Why does IQ cluster around 100 points?

[Jokodo]

What's worse, the IQ scale is actually recalibrated every so often with the express intention to make sure the mean stays at 100. So it doesn't even tell us whether "absolute" intelligence is rising, falling or stagnating.

 

[Jokodo]

The shape of the curve suggests no such thing. If we had a way to measure intelligence on some "objective" and more importantly absolute scale in units derived from metres, seconds and kilograms (which we don't), and if, on that scale, the distribution would be a uniform one with all values in a range from 0 to 5000 objective intelligence units (OIU) equally frequent, the curve as regards IQ would still be a bell-shaped normal distribution: As per the definition of the IQ scale, 2500 OIUs would be mapped to an IQ of 100, 1056 OIUs to an IQ of 85, and 3944 OIUs to an IQ of 115 (that's the mean +/- one standard deviation in a uniform distribution over a range of 0-5000).

That's how the IQ scale is calibrated. If Jack and John have an IQ of 140 and 70 respectively, this does not in any meaningful sense mean that Jack is twice as intelligent as John. It only means that Jack is two and a half standard deviations above the mean, while John is two below. Depending on the the underlying distribution, and pretending that we had an absolute scale to measure intelligence against (which, again, we don't), this could be true if they have almost the exact same intelligence very close to some hard limit (if everyone has essentially the same intelligence, very small deviations can put you several standard deviations away from the mean), or it could mean Jack's intelligence is several 1000 times that of John if the values are all over the place.

Nothing, literally nothing, about the actual distribution of intelligence is implied by the distribution of IQs.

I'm not sure what you're trying to say here in reference to my post.

If we create a test that measures pure problem solving skill, and the results are a bit fuzzy, but generally stable at any given point in time in a population, controlling for other factors, then that means a few things:

1) We do have a reasonable idea of how intelligence, as defined as problem solving skill which is what IQ is, is distributed across a population. As far as I understand it this isn't very controversial science in terms of it's validity, despite the people who object. If you can point me to something that proves otherwise I'll turn on a dime.

2) The shape of the distribution defines how that population scores on problem solving skill.

It would if we were talking about an absolute scale. WE are, however, talking about a scale that's calibrated on the distribution in a way that forces such a shape.

So while an IQ of 140 doesn't say anything in of itself, the characteristics of those who are in the range do, and we can also measure the rarity of those with that IQ in reference to the rest of the bell curve.

The characteristics might. The rarity only tells us whether the test makers know their job. If it ever so happens that the characteristics of those currently scoring 140 become much more frequent, the scale will be recalibrated to make sure they get a Lower score, as has happened in the past.

We can also see how the bell curve is distributed: by your very math an IQ of 1000 is a mathematical impossibility, which suggests some form of phenotypic variation (and upper limit) that clusters in what we've defined as an IQ of 100. This is where biological limits come into play - if the component and/or components of the brain responsible for problem solving skill are the result of a continuum of genes, then we should get a normal distribution [granted this is a bit fuzzy]. And if at some point more problem solving power becomes maladaptive we shouldn't see the brain turn into a pure problem solving machine.

This may we'll be true but doesn't follow from anything you said, least of all from the Distribution of IQ scores.

3) Because IQ does say something about our problem solving skill,

Yes, and what it says is where an individual sits in the population's distribution

it's measurement is generally predictive of, for example, the IQ of people in different professions, how many babies people have, wealth, educational attainment, and a whole host of other things. With that in mind I don't know how you can claim that IQ doesn't measure anything, unless I'm not understanding what you're trying to say.

That's not what I'm saying. Only that conclidong anything from the distribution is circular reasoning

 

[untermensche]

IQ is not problem solving skills. IQ is one particular scale to express problem solving skills, one that happens to be calibrated on the distribution in the population. The fact that the median is is (close to) 100 and the standard deviation (close to) 15 literally only tells us that the people who shipped the latest series of tests did their job right....

There is no reason sores on a test should be a normal curve.

Why just one peak, not two, or three or fifty?

That is the point of the OP.

 

[Jokodo]

IQ is not problem solving skills. IQ is one particular scale to express problem solving skills, one that happens to be calibrated on the distribution in the population. The fact that the median is is (close to) 100 and the standard deviation (close to) 15 literally only tells us that the people who shipped the latest series of tests did their job right....

There is no reason sores on a test should be a normal curve.

Why just one peak, not two, or three or fifty?

That is the point of the OP.

There is when the scale is designed to make it so.

 

[untermensche]

IQ is not problem solving skills. IQ is one particular scale to express problem solving skills, one that happens to be calibrated on the distribution in the population. The fact that the median is is (close to) 100 and the standard deviation (close to) 15 literally only tells us that the people who shipped the latest series of tests did their job right....

There is no reason sores on a test should be a normal curve.

Why just one peak, not two, or three or fifty?

That is the point of the OP.

There is when the scale is designed to make it so.

No.

The scale does not force one peak.

The number of people with a certain score forces it.

But there is no reason why there should only be one peak. Why not a long plateau? Or multiple peaks?

 

[rousseau]

That's not what I'm saying. Only that concluding anything from the distribution is circular reasoning

I disagree. I'll grant you that the distribution is plastic, because people are plastic, but outside of that it tells us a hard fact about human biology, in the same way measuring the distribution of something like extraversion, or sexuality would tell you a hard fact about biology.

Outside of building a test that measures people's problem solving skill, I'm not sure how else you would go about measuring and defining our intelligence, and using what you find to make conclusions about our physiology.

 

[Jokodo]

You're still stubbornly failing to understand what the IQ scale is.

That's not what I'm saying. Only that concluding anything from the distribution is circular reasoning

I disagree. I'll grant you that the distribution is plastic,

The distribution (of IQs) is in fact not plastic, by its very definition. IQ 100 is defined to mean "the population's mean result in an IQ test", IQ 115 is defined to mean one standard deviation above that, that is.

because people are plastic, but outside of that it tells us a hard fact about human biology,

No. It tells us whether the test makers were up to the task of correctly calibrating the difficulty of the questions and their weighting in such a way that the mean result would be the desired 100 points, and the standard deviation the desired 15 points. And that's all it tells us.

in the same way measuring the distribution of something like extraversion, or sexuality would tell you a hard fact about biology.

Yes - and no. The science of psychometry offers a lot of results that do tell us a lot about human biology: The distribution of problem solving skills, and whether and to what degree problem solving skills in different areas are intercorrelated, and at what ages the ability to solve specific types of problems emerges, and how much variation there is those ages of emergence, and to what degree those people who seem to be unable to solve certain types of problems can or cannot solve them in their own pace given more time, etc. all do. The distribution of IQs doesn't reflect any of those results, and isn't designed. It is designed to measure where an individual falls in the population's distribution of problem solving skills (with a somewhat arbitrary weighting of subcomponents), and nothing more.

The observation you made, that the mean is 100 and 68% fall in the range of 85-115 is every bit as surprising as the fact that the numbers in the series 10^n, where n is a non-negative integer, are all written as "1" + n * "0" in the decimal system: That is, it's ceases to be amazing the moment you understand the IQ scale/the decimal system. It follows from their definitions. It's a tautology.

Outside of building a test that measures people's problem solving skill, I'm not sure how else you would go about measuring and defining our intelligence, and using what you find to make conclusions about our physiology.

I don't disagree with that. IQ, however, doesn't "measure people's problem solving skill", it specifically measures where people fall in their population's distribution of problem solving skills. A child of 10 scoring 100, an young adult in the 1970s scoring 100, and a young adult today scoring 100 are each able to solve a different set of problems. The only thing their problem solving skills have in common is that it's representative of the mean of the group they represent.

 

[untermensche]

Intelligence is HOW you solve the problem.

No test can look at that.

If you get the right answer it is just assumed you solved it like everybody else. Or worse how you solved it doesn't matter to the test makers.

This eliminates natural differences.

No two people have the same intelligence.

Even if they both have the same exact score on a test.

Take people and give them an IQ test and then ask them to fix a car.

You will get a similar distribution but a completely different order.

 

[Jokodo]

There is when the scale is designed to make it so.

No.

The scale does not force one peak.

This one does, unless it's miscalibrated, by its definition. IQ 115 doesn't mean 115 IQs, the way 115 metres means 115 times one metre. Neither does it mean 115% of an IQ of 100. What it means is precisely a test achievement 1 standard deviation above the mean when mapping the population's achievements to a normal distribution centered at 100.

The number of people with a certain score forces it.

The number of people able to answer a certain number of questions determines how the questions have to selected and weighted. The expressed goal of that calibration procedure is to make sure the mean is always 100 with an sd of 15. It's how the fucking thing is defined!

But there is no reason why there should only be one peak. Why not a long plateau? Or multiple peaks?

Because then the tests would have to be, and be, recalibrated.

 

[untermensche]

The scale does not force one peak.

This one does, unless it's miscalibrated, by its definition. IQ 115 doesn't mean 115 IQs, the way 115 metres means 115 times one metre. Neither does it mean 115% of an IQ of 100. What it means is precisely a test achievement 1 standard deviation above the mean when mapping the population's achievements to a normal distribution centered at 100.

You can't calibrate one peak. You can only arbitrarily say what that one peak stands for.

If humans taking the same test creates one peak that says something about humans not the test.

The number of people with a certain score forces it.

The number of people able to answer a certain number of questions determines how the questions have to selected and weighted.

A lot of people answer easy questions, a few don't. A few people answer hard questions, a lot don't.

It is easy to imagine a lot of people not able to answer what we call easy questions and a lot of people able to answer hard questions and end up with two peaks.

But that doesn't happen due to the nature of human intelligence.

Most people are at or are very near the mean.

There are a few outliers at either end.

 

[rousseau]

I don't disagree with that. IQ, however, doesn't "measure people's problem solving skill", it specifically measures where people fall in their population's distribution of problem solving skills. A child of 10 scoring 100, an young adult in the 1970s scoring 100, and a young adult today scoring 100 are each able to solve a different set of problems. The only thing their problem solving skills have in common is that it's representative of the mean of the group they represent.

Yes, I get that part, but 'IQ not measuring people's problem solving skill' doesn't follow from how the scale was built. Sure I'll grant you that the IQ of 100 can mean different things at different times, but when measuring a static population, or a static point in time across populations, it measures their problem solving skills. Yes it's fuzzy, but it's the only tool we've got.

 

[Jokodo]

You can't calibrate one peak. You can only arbitrarily say what that one peak stands for.

If humans taking the same test creates one peak that says something about humans not the test.

The number of people with a certain score forces it.

The number of people able to answer a certain number of questions determines how the questions have to selected and weighted.

A lot of people answer easy questions, a few don't. A few people answer hard questions, a lot don't.

It is easy to imagine a lot of people not able to answer what we call easy questions and a lot of people able to answer hard questions and end up with two peaks.

But that doesn't happen due to the nature of human intelligence

Wrong. It doesn't happen because the questions are selected to not make it Happen, to Produce a unimodal normal distribution. You could could easily make it Happen by selecting different questions or a different Weighting.

 

[untermensche]

You can't calibrate one peak. You can only arbitrarily say what that one peak stands for.

If humans taking the same test creates one peak that says something about humans not the test.





A lot of people answer easy questions, a few don't. A few people answer hard questions, a lot don't.

It is easy to imagine a lot of people not able to answer what we call easy questions and a lot of people able to answer hard questions and end up with two peaks.

But that doesn't happen due to the nature of human intelligence

Wrong. It doesn't happen because the questions are selected to not make it Happen, to Produce a unimodal normal distribution. You could could easily make it Happen by selecting different questions or a different Weighting.

No you couldn't.

You couldn't create a test that had both a lot of people with a very low score and a lot of people with a high score.

Not with a random group.

 

[Jokodo]

I don't disagree with that. IQ, however, doesn't "measure people's problem solving skill", it specifically measures where people fall in their population's distribution of problem solving skills. A child of 10 scoring 100, an young adult in the 1970s scoring 100, and a young adult today scoring 100 are each able to solve a different set of problems. The only thing their problem solving skills have in common is that it's representative of the mean of the group they represent.

Yes, I get that part, but 'IQ not measuring people's problem solving skill' doesn't follow from how the scale was built. Sure I'll grant you that the IQ of 100 can mean different things at different times, but when measuring a static population, or a static point in time across populations, it measures their problem solving skills. Yes it's fuzzy, but it's the only tool we've got.

No, you don't get it. It is not the only tool we have. It's not even a tool for that purpose - it's a tool for an entirely different purpose. Cracking hazelnuts open with a chainsaw is a more efficient endeavor than what you're trying to do here.

IQ tests do measure people's problem solving skills and then map them onto a scale designed to tell where a person sits on the population's distribution!

 

[untermensche]

So you agree that a written test has a single peak due to human nature not the test maker?

 

[Jokodo]

You can't calibrate one peak. You can only arbitrarily say what that one peak stands for.

If humans taking the same test creates one peak that says something about humans not the test.





A lot of people answer easy questions, a few don't. A few people answer hard questions, a lot don't.

It is easy to imagine a lot of people not able to answer what we call easy questions and a lot of people able to answer hard questions and end up with two peaks.

But that doesn't happen due to the nature of human intelligence

Wrong. It doesn't happen because the questions are selected to not make it Happen, to Produce a unimodal normal distribution. You could could easily make it Happen by selecting different questions or a different Weighting.

No you couldn't.

You couldn't create a test that had both a lot of people with a very low score and a lot of people with a high score.

You probably couldn't design it in such a way that everyone neatly falls into one of two categories, but a clearly bimodal distribution? Nothing easier than that! just give excessive weight to problems hard enough that most people can't solve them, but easy enough that mostly everyone with IQs above, say, 105-110-ish can. Voilá, two peaks with a valley between them, one for people who fail at most of those questions and one for people who manage to solve most.

Not with a random group.

Yes, with a random group.

 

[Jokodo]

So you agree that a written test has a single peak due to human nature not the test maker?

This does not follow from anything I said.

 

[untermensche]

So you agree that a written test has a single peak due to human nature not the test maker?

This does not follow from anything I said.

...just give excessive weight to problems hard enough that most people can't solve them, but easy enough that mostly everyone with IQs above, say, 105-110-ish can. Voilá, two peaks with a valley between them, one for people who fail at most of those questions and one for people who manage to solve most.

This is not possible.

If a question is easy for a person who has a prior score of 105 it will be easy to many who have a prior score of 100 and easy to less but still many with a prior score of 96.

You will still have one peak.

And every test has questions that most people can't solve.

Giving "weight" to them will not create a peak.

The peak is numbers of people with a score not the difficulty of the question.

 

[rousseau]

I don't disagree with that. IQ, however, doesn't "measure people's problem solving skill", it specifically measures where people fall in their population's distribution of problem solving skills. A child of 10 scoring 100, an young adult in the 1970s scoring 100, and a young adult today scoring 100 are each able to solve a different set of problems. The only thing their problem solving skills have in common is that it's representative of the mean of the group they represent.

Yes, I get that part, but 'IQ not measuring people's problem solving skill' doesn't follow from how the scale was built. Sure I'll grant you that the IQ of 100 can mean different things at different times, but when measuring a static population, or a static point in time across populations, it measures their problem solving skills. Yes it's fuzzy, but it's the only tool we've got.

No, you don't get it. It is not the only tool we have. It's not even a tool for that purpose - it's a tool for an entirely different purpose. Cracking hazelnuts open with a chainsaw is a more efficient endeavor than what you're trying to do here.

IQ tests do measure people's problem solving skills and then map them onto a scale designed to tell where a person sits on the population's distribution!

No, I got it the first time you said it, and I got it when I wrote the original post.

 

[Jokodo]

...just give excessive weight to problems hard enough that most people can't solve them, but easy enough that mostly everyone with IQs above, say, 105-110-ish can. Voilá, two peaks with a valley between them, one for people who fail at most of those questions and one for people who manage to solve most.

This is not possible.

If a question is easy for a person who has a prior score of 105 it will be easy to many who have a prior score of 100 and easy to less but still many with a prior score of 96.

Sure. That's why you wouldn't get a sharp two-camps selection. As I said. But we were talking about a bimodal distribution, not a binary categorical difference.

You will still have one peak.

And every test has questions that most people can't solve.

Giving "weight" to them will not create a peak.

The peak is numbers of people with a score not the difficulty of the question.

And the score is what? The sum of the points awarded for questions they were able to answer.

If you know of any publicly available (anonymised and machine-readable) detailed result set of a random group of several thousand test takers, with the individual's answers to each question specified, I bet you dollars to dimes that I can come up with a weighting that produces a bimodal distribution with less than half a day's work (though the implementation may have to wait till my newborn sleeps through the night).