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Old 06-11-2019, 03:47 PM
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Again, it's not a meaningful question unless you define how you're quantifying intelligence. Let's suppose, for instance, that our test consists of a large number of tasks, at each one of which the subject will either succeed or fail (for humans, these tasks are likely to be answering questions, but they could be anything). Some tasks will be easier than others, so more people will succeed on those. And let's even suppose that we're so good at devising tasks that we can completely eliminate the random element: Anyone who is at least at some level of intelligence can always succeed at this task, and anyone who is not at that level will always fail at it.

Now, I pick out, say, 200 of these perfect tasks, and put them on a test. The number of questions a subject gets right is considered to be their intelligence. How is it distributed? Well, that will depend on the tasks chosen. If I pick one task that 99.5% of the population can succeed on, and one task that 99.0% can succeed on, and one task that 98.5% can succeed on, and so on, then I'll find that the scores have a uniform distribution. If I pick half of my tasks to be really hard ones and half of my tasks to be really easy ones, then I'll see a very narrow distribution right in the middle, because almost everyone will be able to get all of the easy ones right and all of the hard ones wrong. If I pick all of my tasks from the middle, then I'll get a strongly bimodal distribution, because almost half of the people won't be able to get any right, and the other almost half will be able to get all of them right.

Now, if I make one test using one set of those tasks, and someone else makes a different test using a different set of those tasks, our results will be very well correlated, no matter what sets we chose. That's a sign that what we're testing for is a real phenomenon. But it still doesn't let you say anything about just what the distribution of that real phenomenon is.