Variability hypothesis

File:Ci generos.png

Bell curve comparations based in Sex differences in means and standard deviations for Armed Services Vocational Aptitude Battery (ASVAB) subtests and total scores and for Armed Forces Qualification Test (AFQT) scores. Women pink curve and men blue curve.

The variability hypothesis, also known as the greater male variability hypothesis, states that males display greater variability in traits than females do. It has often been discussed in relation to cognitive ability, where it has been observed that human males are more likely than females to have very high or very low intelligence. The sex-difference in the variability of intelligence has been discussed since at least Charles Darwin. Sex-differences in variability are present in many abilities and traits - including physical, psychological and genetic ones. It is not only found in humans but in other sexually-selected species as well.

Early studies

The variability hypothesis originated in the early nineteenth century with Johann Meckel, who argued that males have a greater range of ability than females, especially in intelligence. In other words, he believed that most geniuses and most mentally impaired people are men. Because he considered males to be the "superior animal," Meckel concluded that females' lack of variation was a sign of inferiority.

Later that century the character of the variability hypothesis was altered to coincide better with Charles Darwin's emphasis on the importance of variation from the average for the evolutionary process. Following Darwin, the variability hypothesis was instead put forward as man's greater variability compared to women, and its application was soon extended to sex differences in mental abilities. Thus, men were thought to vary greatly in their abilities, while women were assumed to be basically the same in their abilities. The greater number of men at both ends of the intellectual spectrum (as patients in institutions and as great intellectual achievers) was taken as evidence of man's greater innate variability.

In the early twentieth century, the variability hypothesis flourished in sociological, psychological, medical and educational literature. The hypothesis received support not from empirical evidence, but rather from "armchair dogma" about innate female inferiority. Among the proponents of the variability hypothesis at this time were psychologists G. Stanley Hall, Edward Lee Thorndike, and James McKeen Cattell. One logical conclusion drawn from the variability hypothesis was that since women were not expected to exhibit above-average intelligence, it was unreasonable to expect eminence from them. This led Thorndike and Hall to suggest the adoption of curricula aimed at preparing women for their future roles as mothers and wives. The only significant critic of the variability hypothesis was Karl Pearson, a British psychologist who had studied variability in 1897 and found no sex differences.Template:Cn Pearson's research was the only published scientific investigation of the variability hypothesis prior to the work of American psychologist Leta Hollingworth.

Leta Hollingworth's studies

Template:See also Hollingworth's position at the Clearing House for Mental Defectives allowed her the opportunity to refute the variability hypothesis. By examining the case records of 1,000 patients, Hollingworth determined that, although men outnumbered women in the clearing house, the ratio of men to women decreased with age. Hollingworth explained this to be the result of men facing greater societal expectations than women. Consequently, deficiencies in men were often detected at an earlier age, while similar deficiencies in women might not be detected because less was expected of them. Therefore, deficiencies in women would be required to be more pronounced than those in men in order to be detected at similar ages.

Hollingworth also attacked the variability hypothesis theoretically, criticizing the underlying logic of the hypothesis. Hollingworth argued that the variability hypothesis was flawed because: (1) it had not been empirically established that men were more anatomically variable than women, (2) even if greater anatomical variability in men were established this would not necessarily mean that men were also more variable in mental traits, (3) even if it were established that men were more variable in mental traits this would not automatically mean that men were innately more variable, (4) variability is not significant in and of itself, but rather depends on what the variability consists of, and (5) that any possible differences in variability between men and women must also be understood with reference to the fact that women lack the opportunity to achieve eminence because of their prescribed societal and cultural roles. Additionally, the argument that great variability automatically meant greater range was criticized by Hollingworth.Template:How

In an attempt to examine the validity of the variability hypothesis, while avoiding intervening social and cultural factors, Hollingworth gathered data on birth weight and length of 1,000 male and 1,000 female neonates. This research found virtually no difference in the variability of male and female infants, and it was concluded that if variability "favoured" any sex it was the female sex. Additionally, along with the anthropologist Robert Lowie, Hollingworth published a review of literature from anatomical, physiological, and cross-cultural studies, in which no objective evidence was found to support the idea of innate female inferiority.

Hollingworth's doctoral dissertation also dealt with the psychology of women. Entitled "Functional periodicity: An experimental study of the mental and motor abilities of women during menstruation", it found no evidence of changes in performance associated with phases of the menstrual cycle, refuting a common belief of the time. Hollingworth's graduate supervisor was E. L. Thorndike, himself a supporter of the variability hypothesis.

Modern studies

The results seem to vary based on the type of problem, but some recent studies have found that the variability hypothesis is true for parts of IQ tests, with more men falling at the extremes of the spectrum. In general different studies show different results; for example, males are more variable in mathematical and spatial abilities, but in some others the women are more variable.

Recent studies shows that greater male variability in mathematics persists in the U.S., although the ratio of boys to girls at the top end of the distribution is reversed in some specific immigrant groups. A 2007 meta-analysis found that males are more variable on most measures of quantitative and visuospatial ability. A 2014 review found that males tend to have higher variance on mathematical and verbal abilities but females tend to have higher variance on fear and emotionality; however, the differences in variance are small and the causes remain unknown. A 2005 meta-analyses found greater female variability on the advanced progressive matrices, and no difference in variability on the standard progressive matrices. A 2010 meta-analysis of 242 studies found that males have an 8% greater variance in mathematical abilities than females. A 2017 literature review by Sean Stevens for the Heterodox Academy found that males do tend to be more variable than females on a variety of measures of intelligence and personality and that gender-egalitarian countries demonstrate the greatest differences.

Academic Activists Send a Published Paper Down the Memory Hole

• Academic Activists Send a Published Paper Down the Memory Hole

September 7, 2018

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.

Evidence for this hypothesis is fairly robust and has been reported in species ranging from adders and sockeye salmon to wasps and orangutans, as well as humans. Multiple studies have found that boys and men are over-represented at both the high and low ends of the distributions in categories ranging from birth weight and brain structures and 60-meter dash times to reading and mathematics test scores. There are significantly more men than women, for example, among Nobel laureates, music composers, and chess champions—and also among homeless people, suicide victims, and federal prison inmates.

Darwin had also raised the question of why males in many species might have evolved to be more variable than females, and when I learned that the answer to his question remained elusive, I set out to look for a scientific explanation. My aim was not to prove or disprove that the hypothesis applies to human intelligence or to any other specific traits or species, but simply to discover a logical reason that could help explain how gender differences in variability might naturally arise in the same species.

I came up with a simple intuitive mathematical argument based on biological and evolutionary principles and enlisted Sergei Tabachnikov, a Professor of Mathematics at Pennsylvania State University, to help me flesh out the model. When I posted a preprint on the open-access mathematics archives in May of last year, a variability researcher at Durham University in the UK got in touch by email. He described our joint paper as “an excellent summary of the research to date in this field,” adding that “it certainly underpins my earlier work on impulsivity, aggression and general evolutionary theory and it is nice to see an actual theoretical model that can be drawn upon in discussion (which I think the literature, particularly in education, has lacked to date). I think this is a welcome addition to the field.”

So far, so good.

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.”

Professor Senechal suggested that we might enliven our paper by mentioning Harvard President Larry Summers, who was swiftly defenestrated in 2005 for saying that the GMVH might be a contributing factor to the dearth of women in physics and mathematics departments at top universities. With her editorial guidance, our paper underwent several further revisions until, on April 3, 2017, our manuscript was officially accepted for publication. The paper was typeset in India, and proofread by an assistant editor who is also a mathematics professor in Kansas. It was scheduled to appear in the international journal’s first issue of 2018, with an acknowledgement of funding support to my co-author from the National Science Foundation. All normal academic procedure.

anxiety about gender-parity erupted in Silicon Valley

Coincidentally, at about the same time, anxiety about gender-parity erupted in Silicon Valley. The same anti-variability argument used to justify the sacking of President Summers resurfaced when Google engineer James Damore suggested that several innate biological factors, including gender differences in variability, might help explain gender disparities in Silicon Valley hi-tech jobs. For sending out an internal memo to that effect, he too was summarily fired.

No sooner had Sergei posted a preprint of our accepted article on his website than we began to encounter problems. On August 16, 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…”

A few days later, she again contacted Sergei on behalf of WIM and invited him to attend a lunch that had been organized for a “frank and open discussion” about our paper. He would be allowed 15 minutes to describe and explain our results, and this short presentation would be followed by readings of prepared statements by WIM members and then an open discussion. “We promise to be friendly,” she announced, “but you should know in advance that many (most?) of us have strong disagreements with what you did.”

On September 4, Sergei sent me a weary email. “The scandal at our department,” he wrote, “shows no signs of receding.” At a faculty meeting the week before, the Department Head had explained that sometimes values such as academic freedom and free speech come into conflict with other values to which Penn State was committed. A female colleague had then instructed Sergei that he needed to admit and fight bias, adding that the belief that “women have a lesser chance to succeed in mathematics at the very top end is bias.” Sergei said he had spent “endless hours” talking to people who explained that the paper was “bad and harmful” and tried to convince him to “withdraw my name to restore peace at the department and to avoid losing whatever political capital I may still have.” Ominously, “analogies with scientific racism were made by some; I am afraid, we are likely to hear more of it in the future.”

The following day, I wrote to the three organisers of the WIM lunch and offered to address any concrete concerns they might have with our logic or conclusions or any other content. I explained that, since I was the paper’s lead author, it was not fair that my colleague should be expected to take all the heat for our findings. I added that it would still be possible to revise our article before publication. I never received a response.

Instead, on September 8, Sergei and I were ambushed by two unexpected developments.

First, the National Science Foundation wrote to Sergei requesting that acknowledgment of NSF funding be removed from our paper with immediate effect. I was astonished. I had never before heard of the NSF requesting removal of acknowledgement of funding for any reason. On the contrary, they are usually delighted to have public recognition of their support for science.

The ostensible reason for this request was that our paper was unrelated to Sergei’s funded proposal. However, a Freedom of Information request subsequently revealed that Penn State WIM administrator Diane Henderson (“Professor and Chair of the Climate and Diversity Committee”) and Nate Brown (“Professor and Associate Head for Diversity and Equity”) had secretly co-signed a letter to the NSF that same morning. “Our concern,” they explained, “is that [this] paper appears to promote pseudoscientific ideas that are detrimental to the advancement of women in science, and at odds with the values of the NSF.” Unaware of this at the time, and eager to err on the side of compromise, Sergei and I agreed to remove the acknowledgement as requested. At least, we thought, the paper was still on track to be published.

But, that same day, 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. And so I emailed Professor Senechal. She replied that she had received no criticisms on scientific grounds and that her decision to rescind was entirely about the reaction she feared our paper would elicit. By way of further explanation, Senechal even compared our paper to the Confederate statues that had recently been removed from the courthouse lawn in Lexington, Kentucky. In the interests of setting our arguments in a more responsible context, she proposed instead that Sergei and I participate in a ‘Round Table’ discussion of our hypothesis argument, the proceedings of which the Intelligencer would publish in lieu of our paper. Her decision, we learned, enjoyed the approval of Springer, one of the world’s leading publishers of scientific books and journals. An editorial director of Springer Mathematics later apologized to me twice, in person, but did nothing to reverse the decision or to support us at the time.

So what in the world had happened at the Intelligencer? Unbeknownst to us, Amie Wilkinson, a senior professor of mathematics at the University of Chicago, had become aware of our paper and written to the journal to complain. A back-and-forth had ensued. Wilkinson then enlisted the support of her father—a psychometrician and statistician—who wrote to the Intelligencer at his daughter’s request to express his own misgivings, including his belief that “[t]his article oversimplifies the issues to the point of embarrassment.” Invited by Professor Senechal to participate in the proposed Round Table discussion, he declined, admitting to Senechal that “others are more expert on this than he is.” We discovered all this after he gave Senechal permission to forward his letter, inadvertently revealing Wilkinson’s involvement in the process (an indiscretion his daughter would later—incorrectly—blame on the Intelligencer).

I wrote polite emails directly to both Wilkinson and her father, explaining that I planned to revise the paper for resubmission elsewhere and asking for their criticisms or suggestions. (I also sent a more strongly worded, point-by-point rebuttal to her father.) Neither replied. Instead, even long after the Intelligencer rescinded acceptance of the paper, Wilkinson continued to trash both the journal and its editor-in-chief on social media, inciting her Facebook friends with the erroneous allegation that an entirely different (and more contentious) article had been accepted.

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.

On October 13, a lifeline appeared

On October 13, a lifeline appeared. Igor Rivin, an editor at the widely respected online research journal, the New York Journal of Mathematics, got in touch with me. He had learned about the article from my erstwhile co-author, read the archived version, and asked me if I’d like to submit a newly revised draft for publication. Rivin said that Mark Steinberger, the NYJM’s editor-in-chief, was also very positive and that they were confident the paper could be refereed fairly quickly. I duly submitted a new draft (this time as the sole author) and, after a very positive referee’s report and a handful of supervised revisions, Steinberger wrote to confirm publication on November 6, 2017. Relieved that the ordeal was finally over, I forwarded the link to interested colleagues.

Three days later, however, the paper had vanished. And a few days after that, a completely different paper by different authors appeared at exactly the same page of the same volume (NYJM Volume 23, p 1641+) where mine had once been. As it turned out, Amie Wilkinson is married to Benson Farb, a member of the NYJM editorial board. Upon discovering that the journal had published my paper, Professor Farb had written a furious email to Steinberger demanding that it be deleted at once. “Rivin,” he complained, “is well-known as a person with extremist views who likes to pick fights with people via inflammatory statements.” Farb’s “father-in law…a famous statistician,” he went on, had “already poked many holes in the ridiculous paper.” My paper was “politically charged” and “pseudoscience” and “a piece of crap” and, by encouraging the NYJM to accept it, Rivin had “violat[ed] a scientific duty for purely political ends.”

Unaware of any of this, I wrote to Steinberger on November 14, to find out what had happened. I pointed out that if the deletion were permanent, it would leave me in an impossible position. I would not be able to republish anywhere else because I would be unable to sign a copyright form declaring that it had not already been published elsewhere. Steinberger replied later that day. Half his board, he explained unhappily, had told him that unless he pulled the article, they would all resign and “harass the journal” he had founded 25 years earlier “until it died.” Faced with the loss of his own scientific legacy, he had capitulated. “A publication in a dead journal,” he offered, “wouldn’t help you.”

Colleagues I spoke to were appalled

Colleagues I spoke to were appalled. None of them had ever heard of a paper in any field being disappeared after formal publication. Rejected prior to publication? Of course. Retracted? Yes, but only after an investigation, the results of which would then be made public by way of explanation. But simply disappeared? Never. If a formally refereed and published paper can later be erased from the scientific record and replaced by a completely different article, without any discussion with the author or any announcement in the journal, what will this mean for the future of electronic journals?

Meanwhile, Professor Wilkinson had now widened her existing social media campaign against the Intelligencer to include attacks on the NYJM and its editorial staff. As recently as April of this year, she was threatening Facebook friends with ‘unfriending’ unless they severed social media ties with Rivin.

In early February, a friend and colleague suggested that I write directly to University of Chicago President Robert Zimmer to complain about the conduct of Farb and Wilkinson, both of whom are University of Chicago professors. The previous October, the conservative New York Times columnist Bret Stephens had called Zimmer “America’s Best University President.” The week after I wrote to Zimmer, the Wall Street Journal would describe Chicago as “The Free-Speech University” based upon its president’s professed commitment to the principles of free inquiry and expression. Furthermore, Professor Zimmer is a mathematician from the same department and even the same subfield as Farb and Wilkinson, the husband-wife team who had successfully suppressed my variability hypothesis research and trampled on the principles of academic liberty. Surely I would receive a sympathetic hearing there?

And so I wrote directly to Professor Zimmer, mathematician to mathematician, detailing five concrete allegations against his two colleagues. When I eventually received a formal response in late April, it was a somewhat terse official letter from the vice-provost informing me that an inquiry had found no evidence of “academic fraud” and that, consequently, “the charges have been dismissed.” But I had made no allegation of academic fraud. I had alleged “unprofessional, uncollegial, and unethical conduct damaging to my professional reputation and to the reputation of the University of Chicago.”

When I appealed the decision to the president, I received a second official letter from the vice-provost, in which he argued that Farb and Wilkinson had “exercised their academic freedom in advocating against the publication of the papers” and that their behavior had not been either “unethical or unprofessional.” A reasonable inference is that I was the one interfering in their academic freedom and not vice versa. My quarrel, the vice-provost concluded, was with the editors-in-chief who had spiked my papers, decisions for which the University of Chicago bore no responsibility. At the Free Speech University, it turns out, talk is cheap.

there has undoubtedly been significant bias and discrimination

Over the years there has undoubtedly been significant bias and discrimination against women in mathematics and technical fields. Unfortunately, some of that still persists, even though many of us have tried hard to help turn the tide. My own efforts have included tutoring and mentoring female undergraduates, graduating female PhD students, and supporting hiring directives from deans and departmental chairs to seek out and give special consideration to female candidates. I have been invited to serve on two National Science Foundation gender and race diversity panels in Washington.

Which is to say that I understand the importance of the causes that equal opportunity activists and progressive academics are ostensibly championing. But pursuit of greater fairness and equality cannot be allowed to interfere with dispassionate academic study. No matter how unwelcome the implications of a logical argument may be, it must be allowed to stand or fall on its merits not its desirability or political utility. First Harvard, then Google, and now the editors-in-chief of two esteemed scientific journals, the National Science Foundation, and the international publisher Springer have all surrendered to demands from the radical academic Left to suppress a controversial idea. Who will be the next, and for what perceived transgression? If bullying and censorship are now to be re-described as ‘advocacy’ and ‘academic freedom,’ as the Chicago administrators would have it, they will simply replace empiricism and rational discourse as the academic instruments of choice.

Educators must practice what we preach and lead by example. In this way, we can help to foster intellectual curiosity and the discovery of fresh reasoning so compelling that it causes even the most sceptical to change their minds. But this necessarily requires us to reject censorship and open ourselves to the civil discussion of sensitive topics such as gender differences, and the variability hypothesis in particular. In 2015, the University of Chicago’s Committee on Freedom of Expression summarized the importance of this principle beautifully in a report commissioned by none other than Professor Robert Zimmer:

In a word, the University’s fundamental commitment is to the principle that debate or deliberation may not be suppressed because the ideas put forth are thought by some or even by most members of the University community to be offensive, unwise, immoral, or wrong-headed.

Supporting documentation for this account can be found here.

Ted Hill is Professor Emeritus of Mathematics at Georgia Tech, and currently a research scholar in residence at the California Polytechnic State University in San Luis Obispo. His memoir PUSHING LIMITS: From West Point to Berkeley and Beyond was recently published jointly by the American Mathematical Society and the Mathematical Association of America.

https://quillette.com/2018/09/07/academic-activists-send-a-published-paper-down-the-memory-hole/

See also

• 8chan
• Contributor Covenant (Contributor Covenant Code of Conduct, CCCoC, CCCOC, code of conduct, CoC, COC)
• Sex differences in humans
• Sex and psychology
• Bateman's principle
• Lek paradox
• Feminism
• Political correctness