Beware the Univariate Fallacy

How activists use a simple statistical trick to invent or eliminate group differences to suit their purpose.

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“When the truth offends, we lie and lie until we cannot even remember it's there. But it is still there. Every lie we tell incurs a debt to the truth. Sooner or later, the debt is paid.” — Valery Legasov

In a world flooded with information, the ability to discern fallacious reasoning is an indispensable skill to safeguard oneself against the tides of unreason. A skilled orator or debater, however, can easily obscure their faulty logic through the seductive power of rhetoric. One way to safeguard your mind against such manipulation is to expose yourself to specific fallacies and their related forms in advance so you can better spot them in the wild.

One of the most widespread and effective fallacies that activists, as well as prestigious journals and news outlets, continue to propagate is the Univariate Fallacy. The word “univariate” means “one variable,” and this fallacy works by concentrating on a single variable while ignoring all else in order to deceive people into accepting a distorted picture of reality.

Importantly, there are two versions of the Univariate Fallacy that you should be acquainted with. One version is blatantly applied broadly across many issues and is used to invent or exaggerate group differences, while the other is more cryptic and applied more narrowly to reduce or eliminate appearance of real group differences.

The first, more common version of the Univariate Fallacy serves as the foundation for virtually all “equity” initiatives that aim to eliminate outcome disparities for various identity groups based on immutable traits like race, sex, and gender identity. The reasoning behind this approach is premised on the mistaken belief that group disparities are in and of themselves proof of systemic injustice, such as racism, sexism, homophobia, transphobia, and a host of other -phobias and -isms.

Regrettably, these group disparities are routinely (if not invariably) calculated by comparing population averages of a single variable across groups without considering any confounding variables. This flawed methodology often leads people to adopt beliefs that are true in a very superficial and naive sense, yet false in a much deeper and relevant sense.

For instance, it is often claimed that black Americans are incarcerated at higher rates than other races without controlling for crime rates, or that black Americans are more likely to be victims of police shootings than other races without controlling for police encounters. There’s also the purported “wage gap” that asserts women are paid 77 cents for every dollar a man earns without controlling for differences in occupations, positions, education, job tenure, or hours worked per week. In each of these instances, the apparent disparities dissolve when a more appropriate and rigorous multivariate methodology is adopted.

The second and more cryptic version of the Univariate Fallacy is essentially the inverse of the first version—it is not used to invent or exacerbate perceived group differences, but rather to minimize or eliminate them altogether. This is most often deployed in the realm of sex differences, and even to the categories male and female themselves.

To minimize or eliminate the appearance of real sex differences, it is common for activists and activist scientists to insist that in order for differences to be considered real, they must be absolute; that is, it must be shown that these differences reduce to some single factor that clearly and categorically separate all males from all females. In practice, this means that no matter how stark an average sex difference may be, if someone is able to point to a single instance where that trait overlaps, they will insist the difference is not significant or materially real.

Take height, for example. Males and females differ in their average height, but because this difference isn’t absolute (i.e., some females are taller than some males, and some males are shorter than some females), activists will insist this can be ignored.

This flawed reasoning is frequently used to justify males who identify as women (i.e., “trans women”) to be allowed to compete in female sporting events.

An article in Deadspin, for example, uses the Univariate Fallacy to argue in favor of allowing the male powerlifter JayCee Cooper, who last year broke the Minnesota state record for women’s bench press after only one year of training, to compete in the female category:

When we shove the concept of athletic ability—strength, for instance—into the same black-and-white binary that we try to put gender into, we’re wrong. There is no stark line separating what men can do athletically and what women can. Some women, in fact, are bigger, faster, and stronger than some men.

The same argument highlighting the existence of some overlap in all performance-related traits between males and females was also made in a report by the Canadian Center for Ethics in Sports to justify including male athletes who identify as women in sports.

Since the early 20th century, elite sport policies worked to pathologize and control women’s bodies and enforce dimorphic sex. There is, however, a significant overlap in all sexual characteristics. ‘Male’ and ‘female’ are not mutually exclusive categories and should not be treated as such.

The inability to reduce sex differences in athletic performance to a single factor is thus used to argue against the existence of any inherent male sporting advantage.

But the justification for excluding male athletes from female sports is not predicated on there being no overlap in performance-related traits, but based on the fact that, all else being equal, male puberty gives male athletes an inherent advantage they wouldn’t enjoy otherwise that is not available to females. If the justification for exclusion required the total absence of overlap in performance, then this would prevent athletic leagues and events from excluding adults from children’s leagues or excluding athletes who take performance enhancing drugs (PEDs). After all, some children are bigger, faster, and stronger than some adults, and athletes taking PEDs don’t always win.

The same flawed logic is also frequently used to assert that there are no sex differences between male and female brains. For example, in a review of Gina Rippon’s 2019 book The Gendered Brain: The New Neuroscience That Shatters The Myth Of The Female Brain published in Nature, Lise Eliot claimed that the absence of a “decisive, category-defining” difference in male and female brains means that we cannot claim real sex differences exist.

Yet, as The Gendered Brain reveals, conclusive findings about sex-linked brain differences have failed to materialize. Beyond the “missing five ounces” of female brain — gloated about since the nineteenth century — modern neuroscientists have identified no decisive, category-defining differences between the brains of men and women.

But differences between populations don’t have to be “decisive” and “category-defining” to be measurable and real. As we saw with height, no rational person would believe that male and female height differences don’t exist because all men aren’t taller than all women, and the same goes with brain differences. Sex differences don’t have to be absolute and binary to be real.

There is an even more extreme version of the Univariate Fallacy that moves well beyond attempting to eliminate or minimize sex differences—it is used to argue that the sex categories male and female themselves are merely socially constructed figments of our imagination. To this end, the Univariate Fallacy takes the following form:

The insistence that all categories must be cleanly separable and reducible to a single essential factor in order for them to be considered real or natural.

Below are some examples of prominent outlets using this extreme version of the Univariate Fallacy.

This 2018 New York Times article by Anne Fausto-Sterling uses the existence of intersex individuals and the Univariate Fallacy to deny the existence of males and females as natural categories:

It has long been known that there is no single biological measure that unassailably places each and every human into one of two categories — male or female. In the 1950s the psychologist John Money and his colleagues studied people born with unusual combinations of sex markers (ovaries and a penis, testes and a vagina, two X chromosomes and a scrotum, and more). Thinking about these people, whom today we would call intersex, Dr. Money developed a multilayered model of sexual development.

This 2019 Independent article critical of a ruling that prevents male intersex athlete Caster Semenya from competing against females relies entirely on the Univariate Fallacy nested within an oppression narrative to make its case:

In fact, there’s a range of DSDs that can involve either rare combinations of sex chromosomes (e.g. XXY or XYY) or genetic mutations on other chromosomes that affect sexual development. Thus, no single factor, genetic or otherwise, neatly determines whether an individual is male or female. Furthermore, no formula exists that uses genetic and other data to produce an answer of whether someone is male or female. The IAAF regulation disregards this reality and was surprisingly unenlightened considering the chequered history of genetic sex testing in sport.

This Medium article uses the Univariate Fallacy to argue in favor of allowing Caster Semenya to compete against female athletes:

Yet even after these tests, determining the sex of an individual is not straightforward. There are at least six biological markers of sex: chromosomes, gonads, hormones, secondary sex characteristics, external genitalia, and internal genitalia. Each one contains significant variation, both within and across individuals, including testosterone. As a result, no single marker can decisively categorize a person as male or female.

Vox released this video on YouTube, now with 3.2 million views, that is essentially 12 straight minutes of the Univariate Fallacy regarding sex and its relationship with athletic performance, with special focus on Caster Semenya:

The Univariate Fallacy has also been used in court, as seen in this Caster Semenya vs. IAAF arbitral award, to argue against the IAAF’s decision to prohibit Semenya from competing as a female in some events. Also note that Semenya is a DSD male, not a DSD female as suggested below:

Dr. Vilain stated that as a leading expert in this field he “fundamentally disagreed” with the notion that females with DSD should be “defined” as male and “have male bodies”. That proposition is contrary to the current scientific mainstream, which recognizes that sex is not binary but rather a spectrum, where no single factor (e.g. presence or absence of testes) prevails above all others.

And lastly, this essay in Scientific American used the existence of intersex individuals and their oppression to suggest sex is a spectrum because it can’t be defined in “rigid” (i.e. univariate) terms:

DSDs—which, broadly defined, may affect about one percent of the population—represent a robust, evidence-based argument to reject rigid assignations of sex and gender. Certain recent developments, such as the Swedish adoption of a gender-neutral singular pronoun, and the growing call to stop medically unnecessary surgeries on intersex babies, indicate a shift in the right direction.

The argument that sex categories must be socially constructed and hence arbitrary because we cannot point to a single essential factor that unequivocally separates all humans into two neat boxes labeled “male” and “female” is rooted in the false notion that “male” and “female” are polythetic categories.

Polythetic categories are those that can’t be reduced to a single essential feature, but are instead formed by a series of overlapping similarities, where no single feature is shared by all members of that category. In other words, certain things cluster into categories by having a family resemblance. This applies to things like music and movie genres, games, and even mental disorders.

For a clear example of a polythetic category, take male and female faces. What is the defining feature that makes a face appear male versus female? The answer is that it’s no single feature, but rather the correlational structure between many features such as jaw size and shape, brow ridge prominence, the shape of the lips, nose size, and others. All of these traits taken together cluster into two (overlapping) categories that capture typical male and female face morphology.

(Figure credit: from https://clinicalgate.com/aesthetic-contouring-of-the-craniofacial-skeleton/)

Gender activists want to portray “male” and “female” as polythetic categories, because this would imply that nothing in particular makes someone male or female, but that it’s just a matter of having more male- or female-typical traits in aggregate. This would also imply that a person can cross the statistical threshold between male and female categories by simply altering some aspects of their physical appearance through hormones and surgery.

But males and females are not polythetic categories; their existence is fundamentally rooted in the binary distinction between the gametes (sperm or ova) a person has the function of producing.

If we must reduce males and females down to a single bit of essential anatomy, the best choice is the gonads, as these are the primary sex organs that ultimately produce either sperm or ova. But this misses the point to an extent, because males and females are integrated wholes. Asking someone to single out a single essential feature separating males and females, apart from their biological function, would be akin to asking someone to single out the essential distinction between lions and tigers. Is it the presence or absence of stripes? Color? Body weight? Yes, and no. It is all these things, and not one in particular. But that doesn’t mean lions and tigers are polythetic categories, because you cannot turn a lion into a tiger by giving it stripes, or altering any number of its physical characteristics. They’re different species, and the existence of hybrids, such as ligers and tigons, does not negate the reality that lions and tigers are distinct creatures.

The Univariate Fallacy has proven to be a shockingly effective way for activists to manipulate the masses into adopting false depictions of reality for ideological reasons. By using the two forms of the Univariate Fallacy, activists can present their arguments in a way that suits their purpose. They can use it to invent a difference that doesn't exist in reality to push oppression narratives to justify "equity" initiatives. They do this by comparing groups across a single variable and ignoring all confounding factors. On the other hand, if they want to make a real group difference appear small or nonexistent to justify giving males access to female sports and other spaces, they can insist that the inability to reduce any sex difference to a single unassailable variable means the categories are imagined social constructs.

The statistical nature of the Univariate Fallacy makes it difficult for many to spot, which lends it an air of perceived intellectual sophistication. For the uninitiated, the Univariate Fallacy’s use of statistics and its appeal to reductionism can be alluring. It is not surprising that many people fall victim to these statistical and rhetorical tricks.

However, when academics or editors at respected scientific journals and newspapers use this fallacy to advance ideological or political narratives, it quickly graduates from the status of inappropriate or ignorant analysis to calculated propaganda.

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