tail of cognitive abilities: An update and cross cultural extension. Intelligence Volume 59, November–December 2016, Pages 8–15

In the Abstract they say: Male–female ability differences in the right tail (at or above the 95th percentile) have been widely discussed for their potential role in achievement and occupational differences in adults. The present study provides updated male–female ability ratios from 320,000 7th grade students in the United States in the right tail (top 5%) through the extreme right tail (top 0.01%) from 2011 to 2015 using measures of math, verbal, and science reasoning. Additionally, the present study establishes male-female ability ratios in a sample of over 7000 7th grade students in the right tail from 2011 to 2015 in India. Results indicate that ratios in the extreme right tail of math ability in the U.S. have shrunk in the last 20 years (still favoring males) and remained relatively stable in the verbal domain (still favoring females). Similar patterns of male-female ratios in the extreme right tail were found in the Indian sample.

They plot out the main US results in a dramatic graph.

SAT 700 sex ratios


The detailed results are in Table 1, so see what you think:

SAT maths table sex ratio

Look like sometime between 1996 and 2000 a new score category of 800 was added. Why? 700+ was good enough before. That category shows the biggest male advantage compared to the 700+ column. Looks like either a) students got brighter or b) the test got easier.

However, the EXPLORE-Math score did not show a decline. Whether earlier changes on some tests and the on-going stability in other tests can be explained by potential ceiling effects in the measure in this sample (see Wai et
al., 2012) or other reasons — (e.g., lack of time for any intervention, the effects of test makers purposefully “juking” tests to reduce demographic differences as suggested by Loewen et al., 1988) — is currently unknown

Well, this leaves a lot unknown. The drop in the sex ratio between 1980 and 1990 is enormous. Something must have happened. Crack teams must have fanned out across America, treating Maths anxiety among girls, and giving them special tuition. There must have been summer schools for the brightest girls. I have never seen such a speedy change in a scholastic indicator, and that includes the rise in language ability of first generation immigrants. It is not clear to me whether the authors believe in the change or not, which is a pity, because this is apparently one of the best findings showing that a cultural intervention can overcome an apparently deep-seated biological difference between the sexes. To give the authors their due, they mention that the tests may have been tampered with, so as to reduce sex differences, but they are the ones closest to the data, so I am sure they could tell us a little more. For example, given that this particular period is so extraordinary, why not plot out the results for each year? Big oscillations in the sex ratio during those years would be suggestive of cultural changes coming in, and taking time to spread through all schools. A sharp fall in a single year would suggest that the test had been revised in a major way. Which is it? What did the test makers say about sex differences over the years? Did they ever mention working on items to make sure they were not sex biased?

At the moment all I can think of is that US Maths tests prior to 1991 had the following statement in the instructions: ALL THE QUESTIONS IN THIS EXAM RELATE TO SPARK PLUGS.

Despite all this, as late a 2010 boys outshone girls at 7 to to 1 (actually 6.58 to 1, but I have rounded up for effect). On the ASSET test top score of 35 the ratio is 8 to 1.

It is minor gripe, but having got some great data from India, it was difficult to find it in their table. Please label the Indian results India. Saves time.

Have we yet another result which shows a biologically based male/female difference, which is also subject to strong cultural forces? I cannot be sure. I don’t know enough about the test content, and what questions may have been dropped because of presumed sex bias. I don’t know if the tests have become easier overall, but suspect it, since during recent years GCSEs in the UK became much easier in terms of the overall pass rate, and are now becoming slightly harder again. Test constructors are under pressure to make sure that their tests are fair, and the concept of fair mitigates against finding sex differences, as well as the more familiar race differences.

Despite my uncertainties, this is a good paper, on a very sizeable population of test takers in the US and in India. In my view the authors have not mined the Indian material very much. Surely in these disparate US and Indian tests there must be some very similar test items which would allow a proper comparison between US and India. The authors do some comparisons which assume US intelligence is identical to India, which null hypothesis I think can be discarded. Time for them to team up with Richard Lynn and see if they can do more work on the sex ratios in different Indian provinces, which are extremely heterogeneous in terms of general ability. Not sure what my prediction about sex ratios would be: the brighter the province the higher the sex ratios?

Overall, an intriguing finding, strongly suggesting a change in the sex ratio for Maths, but with relevant points still unanswered. Some specific item analyses could be highly informative.

I have already hinted that I know of work which links intelligence to measured brain volumes of men and women, finding brain size to be a good predictor of sex differences, but that paper is only just now going before reviewers, so whereof one cannot speak one must remain silent.

Keep tuning in to Psychological Comments.



    Super riches

  2. The SAT was recentered in 1995.

    As I'm one of the female over 700 scorers in the 80s, I'll take a stab at listing some possible reasons for the change.

    One reason has to be the increasing use of computers in the classroom and in everyday life, especially for things such as classroom drill. Whereas before, girls might not have received targeted instruction in math, computers don't care about your gender, and they don't laugh at wrong answers. They don't make insults about an interest in math being unattractive. For many girls, the chance to practice at home without adult help may have made a difference.

    Another reason is possibly the death of the secretarial profession. The handwriting (typing?) was on the wall that being able to type would no longer be the ticket to an office job for young women which did not require heavy lifting. Data entry and tech jobs are more attractive, and more available.

    Another reason is accessible divorce. No parent of my generation can count on their daughters being shielded from the employment market by a stable marriage. It is better for them to learn a profession than to be required to start over in their '40s with few skills.

    Another reason is the emphasis upon college for all, coupled with the knowledge that financing that education is made easier with good test scores. So it is known that your bright daughter should be cramming for the SAT, rather than practicing her dance steps.

    Another reason may be immigration. Many immigrant families I know perceive the STEM fields (science, technology, engineering and math) to be more prestigious and more lucrative than other fields. Immigration from Asia has been increasing:

    And yes, there has been a long-term effort to interest girls in STEM. In my opinion, it has now overshot the mark, as all children deserve the chance to find out if they might like STEM. Nevertheless, some time ago in the States, women became the majority in medical schools.

    1. Thank you for your very helpful link about the renorming(s) of the test, and your other observations.

  3. The figures for Math PhDs are pretty stable. Females make up about 30% of recipients. However there is significant degree inflation even at PhD level.

  4. 700+ SAT-M seems to be nowhere close to 0.01% Not even 1%.

    1. Agreed, but remember the 1995 SAT recentering mentioned by East Coast above. Even before 1995 700+ on SAT-M was far from top 0.01% for the normal population taking the test in their junior year of high school (but I can't find a good source for the percentiles).

      I think what is happening is this snippet from the SMPY (pre 1995) "primarily focused on the top 0.01 percentile of these students: those 7th graders who scored 700 or above on the SAT-Math" is being misremembered as applying to the usual population of test takers (who take the test four years later). See for more detail.

  5. Thank you! This seems to be panning out as I expected. Will dive into more of this detail.

  6. O/T: I seek your expert view, doc. On the website of the Old England Journal of Medicine today, I read "Most experts agree that good genes are responsible for between 20 and 35 per cent of extreme longevity, and the rest is down to environmental factors." Is that right, do you know?


    1. Continue with this

    2. Thank you. I didn't really make the kernel of my question clear. It's not so much that I doubt the claimed result (though I do), but that I wonder about the boast that "Most experts agree that ...". I suppose it depends whether "most experts" means 'me, my cronies and my students', or whether it's even dafter, along the lines of '97% of scientists agree that ....'.

  7. start here
    Most of the diet stuff need to be taken with a pinch of genetic salt

  8. It looks like those SAT score percentiles are for the 13 year-olds in the SMPY. For the general population those scores correspond to much less impressive percentiles. The top on the verbal tests is much lower after 1995 and they're much less g-loaded with the removal of analogies. They introduced essentially a second verbal test section "critical reading" and "writing" alongside the math test. Formerly the figure of merit in Ivy admissions was (2V+M)*2/3, weighting the verbal double because of it's higher top. The second verbal section sort of did the same thing, but because the top was now lower, the predictive validity declined. Perfect 2400 scores are about 1 in 5000 now, or 1 in 1430 for 1600 scores not counting writing, whereas before 1995 it was 7 in 1,000,000.

    The math SAT hasn't changed as much in difficulty, though, so the increase in perfect scores and changes in sex ratio at the top are harder to explain. Two-thirds of the math test now allows scientific and algebra-capable calculators, though, which weeds out many basic math mistakes.

    Conclusion: pre/post 1995 SAT scores aren't comparable, especially in the upper ranges.

    1. Thanks for these very useful comparisons.

  9. Recently the Malaysians were freaking out about the missing boys in their universities,

    Using the female gender parity index (GPI=%female/%male),

    """Women also outnumbered men in the field of science, mathematics and computers (1.69), subjects which are often believed to be male-dominated in countries overseas. ... Of the engineering undergraduates in Malaysia, 45 percent are female, as compared with 17 percent in the US."""

  10. Thanks for your comment. The article is interesting, but does not mention that Chinese students (brighter, and 25% of the population) are not treated so favourably as the Bumiputera (less able, and 65% of population). Also, if you look at the universities mentioned, there is clearly a different sex ratio for the technology ones. However, the data on grade point averages for both sexes would be highly informative.

  11. Re: table 1

    The male female ratio about some cutoff score were given. Thus the relative population size of male and female should matters. The female GPI for US age between 10-14 for 2013 is 0.95

    This might become critical for India. For example Lynn's data showed Daman&Diu, Jammu Kashmire as top and bottom IQ states. The female GPI for Daman&Diu is 0.618 (the lowest) and that for Jammu Kashmire is 0.889 (mid range). For some other countries it is even more interesting, e.g. for UAE 0.36, Qatar 0.41 for ages btw 15-65 (too many male migrant workers).

    Just for fun I calculated the relative university female GPI (RGPI) with data from Times Higher Education and pop GPI data for ages 15-65 from wikipedia, where
    RGPI = UGPI/CGPI, UGPI is female university GPI and CGPI is pop GPI.

    rgpi ugpi cgpi country
    7.0 2.85 0.41 Qatar
    5.01 1.83 0.36 United Arab Emirates
    2.09 2.23 1.06 Belarus
    2.06 1.91 0.93 Cyprus
    1.98 1.94 0.98 Iceland
    1.98 2.0 1.01 Romania
    1.93 1.91 0.99 Tunisia
    1.93 1.68 0.87 Jordan
    1.71 1.33 0.78 Saudi Arabia
    1.64 1.61 0.98 Turkey
    1.63 1.63 1.0 Philippines
    1.6 1.54 0.96 Malaysia
    1.59 1.61 1.01 Poland
    1.3 1.3 1.0 France
    1.24 1.2 0.97 United Kingdom
    1.09 1.02 0.93 United States
    1.02 0.98 0.96 Germany
    0.54 0.48 0.88 India
    0.49 0.48 0.98 Japan
    0.41 0.39 0.95 Pakistan

    Malaysia is only slightly ahead of Poland (Many of the smart men have gone to UK?). So they should feel alright.

  12. And that study in Romania that showed little difference between men and women**

  13. The historical record is clear: eminent men predominate by at least 7 to 1 or, in Charles Murray’s “Human Accomplishment” 30 to 0 for the very top thinkers, people like Aristotle, Darwin, Galileo, Newton, Einstein (page 143) .

    Some tautology here? Who decided what Human Accomplishment is/was? Ignoring the cultural context of the time(s) and making some kind of indirect inference about 'sex difference' is pretty lax thinking IMO.

    1. You will need to read the book to understand the methods adopted.

    2. You need to understand that the book is about the highest levels of actual human accomplishment, those that have stood the test of time (Murray cuts it off at 1950). The book is NOT about complaints about what women or men could have done, because there is no way of knowing such things....

  14. Man ''DIS-accomplishment'' was/is also very higher, but doc Murray seems forget this detail.

    1. Try reading the book before making comments....

    2. Nope.

      i do what i want.

      in the end,

      the ''accomplishment'' easily overshadow all the shit that man does,

      usually to the conservs narratives.

  15. The new score category for 800 was added in 1996 because College Board "renormed" the SAT tests by adding between 60 and 100 points to the total score, weighted more toward Math, so there suddenly became many more 800s on the Math test. (I'm not sure what they did on the Advanced Math test.) Before that, there were probably close to zero such scores by girls....

  16. ""

    It's IQ, not race per se (of course race determines median IQ).
    The enormous difference between emigrees from India and "Indian Indians".