"IQ is Gaussian" – it was pointed out somewhere, and only then became obvious to me, that IQ is not Gaussian. The distribution is manufactured.

If you have 1000 possible IQ questions, you can ask a bunch of people those questions, and then pick out 100 questions that form a Gaussian distribution. This is how IQ tests are created.

This is not unreasonable... if you picked out 100 super easy questions you wouldn't get much information, everyone would be in the "knows quite a lot" category. But you could try to create a uniform distribution, for instance, and still have a test that is usefully sensitive. But if you worry about the accuracy of the test then a Gaussian distribution is kind of convenient... there's this expectation that 50th percentile is not that different than 55th percentile, and people mostly care about that 5% difference only with 90th vs 95th. (But I don't think people care much about the difference between 10th percentile and 5th... which might imply an actual Pareto distribution, though I think it probably reflects more on societal attention)

Anyway, kind of an aside, but also similar to what the article itself is talking about

This is a subtle aspect of intelligence measurement that not many people think about.

To go from an IQ of 100 to 130 might require an increase in brainpower of x, and from 130 to 170 might require 3x for example, and from 170-171 might be 9x compared to 100.

We have to have a relative scale and contrive a Gaussian from the scores because we don’t have an absolute measure of intelligence.

It would be a monumental achievement if computer science ever advances to the point where we have a mathematical way of determining the minimum absolute intelligence required to solve a given problem.

IQ scores have proven highly correlated to educational achievement, occupational attainment, career advancement, lifetime earnings, brain volume, cortical thickness, health, longevity, and more.

To the point of being accurate predictors of these things even when controlling for things like socioeconomic background.

It's used because it works as a measuring tool, how the tests are constructed is largely irrelevant to the question of if the outcome of the test is an accurate predictor of things we care about.

If you think you have a better measuring tool you should propose it and win several awards and accolades. No one has found one yet in spite of many smart people trying for decades.

Correct. IQ isn't an effective measurement of intelligence as is typically stated. It is (at best) a measurement of learning disabilities.

I didn't know that about how IQ tests are formed. Would that mean that there could be some sliver of the population that could score in the top %'s on the 1000 question test but due to the selection of questions, scored average on the final IQ exam? If so, that'll be my excuse next time I have to take an IQ exam. I just got the wrong distribution.

Sum of N independent similarly distributed variables (questions), will tend to be normally distributed, that the central limit theorem, no need to manufacture anything.

> and then pick out 100 questions that form a Gaussian distribution. This is how IQ tests are created.

You missed an extremely important final step. People's scores on those 100 questions still aren't going to form a Gaussion distribution. You have to rank-order everyone's scores, then you assign the final IQ scores based on each person's ranking, not their raw score.

It's worse, because every test is obviously bounded, and it's absurd to not expect some noise to be there.

Join those two, and the test only becomes reasonable near the middle. But the middle is exactly where the pick of questions makes the most difference.

All said, this means that IQ is kinda useful for sociological studies with large samples. But if you use it you are adding error, it's not reasonable to expect that error not to correlate with whatever you are looking at (since nobody understands it well), and it's not reasonable to expect the results to be stable. And it's really useless to make decisions based on small sample sizes.

That’s not how IQ tests are made as can be found by reading how they’re actually made via Google scholar. And it would be spectacularly hard to do what you describe.

How they’re actually made is a batch of questions thought to take some form of reasoning are curated, then ALL of those questions are used in the test. It is an empirical fact the percentages of decent sized groups of people will score a bell curve, in exactly the same way humans do on hard calc exams, on hard writing items, on chess problems, and across a bewildering amount of mental tasks, none of which are preselected and fidgeted with to fake a Gaussian.

A simple example: see how many simple arithmetic problems people can do in fixed time. What do you find? Gaussian. No need to fiddle with removing pesky problem. Do reading. Do repeat this sequence for length. Just about any single class of questions has the same bell curve output in human mental ability. The curve may bend based on some inherent difficulty, say addition versus calculus, but there will be a bell curve.

Now take plenty of types of questions to address various wobbles in people’s knowledge, upbringing, culture, etc, giving a host of bell curves per category (and those also correlated by individual). Then the sum of gaussians is gausdian. All IQ tests do is shift the mean score to be called 100 (normalized) and the std dev to match a preset amount of people so such tests can be compared over time.

And the empirical evidence is these curves do strongly correlate over time, so scaling a test to align with this underlying g factor is well founded.

This latter fact, that score on one form of intelligence seems to transfer well to others, forms the basis of modern intelligence research on the g factor. IQ tests correlate well with this g factor. And across all sorts of things the results are bell curves.

For anyone wanting to hear all this and a ton more, Lex Fridman has an excellent interview with a state of the art intelligence researcher at https://www.youtube.com/watch?v=hppbxV9C63g. The researcher goes into great depth on what researchers do know, how they know it, what they don’t know, and what has been proven wrong. This is all there.

People may find that manufactured or "oh IQ is just made up and there is no measure of intelligence". But I find beauty in the way that IQ tests create and reconfigure a distribution across a multi-dimensional vector or dimensional space. It figures out what we need in the general case, and allows us to use and reason with it, without ever having to do the grunt work or arguably impossible task of finding out an actual measure of intelligence or some way to untangle the way a brain works.

Yes, this has always bothered me. IQ doesn't easily correspond to any measurable real-world quality.

For example, if we would postulate that height is gaussian, we could measure people's heights and just ordering them we could create a gaussian distribution. Then we could verify the hypothesis of height being gaussian by mapping the probability distribution function's parameter to a linear value (cm) and find that these approaches line up experimentally.

We could do the same thing with any comparable quantity and make an order of them and try to map them to a gaussian distribution, but we would have no knowledge if what we were making actually corresponded to a linear quantity.

This is a serious issue, as basically making any claim like 'group A scores 5 points higher than group B' is automatically, mathematically invalid.

I think your comment about an easy test having everyone in the “knows a lot” category hints that the reverse (a hard test) would be Pareto distributed.