The past few years have seen an important shift in popular understanding of IQ. Dismissive slogans like "IQ just measures how well you take tests" have been replaced by a growing understanding of how IQ is real, partially hereditary, and predictive of important life outcomes.

Scientific sources like Nature argue that "what most people know about intelligence must be updated,” and popular media including Vox itself reports on the "mountain of research showing that it's a genuinely powerful predictor of your health, prosperity, and well-being.”

IQ denialism seems to be going the same way as climate denialism — complete with overwhelming scientific consensus on one side — and it's about time. But people's concerns about this subject are understandable. Given the role intelligence plays in our society, any number that purports to rank it — rightly or wrongly — is going to touch on a lot of issues close to our self-worth as human beings. Some people with high IQs have always hoped that makes them better than everyone else; other people with low IQs have always worried they might be worse. On a subreddit dealing with psychology and IQ-related issues, I see posts like this one:

This may be completely silly, and it's not something I'm proud of, but given the amount of weight that JBP has given to the predictive powers of IQ, I'm too scared to do a test and find out what it is. It reminds me of the question, "if there was an envelope with your death date on it, would you read it?" I don't like the deterministic nature of what my future holds, as I feel it will become a self-fulfilling prophecy if my IQ checks out low. Especially as what I want to do in life requires a lot of abstraction and creativity, and it leans heavily on one's mentality. If my IQ checks out as low, that'll be one more obstacle in the road to overcome, and I just don't want to invite that.

Or like this:

Hey everybody. I recently did an IQ test and scored 83. I'm really bummed out about this because [University of Toronto psychology professor] Jordan Peterson has mentioned multiple times that IQ is the biggest predictor of success. Also I spend my spare time doing things like reading, watching these and other types of educational videos. Now that I realise I'm so far under average —it really hurts. I don't really know the point of this post, I guess I'd just like some thoughts on this because I'm too ashamed to tell anyone else.

Or this:

When I was 16, as a part of an educational assessment, I took both the WAIS-IV and Woodcock Johnson Cognitive Batteries. ... I never got a chance to have a discussion with the psychologist about the results, so I was left to interpret them with me, myself, and the big I known as the Internet — a dangerous activity, I know. This meant two years to date of armchair research, and subsequently, an incessant fear of the implications of my below-average IQ, which stands at a pitiful 94. ... [I told myself:] stop trying to fit into intellectual shoes that are too big for you. This is your station in life. Accept that it is so statistically improbable that you will not contribute anything useful in STEM-related areas, you might as well minimize your opportunity cost.

These people are really hurting. If their concerns were accurate, then they would just have to learn to live with them. But I think they aren't. There's a middle ground, where people can admit IQ is scientifically useful for discovering statistical truths about society, but remain skeptical of its ability to judge individuals. For one thing, casual IQ testing isn't a great way of measuring individual intelligence. For another, even an accurate measure of individual intelligence can only make statistical predictions, not ironclad prophecies.

In official studies, IQ tests correlate very well with other IQ tests, the same IQ test repeated later on, and other tests of intellectual ability like the SAT. For example, IQ scores and SAT scores tend to correlate at around 0.7, a very impressive match. But I surveyed readers of my blog on their IQs and SAT scores. I told them to only report their scores on real professional tests — none of those internet IQ tests you get to from flashing banner ads with pictures of Einstein's face on them. I got about 500 data points. And the correlation was only about 0.3: far lower than it was supposed to be.

First — though least importantly — lots of IQ tests given outside labs are less than rigorous

Why? SATs are taken in standardized conditions. But it would make sense if people taking my survey got less accurate IQ results than the ones in the official studies. Some may have gotten less-than-kosher tests. Others might have gotten tests given by harried underqualified school counselors who had to rush to finish before lunch.

Others might not have tried their hardest; still others might have been sleep-deprived, or overcaffeinated, or undercaffeinated, or hungover. Some probably took it when they were too young for it to really count — IQ doesn't stabilize until late adolescence. Still others might have taken the test in ideal conditions, received an accurate result, and then forgotten what it was over the years. A few might just be lying. Again, none of this is surprising. Breaking news: Random people haphazardly testing something do worse than trained scientists formally measuring that thing, more at 11.

But these are the kinds of IQ tests those people like the commenters quoted above mean when they complain about their own IQ scores. None of them were in formal studies. None of them have given the sort of information that formal studies would need to make anybody take them seriously. Their scores probably aren't completely useless. But they're probably more like the scores that correlate at 0.3 with SATs than the ones that correlate at 0.7. (Also, intellectuals who are really concerned about their IQ and complain about their unexpectedly low scores are a heavily self-selected sample.)

These problems affect even the best of us. Nobel Prize-winning physicist Richard Feynman talked about getting a 124 on the only IQ test he ever took. 124 is plenty bright — but Feynman was one of the greatest scientists of the 20th century; 124 is about 30 points off the lowest remotely plausible value. Scott Aaronson writes about his own similar experience taking an IQ test at age four and getting a 106 — right about average. Aaronson is a computer science professor studying the intersection of quantum mechanics and computational complexity. Nobody believes 106 is a remotely accurate measure of his intellect. He writes:

[I]f you want to know, let’s say, whether you can succeed as a physicist, then surely the best way to find out is to start studying physics and see how well you do. That will give you a much more accurate signal than a gross consumer index like IQ will —and conditioned on that signal, I’m guessing that your IQ score will provide almost zero additional information.

This isn't to say true scientific genius can't be measured by IQ. Someone formally IQ tested a group of eminent physicists and found IQs in the 150s and above — exactly what you would expect from a bunch of geniuses. The difference between them and Feynman and Aaronson is that the physicists in the sample were tested in adulthood in a formal scientific study, and Feynman and Aaronson are working off half-remembered IQ tests of unclear quality they took in school. If you took some half-remembered IQ test in school and heard you got a 106, then good news: For all you know, you too might have the ability to be a professor of quantum physics.

Even highly elite occupations include people with a broad range of IQ scores

But fine. Suppose you take all of that to heart, you carefully seek out the best and most reliable IQ tests, you take them after age 18 when IQ is most stable, you take multiple tests to double- and triple-check, and you find that you really, definitely, no doubt about it, have a low IQ. Now can you be miserable and self-hating? No. IQ predicts a bunch of things like income and success in various fields, but prediction is not prophecy. You have a somewhat reduced chance of high attainment, but you shouldn't take it as a death sentence.

Consider the gender pay gap. We know that men, for whatever reason, tend to earn more money than women. But we also know that some men are very poor and some women are very rich. Being a woman gives you a disadvantage but doesn't doom you. The same is true of having low IQ. Being a man gives you a leg up, but doesn't guarantee success; the same is true of high IQ. IQ correlates with income at about 0.2 to 0.3, about the same level as parental socioeconomic status. If you're low-IQ, you're less likely to succeed to the same degree that a kid from a poor family is less likely to succeed. But kids from poor families do sometimes succeed — Bill Clinton and Steve Jobs being famous examples.

We can both acknowledge that as a society we're depressingly bad at social mobility and truthfully tell individual poor kids that with enough luck and effort they can have a shot at success. It isn't just that people can compensate for their low IQ with hard work. They can, but it's not just that. It's that IQ is a very noisy measure of all intellectual talents averaged together, and some people with unimpressive general IQs can still be extremely talented in particular fields. Even such a stereotypically intellectual pursuit as chess only correlates with IQ at 0.24. (Though note that there may be limitations to that study — restriction of range — since it was done only on high-level players.)

Former chess champion Garry Kasparov had an IQ of 135 — high, but not so high that there wouldn't be dozens of people "smarter" than him at any decent college. No doubt Kasparov studied very hard — but so does everyone in high-level chess. He just had chess talent way higher than his IQ would have predicted — and this is exactly what we'd expect from the modest correlation between these two variables. Here's a chart of average IQ for various occupations, taken from this paper:

The chart perfectly demonstrates how IQ is both statistically reliable and individually unreliable. On average, intellectually demanding occupations like college professors have higher IQs than less demanding occupations like janitors. But individual janitors are sometimes higher-IQ than individual college professors. And almost every profession draws from a wide range of IQs. The average professor is pretty smart — but a nontrivial number have below-average IQs. Like Kasparov, they probably have some areas where their natural talent greatly exceeds what their IQ would predict — and like Kasparov, they probably supplemented that by working really hard.

This kind of thing matters not just because people worry about their IQ, but because a lot of the most controversial results in social science look kind of like this. Pay gaps associated with race, gender, family of origin, socioeconomic status, and education give some groups a statistical leg up beyond others. More controversially, there's recently been debate over more fundamental gender differences, and new results constantly come out about the genetic basis for various skills and problems.

Whatever direction these findings end up going in, one of the best ways to prevent them from becoming toxic and depressing is to remember that statistical tendencies apply only weakly to individuals — or, in more conventional terms — we should be wary of stereotyping. The problem with stereotypes isn't that they're never true, it's that they take a weak statistical effect and try to apply it to particular individuals. IQ is a real thing — some people really do have higher intelligence than others — but any attempt to use this to make predictions about individuals will fail more often than it will be worth it.

Scott Alexander is a psychiatrist in California. He blogs at Slate Star Codex, where a version of this piece first appeared.

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