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Old 11-12-2018, 11:00 AM
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Obviously a standardized test for bears wouldn't look anything at all like one for humans. And in fact, most of the standardized tests for human intelligence don't look at all like what you're probably imagining. For instance, one test used for humans (which turns out to give surprisingly useful results) consists of asking the subject to draw a picture of a person: The test is then scored on the basis of how much detail the subject included in the picture.

Riemann, I think we may be disagreeing on just how much of a tail truncation is significant. Even if bears have had a long time to evolve away the stupid genes, there are still going to be a few who manage to dumb themselves to death (heck, even a few humans manage that). So you're still going to see some truncation on that tail. And in some sense, any truncation of the tails of a distribution can be significant, since when distributions deviate from a Gaussian, it's usually out in the tails (though more often because the tails are too thick for a Gaussian than because they're too thin).
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Old 11-12-2018, 11:20 AM
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But in evolution, the sensible definition of “significant” is “having a significant effect on allele frequency”, and that’s not arbitrary. The point is that any significant truncation is not a stable equilibrium condition. Significant truncation implies a significant effect on allele frequency, which moves the distribution in the next generation until the truncation is no longer significant. So under constant selection pressure (a stable environment), you will generally see an approximately normal two-tailed distribution.

Now, this is biology, so of course it’s not a perfect model, there will be second order effects, some traits may have genes with larger effect than most, the extreme tails will not be normal, etc. But the basic first order model that quantitative traits controlled by small contributions from many loci will have an approximately normal distribution has a sound theoretical foundation and good empirical support.

Last edited by Riemann; 11-12-2018 at 11:24 AM.
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Old 11-12-2018, 02:54 PM
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See post #8, and Wiki articles on “g”. There is an empirical correlation among a wide variety of cognitive tests in both humans and animals, general intelligence is the factor that explains about half the variance.
But what scale is g on that gives it a numerical value that has a distribution. I can measure person A and person B and say that person A is %10 taller than person B. But what does it mean to say that bear one is 10% smarter than bear 2. Presumably in humans it would mean scored 10% higher on an IQ test. But that is just one possible way to measure intelligence. There are other tests such as the one Chronos pointed out which presumably includes a way to numerically measure detail, and according to that way to measure detail may or may not have a normal distribution, but is very unlikely to be on the scale of IQ. So what is usually done on these circumstances it to associate with each participant the proportion of participants that scored less than they did, which effectively makes the scale uniform, then match those to the percentiles of the IQ test, to provide an IQ value for each participant.

In the same way bear intelligence could be forced to be uniformly distributed or normally distributed, without changing any bears or any tests. So while it makes sense to ask, are the performance of bears on such and such test or in such and such task normally distributed, asking whether intelligence is normally distributed is in and of itself meaningless.

Note that this has no bearing on whether or not g is a real thing. The notion of g relies on the agreement on multiple tests. This agreement can be calculated non-parametrically such that no matter what the distribution of the test results the degree of agreement stays the same.

Last edited by Buck Godot; 11-12-2018 at 02:58 PM.
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Old 06-11-2019, 12:21 PM
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Thank you for that. But is your gut that intelligence among bears is normally distributed? Or are are they all more or less the same, or of two types, or of some other distribution?
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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.
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Old 06-11-2019, 04:24 PM
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there is some harsh selection against dumb ones.
Is there though? I mean how smart does a bear have to be in order to survive and reproduce, and does that smart bear really have *that* much advantage in situations where they're not dealing with human stuff?

I mean even among humans, it used to be easier/less crippling to be slow, and being particularly smart didn't necessarily avail you of much. When something like 95% of people are farmers/farmhands/fishermen/herdsmen, the far tails of the bell curve aren't as important.

I would imagine that like a lot (most?) things in the natural world, bear intelligence does follow a normal distribution.
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Old 07-06-2019, 01:22 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.
If we have reason to believe the population is normally distributed, then how would we responsibly mix those methods to come up with a most telling one?
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