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Culture War Roundup for the week of June 10, 2024

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I mean yes, but I’d consider a 10-15 IQ test differential to be fairly minor, it’s one σ at best. It’s there, but unless you’re doing high level stuff, I don’t think most people would be able to tell the difference at a glance between IQ 115 and IQ 100. At lower IQ it makes a difference sure, but for average IQ levels it’s not that much.

AFAIK as IQ is deliberately intended to be normalized, the gap is exactly the same 85 to 100 as 100 to 115, and if you think that those two aren't the same, you are also inherently saying that IQ is the wrong tool for the job. That's not even getting into the whole "what benchmark do we set 100 at", do we update it year to year or try to peg it to some historical benchmark (though this is not necessarily fatal to IQ as a metric in the same way the first is, it does present a question that must be addressed when using IQ).

Simply using IQ necessitates that you grapple with these things. That's the nature of using numbers to describe something human. You, the invoker of IQ, need to prove the numbers work as numbers and aren't better being left as philosophical concepts or practical examples, or point to something well established that does. The simple, self-evident fact that IQ is fit to a normal curve and you yourself don't seem to believe that a symmetric 15 point gap is equal across the domain is in and of itself a tacit admission that IQ is the wrong tool. Are you familiar with the statistical notions of how an assigned number scale can be nominal, or ordinal, or interval, or ratio? It's not a perfect paradigm by any means, but it's one you must grapple with at least on some level, and happens to be incredibly relevant here in this case. See also OP's initial claim that the distribution has a weird asymmetric tail, also evidence (though more mild) against using IQ as the correct tool. Similarly, the fact that you dodge the 100-center question, which is a fundamentally important question to the use of IQ, is not acceptable.

I mean, I get the whole all models are wrong but some are useful, but these are just the very basics, the fundamentals, they are not nitpicks. An example of something that at least does attempt to address these issues and mostly succeeds is the Likert scale. You might be familiar with it. It's the classic 5 or 7 point scale in response to a question, with "strongly agree" and "slightly agree" and "not sure" and disagree options. There's a natural zero, and at least psychologists attempt to say that the distance between each point is "equal". I know forced normalization distorts this equal-distance formulation slightly, in terms of the math, but two properties that persist across the transformation are the aforementioned symmetry of responses, and also the center point of responses. These two decisions are non-negotiable and mandatory to make and cannot be hand-waved away. They are inherent to the math and the use of a numerical model.

The simple, self-evident fact that IQ is fit to a normal curve and you yourself don't seem to believe that a symmetric 15 point gap is equal across the domain is in and of itself a tacit admission that IQ is the wrong tool

Imagine two groups of children go to a themepark and want to hop onto a rollercoaster, which has a minimum height requirement of 105cm. One group of children has heights that range from 110cm to 150cm, and the other group has heights that range from 70cm to 110cm. The symmetric 40cm gap would not be equal across the domain - is this a tacit admission that height is the wrong measuring tool for the job? A simple 15cm boost would have a different effect on each group's ability to ride the rollercoaster, so how can you say that 1cm is equal to 1cm between the two groups?

This is why a statistics background is helpful. The core idea behind creating an IQ score is this: Raw test scores are forcefully molded into something that looks like a bell curve. That's IQ generation. That's the analogy here of "slapping a number on it". To be clear, anyone can take any dataset ever and make it look like a Bell curve by following this same methodology.

Careful! The thing being measured is by no means required to have a normal distribution itself! Height is actually a bad example here, because we know that due to whatever mechanisms go into a person's adult height, that human population heights are actually approximately normal (I say approximately because technically the normal has an infinite domain, and in practice we never see humans beyond a certain min and max height, but the core part of the distribution is without a doubt very normal; tails beyond a certain number of standard deviations are not as often considered, and are generally not here either for our purposes). In our height example, the difference in both a raw height of 1 cm is the same as a "normal" height of 1 cm. However, in IQ, if you score 1 point different in the raw test data, this could translate to a .5 IQ or a 2 IQ difference depending on where your particular score was forced into a normal distribution, i.e. how far up or down you are, and vice-versa. As I said, it's not symmetric.

Choosing height as your example is actually perfect, then, because it demonstrates that you indeed do not understand IQ on a fundamental level.

So IQ is necessarily ordinal in the sense that the mechanism is ranking and stacking up test-takers, relative to some benchmark. But they never are interval (implying equal-measures) in the sense that neither the core, raw test scores nor IQ are necessarily going to fairly represent what we actually want it to be: intelligence. A misunderstanding betrayed in everything upthread. It gets worse, too, when you consider that most IQ test designers have deliberately messed with the test design to make the test results fit their nice bell curve easier. You can see how this leads to some circular logic and reasoning. This is a MATH ISSUE. You cannot hand-wave it away!

For more, please see for example a technical discussion here, with an excerpt:

It may sound weird to define IQ so that it fits an arbitrary distribution, but that's because IQ is not what most people think it is. It's not a measurement of intelligence, it's just an indication of how someone's intelligence ranks among a group:

The I.Q. is essentially a rank; there are no true "units" of intellectual ability.

[Mussen, Paul Henry (1973). Psychology: An Introduction. Lexington (MA): Heath. p. 363. ISBN 978-0-669-61382-7.]

In the jargon of psychological measurement theory, IQ is an ordinal scale, where we are simply rank-ordering people. (...) It is not even appropriate to claim that the 10-point difference between IQ scores of 110 and 100 is the same as the 10-point difference between IQs of 160 and 150.

[Mackintosh, N. J. (1998). IQ and Human Intelligence. Oxford: Oxford University Press. pp. 30–31. ISBN 978-0-19-852367-3.]

When we come to quantities like IQ or g, as we are presently able to measure them, we shall see later that we have an even lower level of measurement—an ordinal level. This means that the numbers we assign to individuals can only be used to rank them—the number tells us where the individual comes in the rank order and nothing else.

That's a lot of words but I think I may not have been sufficiently clear when making my point because this reply doesn't get at the core of my objection, which doesn't have anything to do with the distribution of the score. I'm aware that height doesn't follow the same distribution curves as IQ, but the point of using height was to make the concept of a threshold or minimum requirement more obvious.

AFAIK as IQ is deliberately intended to be normalized, the gap is exactly the same 85 to 100 as 100 to 115, and if you think that those two aren't the same, you are also inherently saying that IQ is the wrong tool for the job.

The point being made by your interlocutor is not that the 15 points of IQ between 100 and 115 matter more than the 15 between 85 and 100, but that it can be harder to tell the difference externally. To wit:

A fifteen point gap at the higher end of the distribution isn't likely to be noticeable in everyday casual interaction, but at the lower end it can be the difference between someone who can at least tell you their own name and a total potato.

A single casual conversation can give you enough information to determine whether or not someone meets a certain low threshold for IQ, in much the same way that a sign in front of a rollercoaster with a single black line at the height threshold can tell you if someone meets the minimum requirement or not. The fact that the single threshold of the sign gives you a bit of information about the height of people who compare themselves to it but is unable to give you more information about the distribution of heights among people who pass does not mean that a centimetre is measured differently above or below the threshold.

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