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Also regarding the normal distribution. As pointed out by Stephen J. Gould, intelligence is not normally distributed. The IQ test results are. But IQ test resu

Also regarding the normal distribution. 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.

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NoImmatureAdHom 5y ago
This viewpoint is generally acknowledged as wrong by the scientific community, and Gould is generally acknowledged as a hack who sold out by telling people what they wanted to hear in exchange for book sales.
- runarberg 5y ago
  > Gould is generally acknowledged as a hack who sold out by telling people what they wanted to hear in exchange for book sales. 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.
xyzzyz 5y ago
Stephen J Gould was a scientific fraud, with an ideological axe to grind, and repeatedly lied and misrepresented reality to smear what he saw as his ideological opponents. His most famous work on the topic, The Mismeasure of Man, for example, discussed Morton’s skull measuring experiments, who found that people of various races have different average cranial capacities. This is now a well established scientific fact, nevertheless Gould found this so offensive, that he claimed Morton fudged results by putting finger on the scale, based on no evidence whatsoever, simply disbelieving this sort of human variation between populations. Morton’s skulls have been in fact remeasured, and found to match Morton’s measurements within error margin appropriate to the method. This has been communicated to Gould himself, but he did not issue any correction or indeed mention any of it for the second edition of his book, showing clear evidence for his ideologically driven lack of scientific integrity.
- ZeroGravitas 5y ago
  This is a suspiciously specific rebuttle. Morton was wrong. https://en.wikipedia.org/wiki/Samuel_George_Morton 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.
  - xyzzyz 5y ago
    Morton was wrong on many counts, to be sure, just as any scientist worth of salt must be. However, he was not wrong on the very thing Gould accused him of, which was ideologically based fudging of data, something that Gould was in fact guilty himself.
    - ZeroGravitas 5y ago
      He did ideologically fudge his data, though, to the point that he could, incorrectly, make the claim that he already believed, but that wasn't actually there in the data. Gould's point was about inadvertant bias in science and he was correct in this case.
- runarberg 5y ago
  You are doing the very thing you are accusing Gould of doing. Rebutting a claim based on the fact that the person making that claim was wrong in an unrelated claim. This is called an ad-hominen fallacy. 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.
duvenaud 5y ago
I'm not sure I understand the objection. I agree that standardizing to a normal distribution might be arbitrary, but how could one argue what the true transform of the distribution is? After all, a log-normally distributed variable is just exp() of a normally distributed one. Would anything be different if instead of IQ, we called it log-IQ?
- runarberg 5y ago
  I don’t think there is any research into finding “the true distribution” of intelligence. But intuitively intelligence should have a pretty skewed distribution with a long tail on the lower end where people with varying levels of mental handicap are skewing it, most people above average and a handful of people slightly more intelligent then the mode. This aligns with observation of non-IQ measures of intelligence like school grade or the SAT. This also works intuitively how we think of IQ. If you have an IQ of 70 there is probably something wrong, if you have an IQ of 130, you are probably just a normal person that might be slightly smarter then me. 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.
  - duvenaud 5y ago
    I don't understand what one could mean by the true marginal distribution of a latent quantity that's only defined in terms of its joint distribution with measurements. What difference would it make if we transformed IQ scores to a skewed distribution? 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.
    - runarberg 5y ago
      From OP: > 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.

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NoImmatureAdHom 5y ago

This viewpoint is generally acknowledged as wrong by the scientific community, and Gould is generally acknowledged as a hack who sold out by telling people what they wanted to hear in exchange for book sales.

runarberg 5y ago
> Gould is generally acknowledged as a hack who sold out by telling people what they wanted to hear in exchange for book sales. 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.

xyzzyz 5y ago

Stephen J Gould was a scientific fraud, with an ideological axe to grind, and repeatedly lied and misrepresented reality to smear what he saw as his ideological opponents. His most famous work on the topic, The Mismeasure of Man, for example, discussed Morton’s skull measuring experiments, who found that people of various races have different average cranial capacities. This is now a well established scientific fact, nevertheless Gould found this so offensive, that he claimed Morton fudged results by putting finger on the scale, based on no evidence whatsoever, simply disbelieving this sort of human variation between populations. Morton’s skulls have been in fact remeasured, and found to match Morton’s measurements within error margin appropriate to the method. This has been communicated to Gould himself, but he did not issue any correction or indeed mention any of it for the second edition of his book, showing clear evidence for his ideologically driven lack of scientific integrity.

ZeroGravitas 5y ago
This is a suspiciously specific rebuttle. Morton was wrong. https://en.wikipedia.org/wiki/Samuel_George_Morton 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.
- xyzzyz 5y ago
  Morton was wrong on many counts, to be sure, just as any scientist worth of salt must be. However, he was not wrong on the very thing Gould accused him of, which was ideologically based fudging of data, something that Gould was in fact guilty himself.
  - ZeroGravitas 5y ago
    He did ideologically fudge his data, though, to the point that he could, incorrectly, make the claim that he already believed, but that wasn't actually there in the data. Gould's point was about inadvertant bias in science and he was correct in this case.
runarberg 5y ago
You are doing the very thing you are accusing Gould of doing. Rebutting a claim based on the fact that the person making that claim was wrong in an unrelated claim. This is called an ad-hominen fallacy. 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.

duvenaud 5y ago

I'm not sure I understand the objection. I agree that standardizing to a normal distribution might be arbitrary, but how could one argue what the true transform of the distribution is? After all, a log-normally distributed variable is just exp() of a normally distributed one. Would anything be different if instead of IQ, we called it log-IQ?

runarberg 5y ago
I don’t think there is any research into finding “the true distribution” of intelligence. But intuitively intelligence should have a pretty skewed distribution with a long tail on the lower end where people with varying levels of mental handicap are skewing it, most people above average and a handful of people slightly more intelligent then the mode. This aligns with observation of non-IQ measures of intelligence like school grade or the SAT. This also works intuitively how we think of IQ. If you have an IQ of 70 there is probably something wrong, if you have an IQ of 130, you are probably just a normal person that might be slightly smarter then me. 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.
- duvenaud 5y ago
  I don't understand what one could mean by the true marginal distribution of a latent quantity that's only defined in terms of its joint distribution with measurements. What difference would it make if we transformed IQ scores to a skewed distribution? 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.
  - runarberg 5y ago
    From OP: > 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.