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Bill_McGrath comments on Undiscriminating Skepticism - Less Wrong
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Excuse delay getting back to this.
Okay, I think I can explain. Let's say that we have 5 ethnic groups under the umbrella "black." All of approximately equal size. Groups A and B are found to, in general, be slightly above average intelligence, C and D are about equal, and E are significantly below. The average intelligence for "blacks" is now below average, and this is mathematically correct, while in reality, 4 out 5 black people you meet will tend to be of average or higher intelligence.
Perhaps this is a common statistical fallacy, but this is what I mean about the classification being too broad to be useful; with such a broad area to work from, with no internal distinctions being made in a hugely diverse category, the data isn't all that interesting or enlightening.
Ok, that makes sense. The next obvious question, though, is why you think that the category of people labeled "black" fits this pattern, instead of, say, a Gaussian distribution.
Well, I don't neccessarily think it does fit this pattern, I'm just saying it's a possibility, and there's no particular reason to consider it an unlikely possibility. On the other hand, seeing as the argument linking race to intelligence seems to be based on genetics, I feel that there is too much of a broad genetic sample within "black" for race to be a reliable indicator of intelligence, as I outline above.
There is also no reason to consider it to be more likely than the possibility that there are groups A and B with intelligence slightly less than the mean (of everyone in the category "black"), groups C and D about equal, and a group E significantly above average, in which case your argument that the mean value of IQ unfairly discriminates against blacks is exactly reversed.
I see no reason to consider it more likely that the mean unfairly discriminates against blacks as opposed to the hypothesis that the mean unfairly inflates the "true" average intelligence of that group. Your argument that there are multiple ethnic groups is correct, and that does mean that we should give a lower weight to the mean value of IQ. It does not mean that we are licensed to believe that this value is off in one particular direction, because that direction is what we would like to be true.
I agree, but you're strawmanning me here. I never said that IQ discriminated any particular direction, I was arguing that black is too large a group, contaning too much diversity, to give useful results one way or the other. I just happened to choose that specific example.
I've made it pretty clear it's not about what I want to think.
I think this is, in fact, a common statistical fallacy: using the mean instead of the median to represent "average".
Median is often better, but not always - it depends on the purpose you wish to put the data to. With anything less than the full distribution, you'll be able to hit some cases in which it can mislead you.
Edited to add:
Specifically - if you are interested in totals, mean is usually a more useful "average". Multiplying the total number of water balloons by the average amount of water in a balloon gives you a much better estimate (exact, in theory) with mean than with median. If you are interested in individuals, median is usually better; if I am asking if the next water balloon will have more than X amount of water, median is a much more informative number. Neither is going to well represent a multimodal distribution, which we might expect to be dealing with in the great*-grandparent's case anyway if the hypothesis of a strong genetic component to variation in intelligence does in fact hold.
Good point. You should select a metric that would be most useful in any given situation, be it the mean, the median, or anything else.
Ah; so I'm misunderstanding what brazil84 means by average?
No, I think his example of 5 ethnic groups is flawed, because he's using the wrong metric to calculate the average. If he was using the median instead of the mean -- which is the right thing to do in this case -- he'd obtain the result that "most blacks have average intelligence", and his conclusion would no longer follow.
(Edited: typo)
The 5 ethnic groups was mine originally.
But then I have to consider the scenario where the median gives the result of below averge intelligence - will take me slightly longer to puzzle out in my head.