meep (meep) wrote,
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Differing standard deviations give some people the vapors

Here is part two of the three math-related items I mentioned.

To a large extent, the following, like my prior post, is about a lot made out of something that should be minor.

It relates to distributions that could have the same mean, but have vastly different standard deviations. And some people just can't stand dealing with possibility.



via GIPHY



[insert meep saying: DEAR LORD NOT THIS SHIT AGAIN]

The very short story is that some person wrote a paper how different sexual populations can end up with different standard deviations on various dimensions as a result of natural selection. Some people did not like this conclusion, due to practical interpretations, and got the paper yanked from a journal, which replaced the paper with a different one, and left no notice of the de-publication (putting in a notice of withdrawal is the usual practice if the journal withdraws a paper).

Let me link to his actual paper first, and quote the abstract.


An Evolutionary Theory for the Variability Hypothesis

Theodore P. Hill
August 28, 2018

Abstract

An elementary mathematical theory based on “selectivity” is proposed to address a question raised
by Charles Darwin, namely, how one gender of a sexually dimorphic species might tend to evolve with
greater variability than the other gender. Briefly, the theory says that if one sex is relatively selective
then from one generation to the next, more variable subpopulations of the opposite sex will tend to
prevail over those with lesser variability; and conversely, if a sex is relatively non-selective, then less
variable subpopulations of the opposite sex will tend to prevail over those with greater variability. This
theory makes no assumptions about differences in means between the sexes, nor does it presume that
one sex is selective and the other non-selective. Two mathematical models are presented: a discrete-time
one-step statistical model using normally distributed fitness values; and a continuous-time deterministic
model using exponentially distributed fitness levels.



The paper goes onto build a theoretical model to work with the theory of natural selection (do you not believe in evolution?! are you not scientific?), and it's actually not that involved of a model. Just because the females are the choke-point (as it were) in the Homo Sapiens Sapiens subspecies, it follows that the males show the greater variability due to certain assumptions in how natural selection works.

That human males show greater variability on measurable dimensions shouldn't be all that controversial. (Yes, I'm going to ignore the "socially constructed gender" people for right now. There is such a thing as biological sex, and a very small percentage cannot fit in a specific biological gender by genotype/phenotype.)

The most obvious example for measurable sex differences: height. There is quite a large disparity in male & female human heights, indeed, the sexual dimorphism in humans can be extreme compared to other primates. You may not like that that is the case, but reality really doesn't care what you like.

It's not just that males have relatively higher average heights... but also, that there is greater standard deviation in those heights.

Here is a post with the stats on height by sex, and here is a graph of the distribution in height for American men and women:



These are normalized distributions. That means the area under each curve is equal. The female distribution has a higher peak because more females are bunched around the average than males are around theirs... that is, the male distribution is more variable than the female. People do not have an issue with regards to mean or standard deviation in height.

It's when this pattern is shown elsewhere.

I understand not wanting to see that in cognitive terms, there are more males at very low cognitive levels and more males at very high cognitive levels as females. Perhaps all these observations have been wrong... or "culturally constructed" or what have you. But the reality is that when human males are measured on most measurable dimensions, their coefficient of variation (that is, standard deviation divided by the mean) has been greater than that of human females.

Going back to height -- just because the male mean and standard deviation are greater than females', that does not mean no women exist who are taller than most men -- obviously, women who are over 6' tall do exist, as do loads of men shorter than 6'. But the percentage of women above 6' in the U.S. is fairly low compared to the percentage of men in the U.S. taller than 6'.

This also does not mean that no women exist with higher levels of cognitive ability than average men, or even high intelligence men. Just that the percentage is lower.

This is what The paper's author himself had to say at Quillette:

In the highly controversial area of human intelligence, the ‘Greater Male Variability Hypothesis’ (GMVH) asserts that there are more idiots and more geniuses among men than among women. Darwin’s research on evolution in the nineteenth century found that, although there are many exceptions for specific traits and species, there is generally more variability in males than in females of the same species throughout the animal kingdom.

.....
Once we had written up our findings, Sergei and I decided to try for publication in the Mathematical Intelligencer, the ‘Viewpoint’ section of which specifically welcomes articles on contentious topics. The Intelligencer’s editor-in-chief is Marjorie Wikler Senechal, Professor Emerita of Mathematics and the History of Science at Smith College. She liked our draft, and declared herself to be untroubled by the prospect of controversy. “In principle,” she told Sergei in an email, “I am happy to stir up controversy and few topics generate more than this one. After the Middlebury fracas, in which none of the protestors had read the book they were protesting, we could make a real contribution here by insisting that all views be heard, and providing links to them.”
.....
No sooner had Sergei posted a preprint of our accepted article on his website than we began to encounter problems. On August 16 [2017], a representative of the Women In Mathematics (WIM) chapter in his department at Penn State contacted him to warn that the paper might be damaging to the aspirations of impressionable young women. “As a matter of principle,” she wrote, “I support people discussing controversial matters openly … At the same time, I think it’s good to be aware of the effects.” While she was obviously able to debate the merits of our paper, she worried that other, presumably less sophisticated, readers “will just see someone wielding the authority of mathematics to support a very controversial, and potentially sexist, set of ideas…”
.....
But, that same day [Sept 8, 2017], the Mathematical Intelligencer’s editor-in-chief Marjorie Senechal notified us that, with “deep regret,” she was rescinding her previous acceptance of our paper. “Several colleagues,” she wrote, had warned her that publication would provoke “extremely strong reactions” and there existed a “very real possibility that the right-wing media may pick this up and hype it internationally.” For the second time in a single day I was left flabbergasted. Working mathematicians are usually thrilled if even five people in the world read our latest article. Now some progressive faction was worried that a fairly straightforward logical argument about male variability might encourage the conservative press to actually read and cite a science paper?

In my 40 years of publishing research papers I had never heard of the rejection of an already-accepted paper.

.....

At this point, faced with career-threatening reprisals from their own departmental colleagues and the diversity committee at Penn State, as well as displeasure from the NSF, Sergei and his colleague who had done computer simulations for us withdrew their names from the research. Fortunately for me, I am now retired and rather less easily intimidated—one of the benefits of being a Vietnam combat veteran and former U.S. Army Ranger, I guess. So, I continued to revise the paper, and finally posted it on the online mathematics archives.

So it's on arXiv.org, and not an "official" journal.

Others' commentary:

Reason Hit & Run: A Mathematician Says Activists Made His Paper Disappear Because Its Findings Offended Them

Volokh Conspiracy (at Reason): A Mathematics Paper Two Math Journals Were Mau-Maued into Suppressing

Hot Air: How A Scientific Paper On Male Variability Was Made To Disappear

Here's my bottom line: I understand that it upsets some people to think that there are far more male geniuses (and far more male mentally disabled people) than females in the same categories. I have seen evidence of both of these in my life, having looked at the population of children in my son's classes for kids on the autism spectrum (more lopsidedly male than the math team I was on in high school) and having noticed what it looked like at the nerd forums I've been at (no, not ComicCon -- academic stuff). There are loads of potential explanations for this beyond males being generally more variable than female.

In the paper itself, the author also referred to papers that did not find greater male variability:

A.2 Primary Analyses Inconsistent with the Greater Male Variability Hypothesis

“Boys were not found to be more variable than girls” [16, p. 326].

“data from several studies indicate that greater male variability with respect to mathematics is
not ubiquitous...[and] is largely an artifact of changeable sociocultural factors, not immutable,
innate biological differences between the sexes...Our finding...[is] inconsistent with the Greater
Male Variability Hypothesis” [31, pp. 8801, 8806].

“Therefore, we conclude that both variance and VR [variance ratio - ratio of male to female
variance] in mathematics performance vary greatly among countries...These findings are inconsistent
with the greater male variability hypothesis” [35, p. 14].

“the common assumption that males have greater variance in mathematics achievement is not
universally true” [42, p. S152].


Some are specific to math, and one has to do with language acquisition at young ages (the time when sexual selection is not expected... I don't know that too many two-year-olds of either sex have much to do with actually giving birth to additional babies... though, my babies were so cute when young, I definitely wanted more. Maybe that's the connection)

Greater adult male variability on cognitive measures may not be true in that they don't actually exist (either females or males being mismeasured -- or both), may be culturally-dependent (male variability may be lower elsewhere, and female variability higher). It may all be completely illusionary, in that nothing is being measured and people are making stuff up. Any of these are possible before considering any evidence, and all of these explanations are falsifiable.

But if one decides that a priori certain hypotheses are offensive if true......... are you really open to the possibility they are true? Are you really adhering to any scientific standard at all?

Because your desire that something isn't true has very little to do with whether it's true in reality. Physical forces do not care if you "believe" in them - if you step off a cliff, you're not going to hang in the air like a Looney Tunes character because of disbelief in gravity. [I did have fun pondering this possibility in reading scifi and fantasy novels. But I realized they weren't actually true.]

The larger your discrepancy between your beliefs and external reality, the more trouble you're going to have.

But let's ignore that for right now. Perhaps the paper writer's math model has little connection to any sort of reality. Maybe the model is overly simplified to really capture the dynamics of natural selection. I can see that, and somebody should refute it on that basis, if that's where it's weak.

Another possibility: Maybe natural selection doesn't actually hold. Maybe a literal God is directing intelligent design for His own ends, and thus we need not think of reproductive selection. I am willing to entertain that possibility... however, I'm not going to assert that that is scientifically testable.

I am not willing to entertain that the possibility of greater male variability compared to female variability is out-of-bounds for scientific research, much less theoretical math models that can provide the basis for testing various hypotheses.

When you have decided that you've got a set of beliefs such that certain propositions are not to be tested, then you've got a religion on your hands. Don't try to sell it as science. I'm a religious person, so I have no trouble thinking that certain things are out of bounds [such as certain human experimentation, vivisection, etc]. But it's not against my religion to think that the there may be physical differences between the sexes [which can be tested in non-destructive ways].

The journal editors and publishers should be ashamed of themselves. They are moral cowards, intellectual cowards, and just plain weasels for withdrawing a paper without explicitly stating a paper had been withdrawn. I am not disputing the journals' right to withdraw a paper (or not to publish it in the first place) because they don't want to deal in controversy or think the paper is poor -- I am disputing any kind of integrity on their part for withdrawing the paper and replacing it with another with no notice.

Suck it up, you weenies. If you publish and then withdraw... then admit it by writing a notice. That's the minimum expectation.

MORE: The author of this post actually addresses aspects of the model, and why it doesn't work, with additional thoughts

A statement from Amie Wilkinson - she objected to the paper in re: its scientific merits, and did not ask for it to be removed, but asked for rebuttal/reaction papers to be published in follow-up (that sounds good to me).

A statement from Brandon Farb - explains the retraction. As to lack of notice:
I believe that the editor-in-chief should have added a statement about why this was done, but he did not.
Yes, we know.

Terence Tao: On the recently removed paper from the New York Journal of Mathematics


I do not have much of an issue with a retraction of a paper found to be weak. I do have an issue with de-publication and no notice.
Tags: academia, math, women
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