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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:
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.
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 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.
I guess we're in pretty deep, but the original framing was this: a user said any intelligence differences were minor and also hard to tell, another user posts a study claiming basically that we could actually tell, and the OG user said yes that's still a minor difference, I can't tell 100 vs 115. Third user chimes in and says ok, 85 to 100 is the actual difference which implies in context that this 15 point gap is not minor and/or is obvious in casual conversation. At that point I respond about how 115 to 100 != 100 to 85 and that IQ is a stupid measure, which spawned a few subthreads.
Perhaps I conflated a few users or responded to the wrong argument, in retrospect (at that juncture), which maybe contributed to some unwieldy downthread organization. I apologize if my digression the last two replies wasn't strictly relevant, but it does bear mentioning with respect to my overall point. The whole conversation, I was trying to point out, is a stupid one. IQ has poisoned the debate. People want IQ to represent intelligence but it doesn't do so in a very rigorous way, and asymmetry is one of those ways. There are numerous methodological problems as well as fundamental interpretability problems. In a strict sense, sure, we were originally only comparing 100 to 85 and trying to consider it in context. That's kind of fine. The original wikipedia article (about the adoption study) does mention grappling with some but not all of these problems, and only methodologically. And actually, if you look carefully at the article, the parents were selected precisely because of having an IQ of 115 or higher. Maybe it's not a perfect point, but I want to point out that these misconceptions clearly pop up in many places including study design! And this study design did, in fact, have a number of significant issues, despite on its face being a perfect poster child experiment, for example as discussed here.
Inasmuch as we're more narrowly talking about casual conversation, sure, maybe the "test" of "can casual conversation detect someone 85 IQ or below" is perfectly valid and usable as a test (i.e. detecting if someone is sitting somewhere within the binned bottom 16ish percent of IQ scores, on that particular test), though maybe I've misconstructed the test: Is it instead "can you detect the difference between a 100 and 85 IQ" or "can you detect an 80-90 IQ from a 110-120 IQ person in casual conversation" or "can you identify someone's IQ within 15 points in casual conversation, provided they are not over 100" or and many, many other variations... Some might sound similar but from a math perspective might have drastically different actual implications, and even more problems crop up the second we try to equate specific IQ test scores as intelligence directly.
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