I see your point but I’m not sure I agree. Perhaps I’m just reluctant to think in those terms, but I don’t think that’s it. I’m not thinking of this in terms of PC, just in terms of usefulness.
I’m having trouble thinking up an analogy to explain my point; I’ll think about it and see if I can. If not, guess I need to start over.
EDIT: Actually, if we replace “intelligence” with a less loaded or emotive quality, say “height”, I think I’d still be inclined not to consider it useful. But as I say, I’ll have a think about this.
Just to add a note here: using the “height” example, suppose I told you that research has shown black people were on average shorter than white people. Then, it turns out, that my sample of “blacks” was from the area with the pigmy ethnicities, and if I excluded those from my definition of “blacks” then they were on average taller than white people. This is an extreme example, but here the statement “the mean height of black people is less than the mean height of white people” might be TRUE, but it won’t be USEFUL.
This is because your sample of black people contains within it many separate distributions for the same attribute, and simply taking their mean is not helpful. I’m merely saying that in an unhomogeneous group, averages are more likely to be misleading.
Sure, a set of equal numbers of mice and elephants are on average bigger than a set of guinea pigs, but that’s not a useful statement. And a generalisation from that particular sample to “short-haired animals are bigger than long-haired animals” would be outrightly unjustifiable from your data.
His point isn’t actually very good—“worms” isn’t a single category about which you could make many meaningful statements on average either (well, you try coming up with many non-vague true statements that universally apply to platyhelminths, polychaetes, annelids, nematodes...).
Linneaus coined the taxon vermes to hold any non-arthropod invertebrate. Later, cladistics came along and demolished the idea that it was ever a useful biological group.
Whereas “elephants” consists of just a handful of living species in two genera, so we shouldn’t be surprised that they have a lot in common—and even then, if you over-presume on those similarities when making theories, you’ll wind up wrong because you didn’t realize the ways in which they can differ.
worms” isn’t a single category about which you could make many meaningful statements on average
I don’t see what difference this makes. If someone were to observe that “elephants” are generally speaking larger than “worms,” the fact that the two categories are extremely diverse would not preclude you from reasonably asking whether the difference was due to genetics.
The statement that “blacks” have lower IQs than “whites” is both meaningful and true.
I do not think you understand biology (either in the context of the race/IQ discussion or in general) well enough for it to be worth arguing with you further.
I disagree. What I’m doing is to take the exact criticisms made of categories like “blacks” and “whites” and applying them to other biological categories in order to show that there’s a double standard at work.
You’re missing the fact that people are arguing “but the groups are heterogeneous” when they mean “but the different means might be within a standard deviation of each other because single groups have a spread much wider than the difference between them”. That would apply when trying to ascertain whether, say, worms are larger than insects, but NOT when trying to ascertain whether worms are larger than elephants, because the difference between the largest and smallest worms is probably a lot bigger than the difference between the average size of a worm and the average size of an insect. On the other hand, the average size of an elephant is greater than the average size of a worm (any worm) by way more than the biggest worm is bigger than the smallest worm.
Suppose I got together all the worms and all the insects and measured their volume, and found the mean size of a worm and the mean size of an insect. And suppose (I have no idea what the truth is here, but it seems about as plausible as anything else) that I found that on average worms are smaller than insects. Would that be meaningful? I don’t think it would be useful to know.
How big an IQ gap are you saying exists? Are we talking as much as a standard deviation? Then maybe it would be important (if true). But if so, genetics isn’t the only possible explanation. I’d expect upbringing and class to be very important, as well as quality of public schools where they live, perhaps so much so that a genetic difference, if any, could be completely overwhelmed.
but the different means might be within a standard deviation of each other because single groups have a spread much wider than the difference between them
I don’t recall anyone arguing that in this thread, but this argument—to the extent it makes any sense at all—lacks merit.
Let’s take your analogy.
Suppose I got together all the worms and all the insects and measured their volume, and found the mean size of a worm and the mean size of an insect. And suppose (I have no idea what the truth is here, but it seems about as plausible as anything else) that I found that on average worms are smaller than insects. Would that be meaningful?
To make things simple, let’s assume that there are 100 species of worms and 100 species of insects and 1,000,000 individuals from each species. Let’s further assume that there is an animal known as the African Aardvark which eats both worms and insects (and has equal access to all), but eats only individuals greater than a certain size. Now suppose it is observed that the African Aardvark eats 75% insects and 25% worms, and we are presented with two hypotheses to explain this observation: (1) The African Aardvark likes the taste of insects better than that of worms; or (2) the African Aardvark prefers larger individuals to smaller individuals.
In evaluating which of the two hypotheses is correct, is it useful (or meaningful) to know that on average worms are smaller than insects? (And you can assume that the two groups each have a spread much wider than the difference between them.)
But if so, genetics isn’t the only possible explanation.
I’m not sure what this means. To be sure, genetics is not the only reason for the black/white iq gap. At the same time, there is no non-genetic explanation which (1) explains the gap; and (2) is not ridiculous.
To be sure, genetics is not the only reason for the black/white iq gap. At the same time, there is no non-genetic explanation which (1) explains the gap; and (2) is not ridiculous.
I don’t quite understand how you didn’t just contradict yourself.
However, if you want a non-ridiculous, non-genetic explanation that explains the gap, try this one: while whites came to America with diverse socioeconomic backgrounds, the biggest group of black Americans today is descended from slaves, and until recently, there was extreme racial segregation. Hence, rather than just assimilating, they as a group have ended up forming a subculture. (If you don’t believe that, look at the world and try again.) Not all African Americans live in ghettos, but a greater percentage of them than of whites do. (Similarly, not all of them are stupid.) Among their subculture, poverty is high, teenage pregnancy is high, single mothers are common and violence is really common. In such an environment, they’re not likely to have highly-educated parents to nurture their intellectual development. Meanwhile, worldwide, large numbers of blacks live in Africa, which is 1. not a good place, and 2. full of primitive peoples, resulting not only in people (the common people) having less access to education, but also to cultural biases skewing IQ test readings.
Test that would distinguish between this theory and genetics: study IQ among African Americans born after the Civil Rights Movement to married couples whose income is above the poverty line and who don’t live in “bad neighborhoods”. If the gap disappears, it’s more likely environmental; if it doesn’t, that may indicate a genetic difference. But taking the raw IQ data doesn’t distinguish between these; it merely rules out the hypothesis that there are neither genetic nor environmental differences. Since there may even be a big enough population now to survey, someone should do it. The only problem I can think of here is that people who rise above poverty are already selected for intelligence (as well as persistence and work ethic).
In evaluating which of the two hypotheses is correct, is it useful (or meaningful) to know that on average worms are smaller than insects? (And you can assume that the two groups each have a spread much wider than the difference between them.)
Ah, now I see. I couldn’t think of a reason why it would matter in everyday life, because it’s more reliable to just ascertain whether or not people are actually intelligent by getting to know them, not using deeply flawed binary heuristics. However, now I see that you’re worried about whether people will end up assuming someone is being racist when they’re not. That’s fair. In the current political climate, it’s a big risk, for everyone. In that case, whether it’s genetic or environmental doesn’t really matter, though.
However, if you want a non-ridiculous, non-genetic explanation that explains the gap, try this one:
Respectfully, that explanation is ridiculous. If you wish to debate it with me further, please read my blog post and respond there.
However, now I see that you’re worried about whether people will end up assuming someone is being racist when they’re not
Some one, or some organization. Anyway, the issue you are addressing is a slightly different one from what I raised. Basically you are making the “who cares” argument. But the reality is that our society cares very much, just like many Europeans in the middle ages cared very much about devotion to Christianity. Publicly pointing out the weaknesses in the Christian position could get you into serious trouble back then, just like pointing out the truth about race and intelligence can evoke a lot of hostility in modern day Western world.
What you are missing is context—the context to understand what you are arguing about, and the limits of your analogy.
Additionally, you are missing the context needed to understand why the larger argument you’re making cannot effectively be made in those terms. I am no longer interested in discussing it with you.
Fundamentally, the point is that reasoning about race should be subject to the exact same standards as reasoning about any other kinds of categories.
In regular life, and even in science, people readily accept categories which are somewhat arbitrary; which are difficult to define around the edges; which contain pairs of elements more different than some pairs of elements, only one of which is contained in the category; and so on.
I think that for various emotional reasons, people tend to get wound up over the categories “black” and “white” but such considerations should not affect rationalists.
I agree with you here; I don’t think I’m getting wound up for emotional reasons, I just don’t think the category is necessarily a partiuclarly useful one, but for reasons I can’t really articulate. (I am not knowledgeable about statistics and the relevant terminology.)
But yes, there’s no reason to adopt new rules for reason on any topic—that wasn’t what I was arguing, and it’s clearly counter-rational.
for reasons I can’t really articulate. (I am not knowledgeable about statistics and the relevant terminology.
We’ll be all right without formal terminology. I’m not at all sure what it is you’re trying to get at, and I’d be perfectly happy with you describing it as a metaphor, or an example, or really anything other than “I can’t explain why I believe 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.
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.
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.
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.
I see your point but I’m not sure I agree. Perhaps I’m just reluctant to think in those terms, but I don’t think that’s it. I’m not thinking of this in terms of PC, just in terms of usefulness.
I’m having trouble thinking up an analogy to explain my point; I’ll think about it and see if I can. If not, guess I need to start over.
EDIT: Actually, if we replace “intelligence” with a less loaded or emotive quality, say “height”, I think I’d still be inclined not to consider it useful. But as I say, I’ll have a think about this.
Just to add a note here: using the “height” example, suppose I told you that research has shown black people were on average shorter than white people. Then, it turns out, that my sample of “blacks” was from the area with the pigmy ethnicities, and if I excluded those from my definition of “blacks” then they were on average taller than white people. This is an extreme example, but here the statement “the mean height of black people is less than the mean height of white people” might be TRUE, but it won’t be USEFUL.
This is because your sample of black people contains within it many separate distributions for the same attribute, and simply taking their mean is not helpful. I’m merely saying that in an unhomogeneous group, averages are more likely to be misleading.
Sure, a set of equal numbers of mice and elephants are on average bigger than a set of guinea pigs, but that’s not a useful statement. And a generalisation from that particular sample to “short-haired animals are bigger than long-haired animals” would be outrightly unjustifiable from your data.
His point isn’t actually very good—“worms” isn’t a single category about which you could make many meaningful statements on average either (well, you try coming up with many non-vague true statements that universally apply to platyhelminths, polychaetes, annelids, nematodes...).
Linneaus coined the taxon vermes to hold any non-arthropod invertebrate. Later, cladistics came along and demolished the idea that it was ever a useful biological group.
Whereas “elephants” consists of just a handful of living species in two genera, so we shouldn’t be surprised that they have a lot in common—and even then, if you over-presume on those similarities when making theories, you’ll wind up wrong because you didn’t realize the ways in which they can differ.
I don’t see what difference this makes. If someone were to observe that “elephants” are generally speaking larger than “worms,” the fact that the two categories are extremely diverse would not preclude you from reasonably asking whether the difference was due to genetics.
The statement that “blacks” have lower IQs than “whites” is both meaningful and true.
I do not think you understand biology (either in the context of the race/IQ discussion or in general) well enough for it to be worth arguing with you further.
I disagree. What I’m doing is to take the exact criticisms made of categories like “blacks” and “whites” and applying them to other biological categories in order to show that there’s a double standard at work.
What exactly am I missing?
You’re missing the fact that people are arguing “but the groups are heterogeneous” when they mean “but the different means might be within a standard deviation of each other because single groups have a spread much wider than the difference between them”. That would apply when trying to ascertain whether, say, worms are larger than insects, but NOT when trying to ascertain whether worms are larger than elephants, because the difference between the largest and smallest worms is probably a lot bigger than the difference between the average size of a worm and the average size of an insect. On the other hand, the average size of an elephant is greater than the average size of a worm (any worm) by way more than the biggest worm is bigger than the smallest worm.
Suppose I got together all the worms and all the insects and measured their volume, and found the mean size of a worm and the mean size of an insect. And suppose (I have no idea what the truth is here, but it seems about as plausible as anything else) that I found that on average worms are smaller than insects. Would that be meaningful? I don’t think it would be useful to know.
How big an IQ gap are you saying exists? Are we talking as much as a standard deviation? Then maybe it would be important (if true). But if so, genetics isn’t the only possible explanation. I’d expect upbringing and class to be very important, as well as quality of public schools where they live, perhaps so much so that a genetic difference, if any, could be completely overwhelmed.
I don’t recall anyone arguing that in this thread, but this argument—to the extent it makes any sense at all—lacks merit.
Let’s take your analogy.
To make things simple, let’s assume that there are 100 species of worms and 100 species of insects and 1,000,000 individuals from each species. Let’s further assume that there is an animal known as the African Aardvark which eats both worms and insects (and has equal access to all), but eats only individuals greater than a certain size. Now suppose it is observed that the African Aardvark eats 75% insects and 25% worms, and we are presented with two hypotheses to explain this observation: (1) The African Aardvark likes the taste of insects better than that of worms; or (2) the African Aardvark prefers larger individuals to smaller individuals.
In evaluating which of the two hypotheses is correct, is it useful (or meaningful) to know that on average worms are smaller than insects? (And you can assume that the two groups each have a spread much wider than the difference between them.)
I’m not sure what this means. To be sure, genetics is not the only reason for the black/white iq gap. At the same time, there is no non-genetic explanation which (1) explains the gap; and (2) is not ridiculous.
I don’t quite understand how you didn’t just contradict yourself.
However, if you want a non-ridiculous, non-genetic explanation that explains the gap, try this one: while whites came to America with diverse socioeconomic backgrounds, the biggest group of black Americans today is descended from slaves, and until recently, there was extreme racial segregation. Hence, rather than just assimilating, they as a group have ended up forming a subculture. (If you don’t believe that, look at the world and try again.) Not all African Americans live in ghettos, but a greater percentage of them than of whites do. (Similarly, not all of them are stupid.) Among their subculture, poverty is high, teenage pregnancy is high, single mothers are common and violence is really common. In such an environment, they’re not likely to have highly-educated parents to nurture their intellectual development. Meanwhile, worldwide, large numbers of blacks live in Africa, which is 1. not a good place, and 2. full of primitive peoples, resulting not only in people (the common people) having less access to education, but also to cultural biases skewing IQ test readings.
Test that would distinguish between this theory and genetics: study IQ among African Americans born after the Civil Rights Movement to married couples whose income is above the poverty line and who don’t live in “bad neighborhoods”. If the gap disappears, it’s more likely environmental; if it doesn’t, that may indicate a genetic difference. But taking the raw IQ data doesn’t distinguish between these; it merely rules out the hypothesis that there are neither genetic nor environmental differences. Since there may even be a big enough population now to survey, someone should do it. The only problem I can think of here is that people who rise above poverty are already selected for intelligence (as well as persistence and work ethic).
Ah, now I see. I couldn’t think of a reason why it would matter in everyday life, because it’s more reliable to just ascertain whether or not people are actually intelligent by getting to know them, not using deeply flawed binary heuristics. However, now I see that you’re worried about whether people will end up assuming someone is being racist when they’re not. That’s fair. In the current political climate, it’s a big risk, for everyone. In that case, whether it’s genetic or environmental doesn’t really matter, though.
Respectfully, that explanation is ridiculous. If you wish to debate it with me further, please read my blog post and respond there.
Some one, or some organization. Anyway, the issue you are addressing is a slightly different one from what I raised. Basically you are making the “who cares” argument. But the reality is that our society cares very much, just like many Europeans in the middle ages cared very much about devotion to Christianity. Publicly pointing out the weaknesses in the Christian position could get you into serious trouble back then, just like pointing out the truth about race and intelligence can evoke a lot of hostility in modern day Western world.
What blog post?
http://fortaleza84.wordpress.com/2010/03/16/the-race-and-iq-question/
What you are missing is context—the context to understand what you are arguing about, and the limits of your analogy.
Additionally, you are missing the context needed to understand why the larger argument you’re making cannot effectively be made in those terms. I am no longer interested in discussing it with you.
Exactly what context? The history of subjugation and oppression on the basis of race?
Fundamentally, the point is that reasoning about race should be subject to the exact same standards as reasoning about any other kinds of categories.
In regular life, and even in science, people readily accept categories which are somewhat arbitrary; which are difficult to define around the edges; which contain pairs of elements more different than some pairs of elements, only one of which is contained in the category; and so on.
I think that for various emotional reasons, people tend to get wound up over the categories “black” and “white” but such considerations should not affect rationalists.
I agree with you here; I don’t think I’m getting wound up for emotional reasons, I just don’t think the category is necessarily a partiuclarly useful one, but for reasons I can’t really articulate. (I am not knowledgeable about statistics and the relevant terminology.)
But yes, there’s no reason to adopt new rules for reason on any topic—that wasn’t what I was arguing, and it’s clearly counter-rational.
We’ll be all right without formal terminology. I’m not at all sure what it is you’re trying to get at, and I’d be perfectly happy with you describing it as a metaphor, or an example, or really anything other than “I can’t explain why I believe this.”
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.