And re: normal distribution implying some fundamental truth, the same can be said of an iterated guessing game (eg: take the sum of your correct guesses over 100 coin-flips - the population's scores on that game will be normally distributed).
As pointed out by Stephen J. Gould, intelligence is not normally distributed. The IQ test results are. But IQ test results are standardized to be normally distributed. It is an assumption that intelligence is normally distributed, and evidence suggests it is not. More likely—if it exists at all—it is log-normally distributed.
Psychometricians believe that there is some fundimental truth in the normal distributions, and then standardize their test scores so that it follows this distribution in order to gain validity. It is a pseudo-scientific self fulfilling prophesy.
Morton was wrong.
https://en.wikipedia.org/wiki/Samuel_George_Morton
It's great that you found some super specific thing where his wrong answer isn't provably the result of fudging of numbers, but he's still wrong for various reasons. And someone else measured other skulls at roughly same time and came to the correct conclusion that you couldn't really make any such claim based on the data they had.
Gould's point was about inadvertant bias in science and he was correct in this case.
You might be right that Gould was a fraud, however you still have to show that his claim about the fact that intelligence isn’t normally distributed is wrong. In fact the burden of proof is kind of weird here, since assuming a normal distribution is a pretty strong assumption, and rejecting that assumption based on a lack of evidence should be enough. However Gould goes further and cites evidence that intelligence has a pretty skewed distribution.
If you want to reject Gould’s claim here, then do so. Don’t just say he’s a fraud and then assume his wrong about everything.
The problem is assuming standard normal distribution as the true distribution for intelligence is simply bad science. Whatever the distribution truly is (if there even is one) it is not this one. And then psychometricians (including OP) use this as a point in favor of the validity of IQ as a good measure.
To give an uncontroversial example, we use logarithmic scales for earthquakes precisely because the underlying phenomenon is heavy-tailed. It's just for convenience, it doesn't imply anything about the phenomenon being quantified.
> The mere fact that the results of these types of tests on large population groups tend to follow a normal distribution is alone good evidence that they're indicative, as in most things diverse large population groups tend to fall on a normal distribution.
The claim here is that OP is wrong. Firstly OP is wrong because normal distribution is not a sufficient indicator for some underlying phenomenon. Or as yxwvut puts it:
> [...] normal distribution implying some fundamental truth, the same can be said of an iterated guessing game (eg: take the sum of your correct guesses over 100 coin-flips - the population's scores on that game will be normally distributed).
And then secondly because intelligence doesn’t even follow a normal curve (only IQ does because it is transformed to).
What matter here is not the true distribution of intelligence. I’m not even sure there is one. What matters is that proponents of general intelligence use the normal distribution of IQ as a justification. By arguing that intelligence does not fall on normal distribution but rather on a skewed distribution, I’m simply pulling the rug away from this argument.
I admit this is not a strong argument against the existence of general intelligence, since if there exists such a thing, then there is nothing that says such a thing couldn’t exist on a skewed distribution (except psychometricians and proponents of IQ which only accept standard bell curve [I wonder why]). However in this subthread we’re only trying to correct OP’s claim that a normal distribution is indicative for general intelligence.
I actually don’t believe in general intelligence, and I don’t believe intelligence is this one thing that you can measure. So I see how it can be confusing when I go ahead and say: “Intelligence has a skewed distribution.”
But when I’m talking about “intelligence” in this context I’m using working within the assumptions of the psychometric. In other words, I forgo my priors and argue on the terms of my opponents. I.e. given that they are right about the existence of general intelligence and that IQ tests are a good and accurate way to measure intelligence, they are still not correct about it being normally distributed.
To be precise. When I use the term “intelligence” in this context I’m basically using the same operationally defined term as psychometricians. That is: Intelligence is whatever the IQ tests are measuring.
Now as for which distribution to pick for this thing that IQ tests are measuring. Why pick a skewed distribution instead of a normal one? Psychometricians pick the bell curve because they believe it gives this term some validity. I would pick a skewed distribution because that fits our intuition and fits the underlying data. I would call the former justification pseudo-science as you have no reason other then your prior assumptions to do that. Then why do the latter? I would say the only reason to do that is to prove the people doing the former wrong.
Again, regarding earthquakes: Does a logarithmic scale "fit the underlying data better"? I don't think the question even makes sense. It's like asking which font fits the underlying data better. It's an arbitrary choice that doesn't need to affect our predictions or models at all. But you also said that "the only reason to do that is to prove the people doing the former wrong." so maybe we agree on this, too.
I think you might be misunderstanding psychometrics if your objection to IQ is the supposed implication that "intelligence is this one thing that you can measure". As far as I understand, psychometricians would agree that intelligence has many facets, and that most of them are hard to measure. I think the claim that they're making is simply that one can summarize estimates of these facets into a single scalar that will be correlated with all of them. Just like GDP correlates with many hard-to-measure and complicated facets of a country's wealth. Would you say the fact that GDP can't measure some important things about a country's wealth, or that it's a complicated thing, implies that there's no such thing as "general wealth"? The same analogy works for e.g. health, strength, or pretty much any property that we have a word for.
Measuring wealth is an excellent example. GDP might correlated with other measures of wealth, but it hardly explains the whole story. It can be useful in models but you can’t summarize nation’s wealth by only looking at GDP. Similarly IQ can be a useful tool. IQ tests can be used to find people with mental disabilities so that appropriate accommodations can be provided (although most of the time, there are easier, cheaper and better tools to diagnose mental disabilities). However by looking at the IQ alone (especially around and above the mean) you really can’t say much about about the mental capabilities of a person, only correlations of varying usefulness..
There is an important distinction though. I would argue that GDP (arguably) proves it’s usefulness in different economic models. However the same cannot be extended to IQs. I don’t know of many psychological models which use IQ (or any notion of general intelligence for that matter) to explain behavior (other then a hacks trying to prove the superiority of the white race, but let’s ignore those, what they are doing, it is not science).
How is IQ not "explaining behavior" a problem? We also wouldn't say that GDP "explains the economy", but that's not necessary for it to be useful. Both of these statistics are relatively strongly correlated with many outcomes we care about, compared to other things that are about as easy to measure. I think that's the main reason people use them, and it's a good one.
It sounds like you've seen people over-use aggregate statistics as a way to downplay nuance. That must be annoying. But that doesn't make their use philosophically or scientifically invalid.
Yes. That pretty much summarizes it. If IQ doesn’t further our knowledge of human behavior nor the human mind it is at best a useless construct. We have other more targeted measures (such as SAT) which are easier and cheaper to administer, and are far more useful in both models and evaluations/diagnostics. GDP has the benefit here of being extremely easy to measure and is therefor useful in more general models. IQ doesn’t have this quality, so that is not why most people use it.
Now if that was the only problem with IQ I wouldn’t be so bothered by it. Scientist are allowed to use an inefficient means of measuring their constructs. However IQ advocates often have a vested interest in an IQ that is immutable and (to some degree) heritable. This is often assumed to be true and IQ tests are later fixed in order to make them more robust in score against subsequent trails. This—off course—is circular reasoning (or a self fulfilling prophecy) and is not good science. But it is still used to explain group differences. This is where using IQ becomes scientifically invalid.
Now without the claim of immutability and heritability this wouldn’t matter. We would see a group difference and then we could then go on and try to explain it (e.g. within the context of sociology). However with immutability and heritability, you don’t have to explain it further. The answer is in psychology and genetics. (This is by the way the basis for scientific racism mentioned before).
I mean, I think it does further our knowledge of these things, but even if it didn't, that wouldn't make it useless, because it still predicts things we care about pretty well.
> GDP has the benefit here of being extremely easy to measure... IQ doesn’t have this quality
Which measures of intelligence do you think are easier to measure than IQ? You mention the SAT positively below, which is very similar to an IQ test.
> IQ advocates often have a vested interest in an IQ that is immutable and (to some degree) heritable. This is often assumed to be true...
I mean, every researcher would say that it's only immutable and heritable to a degree, and there's tons of research quantifying the degree of mutability and heritability (e.g. twin studies, admixture studies).
> But it is still used to explain group differences. This is where using IQ becomes scientifically invalid.
Is there a specific claim you have in mind that you consider invalid? Can you give me an example of an explanation of group differences that you would consider scientifically valid?
> with immutability and heritability, you don’t have to explain it further. The answer is in psychology and genetics.
Are you saying these claims happen to be false, or that they're categorically impossible / bad explanations? Is there any aspect of human behavior that you think can be explained by psychology or genetics?
Yes. The Bell Curve by Richard J. Herrnstein, Charles Murray (1994). I’m currently having a debate about it in another thread. It uses these assumptions about IQ and the demonstrates group difference with flawed studies, which it then goes on to justify conservative policies.
An example of valid—albeit trivial—group difference on the is height difference across genders. A more interesting group difference is how a mock jury is less likely to convict a minority group if a member of that minority is present in the jury. Then of course the field of medicine has many examples of interesting group difference based on genetics. However as a species we humans are remarkably homogeneous so if you find a group difference in behavior based on genetics it will most likely have an extremely small effect size, and as such be of limited interest. At best this is where IQ research falls in.
> There's tons of research quantifying the degree of mutability and heritability (e.g. twin studies, admixture studies).
These are still up for debate and not without bias. The original twin studies by C. Burt were likely falsified (https://en.wikipedia.org/wiki/Cyril_Burt#%22The_Burt_Affair%...) later efforts of reproducing the results are not without controversies either. And even if you look beyond these controversies there is an inherent bias as adopted twins are way more likely to be adopted within the same socio-economic group, adjusting for that is really tough. I’m not aware of any admixture study which explains a significant group difference in behavior, so I can’t comment on this. But I’ll leave this quote from Wikipedia instead (https://en.wikipedia.org/wiki/Race_and_intelligence#Racial_a...):
> Reviewing the evidence from admixture studies Hunt (2010) considers it to be inconclusive because of too many uncontrolled variables. Mackintosh (2011, p. 338) quotes a statement by Nisbett (2009) to the effect that admixture studies have not provided a shred of evidence in favor of a genetic basis for the IQ gap.
It’s funny you should say that. Because I generally regard the authors Gould is addressing in his book Mismeasure of Man, including S.G. Morton, C. Murray, A. Jensen, etc. as hacks that used questionable scientific means to tell people what they wanted to hear—namely the superiority of white men—in exchange for book sales.
(It doesn't exist)
See for instance:
Castejon, J. L., Perez, A. M., & Gilar, R. (2010). Confirmatory factor analysis of Project Spectrum activities. A second-order g factor or multiple intelligences?. Intelligence, 38(5), 481-496.
Visser, B. A., Ashton, M. C., & Vernon, P. A. (2006). Beyond g: Putting multiple intelligences theory to the test. Intelligence, 34(5), 487-502.
The fallout from eugenics gave social science a complex. Innate difference and especially innate superiority of one person over another is taboo. The field is poisoned by motivated reasoning.
>At the height of the controversy, during the 1970s to 1980s, the debate was highly ideologised. In Not in Our Genes: Biology, Ideology and Human Nature (1984), Richard Lewontin, Steven Rose and Leon Kamin criticise "genetic determinism" from a Marxist framework, arguing that "Science is the ultimate legitimator of bourgeois ideology ... If biological determinism is a weapon in the struggle between classes, then the universities are weapons factories, and their teaching and research faculties are the engineers, designers, and production workers." The debate thus shifted away from whether heritable traits exist to whether it was politically or ethically permissible to admit their existence.
https://en.wikipedia.org/wiki/Nature_versus_nurture#Determin...
It's also possible that single cultural factors could be so pervasive that they overwhelmingly swamp any signal by forcing a correlation just on its own.
eg: Before the 1960s or so, you could look at every society that had ever existed and make the observation that, except for a countable list of exceptions, men received more education that women. This might lead you to a natural conclusion that men have some natural innate advantage in receiving education that women lack.
Except that's not the truth at all, the truth is that patriarchy was such a universal of the human condition that it affected every single corner of the planet to such an extent that there was no control group until very, very recently. So much so that even the slightest letting off of patriarchy shows women are so much more innately suited to education that colleges have had to quietly implement affirmative action programs for men simply to keep their gender balances even remotely in check.
Many people would argue that classism and racism so thoroughly pervades our understanding of intelligence that we will simply never get our control group until some future date when they recede enough for us to truly see their effects.
I think that the treatment of things like time factors and tool use is also somewhat trivialised. Those that play chess will note that excellent Rapid or standard players can be terrible Bullet or Blitz players.
Roger Penrose -- nobel prize winning mathematical physicist -- was held back a year on count of his arithmetic being that bad. Yet he is a shockingly good mathematician mostly qua geometrical intuition to which he can convert other things. Who cares, Penrose can just use a calculator. Similarly, I'd say that many IQ tests are just symbolic regression. What if I was brilliant at stating symbolic regression problems, but poor at solving them? Then me + solver would make all the difference, unlike if I was poor at stating them ...
And so on.
Showing outliers just proves there are outliers not that the averages are uselesss.
>Those that play chess will note that excellent Rapid or standard players can be terrible Bullet or Blitz players.
I play chess and those are definitely highly correlated, I suspect at least r of 0.7 especially for those who have put decent time into the different controls.
Regarding chess, research suggests you're wrong:
https://www.sciencedirect.com/science/article/abs/pii/S14690...
https://hvandermaas.socsci.uva.nl/Homepage_Han_van_der_Maas/...
I think part of the issue is that it's very hard to measure intelligence accurately (whatever that means) across cultural divides. If you gave an American IQ test (e.g. an SAT) to Europeans, Asians, and Africans you'll likely get different results, not (necessarily) because of innate differences but because of educational/cultural backgrounds. Poverty levels can also change scores.
This makes it tricky to know what to do with these scores and we need to acknowledge that. This leads some to conclude that we should get rid of the notion of a measurable IQ altogether. That goes too far in my opinion but I understand their concern.
I think you're on the right track, though. But the key sticking point is this: many people are very uncomfortable with the idea that there are differences in intelligence among people, both within and between populations. Unfortunately, that is undeniably true. And so we get this ridiculous, unproductive dance.
Also, just as an aside, the latest evidence around the "poverty actually makes you literally stupider" claim is that it's not supported--studies aren't replicating. Which makes sense because the claim is prima facie crazy, but I digress...
The results do not follow a normal distribution though. IQ is forced into a normal distribution with a standard deviation of 15 by definition, it is constructed in such a way that it's forced into that distribution. The actual measurements, ie. raw test scores, are not normally distributed.
If SAT score were measuring some immutable value, then it wouldn't be so easy to improve one's score with revision, and tutors.
0. https://en.m.wikipedia.org/wiki/Intelligence_quotient
1. https://www.manhattanreview.com/sat-retaking/#:~:text=The%20....
So SATs are not generally trainable by a universal approach -- including personal tuition. I think that is believable. However, that for any given individual there is no intervention which will substantially improve their SAT results is a much stronger statement which I find less believable.
Most money spent on test prep is just wasted.
Consider the physical fitness correlations in the article - I don't think anyone would argue that your level of physical fitness is immutable. But just because the value is mutable is no reason to disregard the current value - it can still be a meaningful and useful indicator.
I think that thinking processes is very much in that category, and I think that the investment in time is considerable. I think its typical to expect gradual improvement -- a constant response to training. Anecdotally, it doesn't work like that.
> For reasons I don't fully understand, there's a lot of folks in the social sciences these day that seem to be waging war on the very concept that you can describe intelligence generally (and IQ tests specifically).
The unfortunate reality is that social sciences are largely corrupted by political activism. Their activities are often prescriptive social engineering that attempt to use their perceived scientific authority rather than actual descriptive science. Put simply, they are saying what they want to be so, rather than what is so.
I think it's reasonable to conclude that measuring intelligence isn't valuable enough for all of the negative externalities attached to it given how the world currently is. But then from there it's easy to make the easy jump to saying it's impossible to measure intelligence without those negative externalities, which is probably not true. But if you can't measure intelligence without significant bias, you aren't really measuring it at all, you're just measuring your biases.
Do you have some specific examples of this purported bias?
> Unfortunately some were also very deliberate spins (one notable example being the book The Bell Curve).
Specifically what spin are you referring to?
> I think it's reasonable to conclude that measuring intelligence isn't valuable enough for all of the negative externalities attached to it given how the world currently is.
Insufficiently valuable to whom?
So I think to get everyone on the same page, you have to address that concern in some form, or there will be some people who are always against the idea of measurable intelligence.
It's a reasonable argument, and one I personally tend to lean towards, but you can't meaningfully debate it if you don't have a shared understanding that a general factor does indeed exist.
I think it's basically coming down to a battle of the mathematically literate vs. not, and unfortunately the non-literate have a lot of stickiness in academia because they can generate ideas people want to believe with no empirical "where the rubber meets the road".
The reason is that general intelligence tests show differences between racial and ethnic groups. Which isn't shocking, as intelligence is certainly driven by genetics and compounded by culture. But because it is, it upsets people.
IQ testing is a pretty valuable filtering mechanism. Smart people are really important to advancing society. Replacing it with some other, more subjective metric just moves the filter into the realm of political control.
Which seems like a bad idea to me, but what do I know? I'm not a genderqueer left-handed ginger aboriginal, so I'm not very smart.
Given that we cannot say what intelligence is better than "its what intelligent people do", I'd say we were far from the "whole story".
I think pretending that there is no "whole story" and using IQ to make policy decisions about populations is political. I don't think anyone cared that a bunch of researchers were tinkering with some psychometrics. They cared that a whole racial group could be shut out of certain jobs on the basis of a half baked abstract reasoning test.
I'm not opposed to this, and I doubt most people would be either. Take college admissions as an example. A low-SAT, low-GPA student in a one-on-one interview with an admissions officer could dazzle the interviewer to such a level that admission with a scholarship could be guaranteed.
We don't do that often for a variety of reasons, but one would certainly be because of the quasi-legal requirement to tick certain boxes to avoid trouble. Okay, but that has costs. We've been able to paper over a lot of this with economic good times, but that's unlikely to last forever. Hard reality always wins in the end.
It's the social sciences version of technical debt.
> we value not upsetting people, that's the metric we optimize for.
From the HN guidelines (https://news.ycombinator.com/newsguidelines.html):
> Eschew flamebait. Avoid unrelated controversies and generic tangents.
I’m a prime target for this flamebate, and you’ve managed to upset me quite a bit. I’m actually surprised I didn’t bite already. Indeed I’ll actually just leave it at that and pat my self on the back for resisting.
If there is a general intelligence—which I very much doubt—our current tests don’t even come close to measuring it.
Then why do they correlate with outcomes so well ?
All of the evidence we've gathered over decades seems to indicate that there is a general factor for intelligence. But as he points out in his conclusion, this is /descriptive/, meaning we can arguably accurately determine someone's intelligence via testing and that single general factor accurately describes their intelligence in relation to others. It does not in any way imply we understand the causative factors that lead that score to go up or down in any meaningful way.
For reasons I don't fully understand, there's a lot of folks in the social sciences these day that seem to be waging war on the very concept that you can describe intelligence generally (and IQ tests specifically). The mere fact that the results of these types of tests on large population groups tend to follow a normal distribution is alone good evidence that they're indicative, as in most things diverse large population groups tend to fall on a normal distribution.