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This was more a general statement about areas of science where complex systems are involved. Not specifically a criticism. It is very difficult to explain why these types of studying can be lacking.

This particular study is not as narrowly focused as some studies I have seen. However, I would need to analyze the test questions on these various classes of tests to see how much variation there is in the complexity. How people view the complexity of testing is definitely a topic of debate.

I would say this particular study is definitely telling us further study is required. The information is interesting, but on it's own, it gives no indication as to why the results are what they are. At least the information tells us that the idea of males being better in math as found in other narrow studies may not be right.

Back in the 70s and 80s, we were constantly hearing how almost everything was found to cause cancer. The experiments were done using 2 control groups of rats. One group had none of the substance and the other group was given an extreme dose of the substance. Almost every substance tested was shown to cause cancer.

Later when much better science was used to test for the effects of cancer, many control groups were tested with each having gradually increasing doses of the substance. A graph where the incidences of cancer gradually increased as the dose increased were considered to be evidence the substance caused cancer.

In cases where no cancer appears to be caused by the substance until an extremely high dose is applied are considered not to be evidence the substance causes cancer. The graphs in these cases will suddenly spike at the high dosage levels. What this early poor science had discovered was that almost any substance can cause cancer at overdose levels. It was the interpretation of the findings which was flawed.

If I was to do a study to determine if one gender was better in math than another, I would first have to ensure the control groups were similar in almost every way other than gender. This study compares results between different cultures and this adds too many variables into the equation. You would also have to ensure as many factors as possible were the same between the male and females in the study. This is virtually impossible to guarantee.

A study specific to math ability would just have too many variables involved. Now if we can find the pattern of cognitive abilities across a wide variety of skills, this can remove a degree of error resulting from nurturing variations due to gender. This requires an understanding of how various skills are related to work, but I believe this is the minimum it would take to have anywhere near convincing evidence.

What I have been trying to do is come up with what I call the periodic table of cognitive ability. In chemistry, they had once tried to do chemistry using earth, wind, fire and water. The periodic table is what moved chemistry forward. I feel the same about analyzing human cognitive abilities using high level subjects like math and science. This is feel will not get us anywhere in understanding human cognition.

If you ask me who is better at math, I will tell you my answer is I don't know. If the question is which gender would statistically be faster at solving a Sudoku puzzle, I would take a guess it would be males. This is a specific enough skill, I have a fairly good idea of what neural mapping would suit this skill. Males on average have much more tightly wired neural mapping with greater localization of neural connectivity. For a very focused simple skill, this is probably ideal. For a more advanced skill, I wouldn't hazard to guess.

I'm hoping the cancer study info helps with understanding how the shape of the graph comes into play.

Don't take the cognitive stuff too seriously. Any statement I make regarding the brain are at best slightly educated guesses. I just don't want to have to say I think or speculate constantly.

Well, of course, this sort of thing is virtually never possible in the social sciences. Nevertheless, of course studies do control for such things as much as possible. But...neither of these studies are trying to PROVE that boys and girls are equal. Rather, they are trying to DISprove the Greater Male Variability Theory, which holds that it is a biologically immutable fact that boys have more variability in their math performance and are overrepresented in both tails of the bell curve. If this is true, then it should be true universally, since it's purportedly a biological, hard-wired difference. One's nation of origin should make no difference.

At the elite college I attended, there were lots of male Chinese math professors, but I do not recall any female ones. If the right-tail effect is not present in the Chinese, for example, where are the great female Chinese mathematicians? Similarly, I can think of many more great Russian male mathematicians than female ones. Can you name a country where there are as many top-notch female mathematicians as male ones?

The various links have included many conclusions drawn from tests aimed at the middle, and it is to those that I was referring. I did look at the AMS link, but it clearly didn't reach the same conclusions I was objecting to so I didn't feel the need to respond to it. I'll resist the urge to snark back here.

From the AMS link:
The earlier articles were claiming to have data that contradicted variability by looking at data which would be least likely to show it, whereas this article looks at the right kind of data, and explicitly says it remains an open question. These are not the same conclusions at all.

If there were data on the high end (IMO, USAMO, SET, etc) showing the split was 1:1 for at least some statistically significant areas, then this would be very convincing evidence against variability, but that data doesn't show 1:1, it shows 3:1 or more in many cases. This certainly doesn't prove variability true, but it also doesn't prove it false.

Arguing on the internet ... I'll leave the last word to you.

I made some very rough and probably highly inaccurate bell curves for both genders based on a figures from a number of scientific studies. Some of the variables were guesses as well, so I don't have a lot of confidence in the graphs.

The graphs were interesting in that there was a mere 4% shift of the bell curves between the genders based on the numbers from US studies. If this was in any way accurate and what my graphs represented from a neurological point of view is in any way accurate, then on average, there is almost no difference in the male and female brains.

Now this small shift in the bell curves did result in a very small portion of the population being in the autism spectrum with males being significantly in higher numbers. The autism spectrum in my opinion has extreme variability in how it affect cognitive abilities. In some portions of the spectrum it can result in severe disability, whereas in other portions, it can result in extreme talents in very specific areas.

Given that males are highly represented in this spectrum, I could see this as being the cause for Greater Male Variability at the tails of the bell curve related to IQ scores.

If you have ever heard of the Male Birth Order Effect, it suggests cognitive characteristics are altered according to birth order in males. From what I have read, first born males would be shifted more toward the female side of the spectrum and later born males would be shifted more toward the male end of the spectrum. if this is true, then the bell curves for male and females would be more similar if the average family size is smaller.

So if this Male Birth Order Effect has any merit, there could be regional differences due to cultural differences affecting family sizes.

Interesting theory, Jamie! However, first-born boys are still boys, you know? I don't think you can say "Boys are better are math," if your corollary is "As long as you leave out first-born boys" (of which there are an awful lot!)


Sure. But 20 years ago, it was 13:1. 20 years is an evolutionary microsecond! I'm willing to wager that the ratio will continue to decrease.

This goes to my earlier point about it being ludicrous to conclude that just at THIS very instant we have magically reached the point where the differences are all biological and no cultural issues remain. Surely you would agree that there remain many cultural stereotypes steering girls away from math?



The earlier study had several parts, one of which looked at NCLB-type state exams (which I agree do not disprove variability, though they disprove a generalized "Boys are better at math than girls, on average" belief, which IMO is held by 80-90% of the American public) and one of which looked at the Study of Mathematically Precocious Youth, where they give the SAT to kids under age 13. Perhaps some would argue that this is still not a high enough standard, but I think most on this board would agree that scoring over 700 on the math SAT at age 11 is indicative of giftedness in math.

Sorry, I'm not suggesting either boys are better at math or that biology is the only factor. I was trying to bring the nature side into the discussion. Also, I was also trying to bring forward the idea that cognitive ability is not subject specific. So a person good in aspects of math may not be good in other aspects of math.

I find so many people are focused on the nurture side, I figured this side is covered in most of these discussions. This is why I am bringing the nature side into it.

I know I need to let this go, but you keep putting up straw men and implying they are my position. Please go back and re-read exactly what I claimed.

I didn't actually mean that your personal position was that we have indeed reached that point; more that many people do. I was referring back to an earlier post.

I do take issue with saying a study in the Proceedings of the National Academy of Sciences is junk science without having read the full text. I suppose I expect a certain amount of respect for peer-reviewed science published in reputable journals on these boards.

Bostonian, did you read the open-access article I linked? As to why there are fewer female mathematicians, while it's possible genetic difference plays some slight role, there are of course MANY other better explanations. As is explained in several of these articles, even if we look purely at raw data among those who are highly talented, the ratios we see (3 or maybe 4 to 1 M:F, at present) do not represent the actual ratios of men to women in the field. Obviously, something else is at work.