This essay is part of Legacies of Eugenics, a series of essays by leading thinkers devoted to exploring the history of eugenics, and the ways in which it lives on in our habits of thought, and in aspects of the sciences and medicine.
¤
IN 2013, A SERIES of ads about the dangers of teen pregnancy appeared on New York City subway trains. Sponsored by the city’s Human Resources Administration, the ads cautioned prospective teen parents that babies were likely—surprise!—to exact a heavy toll on their finances, relationships, and job prospects. The ads were formulated as plaintive messages from the babies themselves. One teary-eyed toddler lamented: “I’m twice as likely not to graduate high school because you had me as a teen.” As then-mayor Michael Bloomberg explained, “This campaign makes very clear to young people that there’s a lot at stake when it comes to deciding to raise a child.” The ad campaign was quite rightly ridiculed, in large part because it offered no support services for teens who were, or might become, pregnant.
From a statistical point of view, though, the most objectionable part of the whole campaign was a single word—“because.”
At the bottom of the poster, a footnote contained this statistic: “Kids of teen moms are twice as likely not to graduate than kids whose moms were over age 22.” But such a statistic, accurate or not, represents an entirely different claim from the one in the ad. The footnote’s claim is strictly observational and expresses a correlation—as a matter of record, children born to teen mothers are less likely than others to finish high school. The statement in the body of the ad is by contrast a causal claim: it predicts the results of an intervention—like having a baby in this case. The causal result: Your child’s likelihood of graduation decreases. One could, for example, imagine a similarly worded ad urging prospective parents to buy luxury cars, supported by statistical evidence such as the fact that “children of parents who own BMWs are twice as likely to attend college as their peers.”
That “correlations” are not “causes” is no surprise to anyone who has taken an entry-level statistics course. Two variables may be correlated but not because one caused the other, as in standard examples like a child’s shoe size being correlated with spelling ability (both are a function of age), or ice cream sales being correlated with deaths by drowning (both happen more frequently in warmer months). But like a hand-lettered sign above a public toilet admonishing users to “please flush twice!!” the ubiquitous statistical aphorism “correlation is not causation” indicates a design problem more than a user error. Correlation, one of the most used and least understood concepts in statistics, is easy to mistake for causation because it was made that way intentionally; it’s precisely because of its potential to be misunderstood that it remains so popular. Since its introduction over a century ago by statistician-eugenicists Francis Galton, Karl Pearson, and Ronald Fisher, correlation has been put to the exact purpose that students are now—at least in theory—warned against: drawing causal conclusions where only observational data exists. Often, as in the work of those statistical titans, this deliberate conflation has served political agendas, including eugenicist ones. The eugenics movement was built out of correlations.
In recent years, widespread efforts to question the legacies of eugenicist scientists and statisticians have resulted in the renaming of institutions such as the Galton and Pearson lecture theaters at University College London and the Fisher Award and Lectureship given by the Committee of Presidents of Statistical Societies. Previously, I have argued that the eugenics movement also had a heavy, mostly invisible, influence on the philosophy of statistics and the development of core techniques such as significance testing. My claim here is that remnants of this influence can be found in such apparently innocuous ideas as correlation and related measures of association, and in the new areas of science embracing them as central to their methodology. In what follows, I continue to excavate the disturbing social and historical settings from which most of modern statistics originated, with a focus on the continued overuse of correlation measures, asking what it reveals about the ideologies guiding science today.
¤
Galton (1822–1911) first came up with correlation around the same time he was founding the modern eugenics movement in the 1880s. Pearson (1857–1936), Galton’s protégé and also a key player in the eugenics movement, was an enormous booster of the concept. The most common measure of correlation is named for him: the “Pearson correlation coefficient.” (A search on Google Scholar for this term in 2024 returned over 2.1 million publications.) Fisher, who succeeded Pearson both as the Galton Chair of Eugenics and as editor of the Annals of Eugenics, earned his reputation as a statistician in large part by extending the theory of correlation.
Correlation was the solution to a practical problem faced by all three men: they wanted to argue for radical eugenicist proposals like selective breeding that would favor accomplished elites (people like themselves) and dilute the contributions of those they deemed unfit, such as poor people, criminals, or people with disabilities. At the same time, they wanted such proposals to come across as inescapable consequences of the data itself. This was, of course, strictly impossible—no such programs had ever been implemented before, and so no amount of pure observation could show whether they would succeed. Instead, the eugenicists needed a way to guide their audiences to particular conclusions beyond the data while appearing to have no hand whatsoever in the guidance.
Correlation has just such a dual nature. According to its definition, it simply and objectively summarizes the data at hand: if one variable being higher or lower tends to go along with another variable doing the same, the two are said to be (positively) correlated. It comes tantalizingly close, however, to implying causal relationships, hence the ample reminders that it should not be interpreted that way. It’s dangerously easy to let correlations trick you into thinking causally. Our minds appear to be designed to fall for this fallacy. Sometimes that trick serves a rhetorical purpose, by allowing the numbers to appear to speak for themselves. Like a ventriloquist’s dummy, though, the data can only speak for itself thanks to an illusion pulled off by a skilled performer. “Correlation is not causation” is like a disclaimer before the act, cautioning viewers that the dummy isn’t really able to talk. But why perform the trick at all unless you want the audience to believe in it at least a little? Galton, Pearson, and Fisher were all masters of this technique.
Originally, Galton became interested in statistics because he was searching for the processes underlying heredity. An obstacle to his eugenicist objectives was the famous phenomenon that would come to be called “regression to the mean,” the observed pattern that exceptional people, both at the top and bottom of any distribution, tend to have children who are somewhat less exceptional than themselves. A pair of six-foot-six-inch parents, for example, might be expected to have taller-than-average children, but not as far above average as the parents. This meant, to Galton’s consternation, that selecting only the most successful people (by any measure) to have children might not produce the utopian outcome he envisioned.
Galton would create the basic vocabulary of statistics that removed causes altogether—but his earliest writings reveal that his goal was to discover causal mechanisms. At first, he theorized that regression to the mean as applied to human breeding was due to the influence of distant ancestors with impure bloodlines: “A child inherits partly from his parents, partly from his ancestors […] the further his genealogy goes back, the more numerous and varied will his ancestry become.” When doing practical demonstrations using his “Galton board,” which consisted of tiny metal balls bouncing left or right down through a set of pegs (like the game Plinko from The Price Is Right), he explained that regression to the mean acted like a set of chutes pointed diagonally toward the middle of the board, thus forcing the balls to drift away from the extremes back to the mean. These explanations were causal explanations, however, for what was an empirical observation.
Later, after developing a formula for this effect and seeing the symmetries in the mathematical relationships, Galton realized the same pattern would occur if the data were organized backwards. Extreme offspring were more likely to have been born from parents closer to the mean than they themselves were—the regression goes both ways, in other words. He also observed the same patterns in different measurements within the same person: a very tall person might have longer-than-average fingers but not as far above the mean as their height. These observations meant his theories of regression due to mixed ancestry could not hold up. But that was acceptable to Galton. By this point, he was so enchanted with discovering order within the chaos of his measurements that he started to think purely in terms of associations within the data. He coined the term “co-relation” to describe the tendency for a pair of variables to vary together.
Pearson, having spent his early career studying philosophy, had become what might be described as a causal nihilist. Causality as a concept, he declared, is too slippery, and risks being contaminated by personal and cultural prejudices. People’s fixation with the causes of things is a “fetish amidst the inscrutable arcana of modern science.” Data-gathering, by contrast, is immune to the whims of time and place: “A careful record of facts will last for ages, but theory is ever in the making or the unmaking, a mere fashion which describes more or less effectually our experience.”
Worst of all, causal relationships cannot possibly be proved right. As Pearson wrote, “That a certain sequence has occurred and recurred in the past is a matter of experience to which we give expression in the concept causation. […] Science in no case can demonstrate any inherent necessity in a sequence, nor prove with absolute certainty that it must be repeated.” Any physical theory of causes was, then, indistinguishable from myth. He thought, for example, that “force as a cause of motion is exactly on the same footing as a tree-god as a cause of growth.” In his landmark book The Grammar of Science (1892) and frequently thereafter, he argued that the true function of science was merely the accumulation of observations and measurements. “The mission of Science is not to explain but to describe; to discover a descriptive formula which will enable men to predict the nature of future perceptions,” he wrote.
Galton’s statistical machinery of correlation gave Pearson exactly what he needed to make this philosophy quantitative. Reflecting on his career in 1934, Pearson said his epiphany had been that “there was a category broader than causation, namely correlation, of which causation was only the limit, and that this new conception of correlation brought psychology, anthropology, medicine, and sociology […] into the field of mathematical treatment.” Galton’s insight, he wrote elsewhere, has not only “enormously widened the field to which quantitative and therefore mathematical methods can be applied, but it has at the same time modified our philosophy of science and even of life itself.”
Pearson applied correlations with aggressive zeal to eugenics, in particular. It would be difficult to overemphasize how enmeshed statistics and eugenics were for him. Many people today credit Pearson with founding the first academic department of statistics, but in fact the only academic appointment he held at University College London was the Galton Chair of Eugenics. Upon Pearson’s retirement in 1934, the university decided for political reasons to split the eugenics position in two and create separate departments of statistics and eugenics. Pearson objected to the plan as nonsensical. While serving as a professor, he was also the director of the Galton Laboratory for National Eugenics, and he founded two journals: Biometrika (which was more statistics-flavored) and the Annals of Eugenics. There was, predictably, abundant crossover between them.
Consider a 1904 paper published in Biometrika, in which Pearson concluded an analysis of the reported mental characteristics of thousands of pairs of siblings with the claim that the numbers demonstrated these characteristics were inherited. Instead of stopping there, he offhandedly cautioned that Britain was “ceasing as a nation to breed intelligence as we did fifty to a hundred years ago. The mentally better stock in the nation is not reproducing itself at the same rate as it did of old; the less able and the less energetic are more fertile than the better stocks.” “The only remedy,” he advised, “is to alter the relative fertility of the good and the bad stocks in the community.”
In 1907, in an address titled “The Scope and Importance to the State of the Science of National Eugenics,” Pearson described the methods of “eugenics theory” to an audience at Oxford University. Correlation featured prominently in his remarks as what he would later call a “category broader than causation.” Since “we cannot experiment on individuals,” he said in his address,
our methods must therefore be those applicable to mass-observations—that is to say, those actuarial methods applied to biological data which we now term the methods of biometry. […] Suffice it to say that they appear to measure effectively the relationship between factors which are not causally linked together. For the explanation of what follows I would state that the arithmetical value of a certain quantity—the so-called coefficient of correlation—is chiefly used to measure this relationship.
A few minutes into this fairly dry technical description of statistical methods, Pearson’s speech turned into a fiery rant about humanity’s various existential conflicts:
The struggle of man against man, with its victory to the tougher and more crafty: the struggle of tribe against tribe, with its defeat for the less socially organized: the contest of nation with nation whether in trade or in war, with the mastery for the foreseeing nation, for the nation with the cleaner bill of health, the more united purpose of its classes, and the sounder intellectual equipment of its units.
He went on to decry the expansion of various social programs and public health reforms, saying, “The growth of human sympathy […] has been so rapid during the century that it has cried Halt! to almost every form of racial purification.” He urged his audience of junior scientists to push for policies restricting reproduction to the better stocks as a matter of racial duty, saying,
Education for the criminal, fresh air for the tuberculous, rest and food for the neurotic […] will not save the offspring from the need of like treatment, nor from the danger of collapse when the time of strain comes. They cannot make a nation sound in mind and body, they merely screen degeneracy behind a throng of arrested degenerates.
He closed the polemic by characterizing the situation as urgent: “If I speak strongly, it is because I feel strongly” about what he concluded was “Race-Suicide.” If it were written 30 years later, the speech, minus the methods section, could easily have been declaimed at a rally in Nazi Germany.
For Pearson, eugenics followed directly from his theory of heredity, and heredity was defined in terms of correlation. For example, his claim that mental characteristics were heritable was based on a correlation analysis of personality ratings in children (as reported by their teachers) and the fact that these ratings were correlated among siblings about as strongly as stature or eye color. His warnings about “Race-Suicide” were built on observed correlations between fertility and “undesirable” social traits, such as being a “general labourer” or “pawnbroker,” having children aged 10–14 who already held jobs, or dying from tuberculosis. And his injunctions against letting criminals and people with diseases or mental illness back into free society to intermingle with their “betters” was supported, as Pearson put it, on “two great principles: (a) the inheritance of variations, and (b) the correlation in heredity of unlike imperfections.” In other words, from a simple table of correlations, Pearson claimed to construct a profile of an individual’s life trajectory, and based on a few known facts, he claimed to be able to predict the diseases they would likely have, the social ills to which they would contribute, and the ways in which their children would dilute the racial purity of the next generation if allowed to.
Fisher (1890–1962), the third of the statistical titans, likewise made no efforts to separate his eugenics advocacy from his other scientific work. The last third of his book The Genetical Theory of Natural Selection (1930), simultaneously a groundbreaking work of research in evolutionary biology and an unhinged eugenics pamphlet, articulates Fisher’s theory of human heredity and how it relates to the rise and fall of nations. Using census data, he concluded that Britain suffered from an “inverted birth-rate”—lower socioeconomic classes were having more children than upper ones. The basis for this imbalance was, he claimed, genetic.
As in Galton and Pearson’s work, Fisher’s arguments depended heavily on correlation analysis. One key finding was that, within his dataset, the number of children women had was positively correlated with the number of children their mothers had and with the number their mothers had, to a degree predicted by his hereditary models. He described the coincidence as “unequivocal confirmation of the view that the relationship observed between mother and daughter is essentially one of organic inheritance.” Because genes for fertility were highly selected for, the consequences would be apocalyptic. The “biologically successful” are overrepresented among “social failures,” he concluded. Society would soon implode.
¤
The case for eugenics as laid out by Galton, Pearson, and Fisher relied almost entirely on statistical evidence expressed through correlations. But in retrospect, it’s obvious that correlation on its own could never fulfill the eugenicist purposes it was made to serve. At best, correlation measures the association between variables within a data set collected under conditions held more or less constant. It can be useful for predicting the value of a missing observation if we only have values known to be correlated with it. So, for instance, if previous records enable us to estimate a relationship between French army soldiers’ heights and hat sizes, then we can judiciously guess which size hat to order for a new recruit of a known height. A high correlation would give us a high degree of confidence in our estimate.
However, eugenics was never about passive best-estimate prediction but rather about advocating for programs like sterilization to bring about desired changes in society and arguing it was futile to attempt to do so through improvements to living conditions. It was, in a word, about interventions. Galton, Pearson, and Fisher realized on some level that something more than correlation was necessary, as evidenced by their willingness to create causal theories to fit the data.
When he jumped to his eugenicist conclusions from a handful of correlations, Pearson deviated from his own mission statement that the duty of science was “not to explain but to describe.” Repeatedly, he theorized explanations for patterns in the data, and invariably those explanations suited his agenda. In his Oxford eugenics address, he spoke about the “taint” of criminality and disease as being “products of the somatic cells” and theorized that “defects” might manifest differently in parents and children—alcoholism in one generation could be linked to physical disability in another, and so on—due to a “general defect in the gamete” and a “general inheritance of degeneracy.” Conversely, Pearson often dismissed some observed correlations as “spurious,” but what’s a spurious correlation to a causal nihilist? Without causal assumptions in mind, all correlations should be considered equally meaningful.
Fisher’s analysis of the inheritance of fertility, a necessary ingredient for his theory of the evolutionary calamity contained in the “inverted birth-rate,” is particularly telling. Recall that Fisher thought fertility must be inherited because of a correlation in the number of children born to women across generations. What about environmental influences such as cultural norms or religious teachings about family planning? Fisher speculated that these were also hereditary. What about girls just wanting to follow their mothers’ examples and have large or small families consistent with how they grew up? Fisher guessed that influence would be canceled out by a desire to be unlike their mothers, since “the example of a mother must act both by suggestion and by counter suggestion, and it would seem hazardous to assume that girls are more strongly influenced, in practice, by a consciousness of the special advantages of their home environment, than by a consciousness of its special disabilities.” That this evidence—two correlation coefficients and some creative speculation—would add up to “unequivocal confirmation” seems like a case of extreme overreach.
Following Galton, Fisher theorized that the origin of the class difference in fertility lay in a structural problem in society: too many aristocrats were marrying rich heiresses. At the time, to be an “heiress” almost by definition meant that the woman in question came from a family without sons, and these families therefore tended to be smaller than average. Ergo, societal forces pushed women from smaller families upward through the ranks, and since their relative lack of fertility was hereditary (see above), this polluted the upper-class gene pool with “small-family” disease. Fisher generalized this theory to include the social promotion of the “less fertile stocks,” which he thought destructive for society in general. It was all guesswork unsupported by evidence, yet Fisher considered the theory compelling enough to justify radical eugenicist reforms.
Fisher’s arguments and rhetoric were reminiscent of Pearson’s, especially in his 1904 publication on the inheritance of mental qualities in humans where he concluded that “we are forced, I think literally forced, to the general conclusion that the physical and psychical characters in man are inherited within broad lines in the same manner, and with the same intensity.” Pearson would use the apparent solidity of the numbers to argue for immigration restrictions, forced sterilization, and genocide. Suffice to say, he was wrong: we are not “literally forced” to any such conclusion.
¤
Scientists need causal explanations for phenomena so that they can recommend the best course of action to achieve a desired effect. A correlation between taking a medicine and recovery from illness is useless by itself if we’re trying to decide whether to approve the drug. A correlation between CO2 levels and global temperature isn’t enough on its own to justify lowering carbon emissions to achieve lower temperatures. A correlation between the number of words spoken to a child at a young age and that child’s educational achievement, as referenced recently in the president’s State of the Union address, is meaningless as a basis for recommending early childhood exposure to reading.
And yet many branches of science are hopelessly stuck in a correlation mindset. While they may use the ordinary correlation coefficient less often than its more sophisticated descendants (like the “coefficient of determination” and “Akaike information criterion”), the guiding principles are the same as in Galton’s day. For example, the machine-learning models that have become so popular over the last decades, revolutionizing fields from marketing to healthcare, are, by and large, sophisticated correlation engines. They are newer, fancier versions of Pearson’s “descriptive formula.” The algorithms that drive these models are designed to find associations in the training data, often obscured inside a black box of model structure, without regard to which features of the data are causally related to which others or how they are causally related. This has proved to be a successful general approach, leading to AIs that can perform as well as or better than humans at such tasks as image recognition and games like Go and Chess.
However, while a theory-agnostic prediction machine can perform well within the context in which it was trained, it will often fail at generalizations. An image classifier may struggle with pictures from a different camera or taken under different lighting conditions. An AI without an understanding of causality can never be useful for tasks that require it to operate outside its comfort zone, such as predicting weather events under new climate patterns, solving novel logic puzzles, guiding a robot to navigate a space it hasn’t encountered before, or recommending a personalized course of treatment to a cancer patient.
The field of science most haunted by the specter of correlation is biology, particularly genetics, where “heritability” is still thought of in Pearsonian terms as the correlation between an observed trait and the DNA that might influence it. If a particular trait is highly correlated with a particular gene in a population, the trait is deemed to be highly “heritable.” In even more suggestive language, the variation in genotypes is often said to “explain” some portion of the variation in phenotypes. Here, in a manner entirely consistent with the eugenics movement, heritability is frequently used as an argument for the futility of improving environmental conditions, since genes, according to popular understandings, are immutable blueprints for who we are and how we move in the world. Studies showing the heritability of traits are often reported on with breathless enthusiasm using fatalistic language like “criminals are born, not made,” “infidelity lurks in your genes,” “bisexual behavior [is] genetically tied to risk-taking,” and so on.
As David S. Moore and David Shenk argued in “The Heritability Fallacy” (2017), defining heritability according to correlations—instead of actual causal inheritance—can give a distorted picture of how genetics and environment combine to influence traits. The main problem with this approach, like the problems of machine learning described above, is that the “variation” used in heredity calculations is only measured within a given setting, where some key environmental factors may be held constant. Moore and Shenk illustrated this with a thought experiment about a neighborhood in which several houses experienced fires: after some investigation, it’s revealed that the houses that caught fire had space heaters in them; according to heritability math, this would mean 100 percent of the variation in house fires was “explained” by the presence or absence of space heaters. However, suppose that it turns out that all the houses in this neighborhood were constructed using combustible materials, such as flammable paints. That factor would be ignored by the correlation measure of attribution (i.e., the one that blamed the space heaters), because the factor does not vary in the data. This and other critical flaws led Moore and Shenk to conclude, “The term ‘heritability,’ as it is used today in human behavioral genetics, is one of the most misleading in the history of science.”
With an awareness of the eugenicist roots of these ideas, we can go a few steps beyond calling the correlational definition of heritability “misleading.” It participates in a long and toxic tradition of pretending the data contains everything we need while winking suggestively at the explanations we favor. But talking explicitly about heritability—and scientific theory-making more generally—in terms of causes rather than correlations is not easy. It means being vulnerable to an entirely new onslaught of criticism. Causal inference is slippery. It often requires counterfactual reasoning. If things weren’t how they are, how would they be? This kind of speculation is, by its nature, subjective. It is antithetical to the dispassionate calculations contained in Galton, Pearson, and Fisher’s version of correlation-based inference. As Judea Pearl and Dana Mackenzie wrote in The Book of Why: The New Science of Cause and Effect (2018),
Counterfactuals have a particularly problematic relationship with data because data are, by definition, facts. They cannot tell us what will happen in a counterfactual or imaginary world where some observed facts are bluntly negated. Yet the human mind makes such explanation-seeking inferences reliably and repeatably.
For all their rhetorical bluster about “objectivity,” the eugenicist founding fathers of statistics revealed in their own work how objectivity was really just a weapon to deploy against opponents. They made room for subjective interpretation when it suited them. Fisher, for example, who was a lifelong smoker, spent the last act of his professional life—until he died from complications due to cancer in 1962—as a paid advocate for the tobacco industry. His argument was that the observed correlation between smoking and cancer did not necessarily prove a causal relationship. An unobserved inflammatory condition could, he said, cause both a higher rate of cancer and the type of discomfort that was alleviated by smoking. Fisher was right that the correlation did not prove a cause, as any first-year statistics student can tell you. However, the same is true of all correlations, including those in his and Pearson’s arguments for eugenics. Proof was never an option. Pearson was right to say that causes can’t be proved correct, but in a sense, his nihilism wasn’t nihilistic enough. The process of data interpretation is never-ending, with no one having the final word.
As the biologist Richard Lewontin explained in Biology as Ideology: The Doctrine of DNA (1991), when we use our causal imaginations, we implicitly assume some aspects of the world are held fixed while others vary, and this can reveal our deep ideological commitments. Lewontin gave the example of tuberculosis in Britain, where the spread through bacterial infection was greatly exacerbated by harsh labor conditions and poor nutrition. He wrote, “Although one may say that the tubercle bacillus causes tuberculosis, we are much closer to the truth when we say that it was the conditions of unregulated nineteenth-century competitive capitalism […] that was the cause.” It’s easy to imagine a bacterium being present or absent; it’s somewhat harder to imagine material economic conditions being other than they are.
Correlation, the “diet” version of causation, was falsely advertised as having all the benefits of causal reasoning without the painful questions about our assumptions. Examining correlation’s rise to prominence and triumph over causal reasoning reveals, therefore, a great deal about how societal movements like eugenics have shaped science over the last century. The interrelated histories of the eugenics movement and statistics, particularly as they overlap in the concept of correlation, should caution us against being taken in by the seeming neutrality of mathematical formulae. We should not imagine that conclusions drawn from so-called hard data are set in stone. Statistical tools are never neutral. To call the act of letting correlational statements masquerade as causal ones “a misuse” is in some sense ahistorical; arguably, it’s what the tool was expressly designed to do, the same way an AR-15 rifle is clearly designed to kill people despite the possibility of other applications. We should, instead, work hard to ensure we systematically misuse correlations by handling them with a level of caution and circ*mspection that their designers did not intend. We should, in other words, handle the data we use to tell grand stories with self-conscious skepticism, keeping in mind that when numbers summarize people’s lives, they are often infused with various forms of oppression. Whether in Victorian England or the New York subway, our societies are awash in unobserved environmental factors that our correlation coefficients cannot hope to capture and our causal models too often overlook.
¤
Featured image: Louis Darget. Rayonnée, 1898. Getty Museum (84.XX.1436.37). CC0, getty.edu. Accessed July 16, 2024.
