Why does IQ halve when people write about IQ
Robert Waldmann
So it turns out that extreme liberals have higher measured IQs than extreme conservatives and atheists have slightly higher IQs than biblical literalists.
What does this tell us ? Matthew Yglesias sent me to this and I learned that people will not accept the fact that not all stochastic variables are normally distributed.
I mean the extreme blind faith in the normal distribution is just not normal.
Razib Khan wrote
“Assume the “very conservative” and “very liberal” categories are normally distributed in intelligence. The mean is 95 and 106. What percentage of people within each category are going to have IQs of 130 and above?
Assume the “very conservative” and “very liberal” categories are normally distributed in intelligence. The mean is 95 and 106. What percentage of people within each category are going to have IQs of 130 and above?0.92% of “very conservative” individuals
5.48% of “very liberal” individuals
That’s like writing “Assume my grandmother has balls. Is she my grandfather? 100% of my grandmother is male.”
Anyone who knows anything about IQ scores knows that they are not normally distributed. IQ scores have a fat upper tail. In other words the calculation is total nonsense and has nothing to do with any intelligent estimate of the fractions of very liberal and very conservative people with IQs over 130.
I mean if one is going to make assumptions which are demonstrably false, one might as well assume the conclusion (yes economics profession I am thinking of us too).
I am very liberal and atheist and *I* think this post (to which Yglesias linked) is clearly total nonsense.
i know about the fat tail. it’s not total nonsense. i just think it’s ok to use the normal approximation around 2 standard deviation intervals. it isn’t total nonsense just because you say it’s so 🙂
fwiw, i constructed a quick & dirty calculation by using a function based on the terman data set. here are the ratios for normal vs. “real” number of IQ at a given std. a measure of fat tailing
2 std 1.06
2.5 std 1.29
3 std 2.1
3.5 std 4.99
4 std 15
about 2% of the pop has an IQ above 130, std. only ~0.1% of the population has IQs above 145, 3 std. so most of the high IQ population
is in the region where fat tailing is least significant.
I spent about fifteen years doing IQ testing with a population that was well below the norm. Specifics are not important. Yes, I had a Master’s degree and reasonably well trained on administration of the tests. At the time the usual instruments were the Wechsler Adult Scale and the Stnaford-Binet. One on one administration, all verbal subjects. After a few years of doing this work it occured to me that by test construction and standardization definition half the population was below the mean, at the time 100-110. Of course there’s a small degree of error in any achieved score. And then suddenly a disturbing realization began to set in. Get your self a copy of said tests, either one. Scan the questions and requirements of the sub-tests. Realize what it takes to score 100-110. Now go back to the realization that half of the population of the US can’t do any better than that. Now you can understand why we are in such deep shit.
You don’t have to have a high IQ to vote. You don’t have to understand even the most superficial aspects of important social and economic issues in order to vote. You don’t have to know anything in order to vote. You only have to know when to go and where to go to get to a voting machine, and even then someone else can lead you in. It’s a scarry realization, but it’s reality. Half the country is below average intelligence, by definition. And it’s real easy to score that level, but half the country can’t do it. Now you know why we have the Congressional representation that we do. Mitch McConnell was elected by a majority of the voters in Kentucky. That should settle the issue of IQ and its relationship to government.
Hey Raz, long time. Anyway, it doesn’t matter what the distribution of IQs are in the political spectrum, as there are many ideas that are so stupid, only intellectuals at the extremes believe them (Barry’s health care plan will lower costs, libertarians can build roads etc). Fundamentally, there might be more highly intelligent “liberals” (by which we mean leftists). Why are they liberal/leftist? Because they really really believe if you only put smart people in charge and give them lots and lots of power over our lives, we’ll have paradise. Typically they’re also products of their environments–only college-educated and above parents, friends, upper middle class or higher “elites” etc. Us possibly smart (1480 pre-norm SATs etc) “conservatives” (libertarian leaning) don’t buy this because we’ve either 1) lived with less-educated/less-intelligent folks, managed such people, or possibly realize that we don’t have all the answers and don’t want to give a bunch of power to supposedly smarter people so that they run our lives.
Anyone who knows anything about IQ scores knows that they are not normally distributed. IQ scores have a fat upper tail.
Is this true? According to Wikipedia,
“The modern IQ score is a mathematical transformation of a raw score on an IQ test, based on the rank of that score in a normalization sample. Modern scores are sometimes referred to as “deviation IQ”, while older method age-specific scores are referred to as ‘ratio IQ.’ …
“Since the publication of the Wechsler Adult Intelligence Scale (WAIS), almost all intelligence scales have adopted the normal distribution method of scoring. The use of the normal distribution scoring method makes the term ‘intelligence quotient’ an inaccurate description, mathematically speaking, of the intelligence measurement, but “I.Q.” still enjoys colloquial usage, and is used to describe all of the intelligence scales currently in use.”
This is Wikipedia, so this description may well be inaccurate, Can you point to more accurate information?
***Is this [IQ scores are not normally distributed] true? …***
Strictly speaking, probably it is true. For one thing IQ is a discrete distribution. The Normal distribution is continuous. For another, IQ is somewhat compressed on the low side. And IQ scores themselves aren’t really interval data, they are ordinal data. That is to say that they are ordered, IQ 81 is more than IQ 80. But the difference between, for example, 80 and 81 is not guaranteed to be the same as the difference between 81 and 82.
That said, IQ scores seem to be a pretty good approximation of normally distributed data for most purposes.
Guys this idea that IQ measures much of anything seems a liitle nuts (sorry). I used to believe that IQ meant something but I gew up and realized most IQ tests are not really testing how smart you are but how well you took tests. I’ve seen way to many people who are brilliant in certain areas but should not be allowed to balance a checkbook without assistance. I grew up around way to many farmers who couldn’t tell you which country Napoleon came from or who he was, but still raised great kids and produced a bumper crop year after year. I bet everyone here has had the same experience. So shoot me if I say I’m not impressed.
Then your link to Matt Y. who is probably one of the most numerically illiterate high-profile blogger I know of (left or right). He is a poster child for the argument that Harvard is not an ‘elite’ university in any sense of the word. I mostly blaime Harvard for this and I find that you can graduate from Harvard basically illiterate to be a tragedy. So much for higher education.
Lastly, if you truely start going down that path of IQ and human value you better get ready for the whirlwind of racial charges. There is distinct differences in group/race/national IQs that people really don’t want to delve into. We are not all made equal. The idea of someone with a higher IQ being able to get better results than people with lessor IQs (assuming IQ tests actually measure something) should take one look at are suppossidly intellegent national leadership, or Wall Street, or way to many of our colleges PhDs…
YMMV
Islam will change
Guys this idea that IQ measures much of anything seems a liitle nuts (sorry).
It’s only one of the strongest predictors of income and success in life. Spare us the faux-apologetic tone and the shitty anecdote-based arguments; you’re clearly familiar with the evidence and just plain don’t want to believe it.
Lastly, if you truely start going down that path of IQ and human value you better get ready for the whirlwind of racial charges.
Who said anything about human value? And what do you mean ‘get ready for’; the charges have been flying for thirty years. Anyone who wants to defend the truth in this area is just going to have to suck it up. As for being ‘made equal’: there is equality in ability (and few would seriously claim that all people are born with equal ability), and there is equality before the law, and equality before God; these are different claims.
bbartlog,
Define “success”.
High income does not necessarily mean high IQ. Ask any player in the NFL, NBA, heck even old Tiger. I would garner that my friends and neighbors, without the high income nor the high IQ, were very successful.
Lastly, yes I never believde all men are made equal *except as you mentioned before the law and God). And I do know the data. the fact that most of Africa runs 20 IQ points below the US. BUt if you bring the data up, or even mention doing research on this, you will be called a rascist in many quarters. I believe a College President (Harvard – forgot the guys name) got run out of his position becuase he had the temerity to suggest that men at the right side of the distribution curve may be more numerous than women in the field of mathematics. Basically when you start delving into IQ it very un PC and the left and right will attack you mercessly…and it doesn’t matter if your correct or not.
We as a people have no problem with noticing differences in athletic ability in groups but bring that up for intellectual abilities and you will get hanged…just life.
And you have to define success – and it can’t be determined by income, Paris Hilton does very well on that scale…
Islam will change
I don’t have the research at hand, but I believe IQ and success in school performance is most strongly correlated. So whatever schools actually teach, part of which is content, part of which is learning style and how that relates to school presentation of material, and part of which is ‘attitude’ to learning in a loose sort of way is more relevant than to life.
Now arguing how schooling relates to life is also well studied, but again also tends to bypass exogenous factors.
Schools are tough places to research as well. New ways had to be devised to get at patterns, coming more from anthropology than psychology or sociology, as classrooms are not labs and are well protected from prying by various constituencies (parents for one).
Use of IQ score ‘totals’ tends to be for rough approximation of diagnostic categories (developmental delay for one) of intellectual functions and of learning modalities, and the total score is rarely used anymore as a guide for most students, but the 12 to 14 tests that make up the Stanford Binet are used to diagnose patterns of how kids learn.
*** For one thing IQ is a discrete distribution. The Normal distribution is continuous. ***
Well, yeah, but that’s not the point that Robert is making.
*** That said, IQ scores seem to be a pretty good approximation of normally distributed data for most purposes. ***
According to the Wikipedia entry, the scores are *defined to be* normalized. Deviations from normality would come from errors in the normalization sample.
*** That is to say that they are ordered, IQ 81 is more than IQ 80. But the difference between, for example, 80 and 81 is not guaranteed to be the same as the difference between 81 and 82. ***
We wouldn’t expect this property of a normalized anything, since the normal distribution isn’t linear. Given a normalized definition, we would expect to see the difference between 80 and 81, however, be equal to (in some sense) the difference between 119 and 120.
Leaving IQ scores aside what amuses me is that people are stuck at the correlation and unwilling to jump forward to the causation.
To me the answer is pretty easy: Enlightenment = smart, Reaction = dumb. Over the last few centuries each generation has had to decide whether they were going to embrace fresh, new thinking or stick to old ways, and in the process intelligence, at least the kind of intelligence scored in IQ tests got tied to progress and hence ultimately to those movements identified as Liberal.
Biblical irrerrancy and literalism simply does not survive a critical reading of the text coupled with a historical understanding of who decided which parts of the final work were Canonical and which were Aprocryphal. And then you have to factor in issues of textual transmission and translation. I suppose you could embrace a doctrine that holds that every decision about text and doctrine made by the Fathers of the Church at the Four Great Councils and every translation decision by King James and his advisors in translating the Bible was divinely inspired, but frankly you have to be a little dim to do so.
This doesn’t mean religious belief is moronic, just that anyone who thinks his modern English Bible is somehow a word for word transcription from God is likely someone not quite bright enough to have taken advantage of his educational opportunities. It is not a crazy stretch to hold that flexibility and originality in thought is tied to progress in learning which in turn has been associated with Liberalism (we call them the Liberal Arts after all). Smarter people are just more open to new structures of thought and more willing to set aside the old, why wouldn’t we expect that to lead to some selection bias in partisan id that in turn shows up in a statistically valid way on IQ tests?
Bruce,
You really shouldn’t bait Cantab. Its not very nice…
🙂
Islam will change
An IQ score represents a response to test questions. The test question in the case of both the Stanford-Binet and the Wechsler scale evolved out of a lengthy process of standardization. Standardization means that a given population was pre-defined for the purpose of both the construction of the test and its application and usefullness. That is that the test developeprs had to limit their goal concerning who would be measured by the test. That is due to the fact that the questions must relate to the individual’s life experiences. What else could the individual be asked to know about. it would be a lot simpler if brain wave patterns could be shown to be indicative of intelligence. It hasn’t yet been.
So what does the IQ test measure if not brain activity which may or may not be indicative of intelligence? The field of psychological testing and measurement long ago decided that the best indication of intellect was one’s ability to learn about one’s environment. I don’t mean you neighborhood. How much information has the individual absorbed and retained from his’her daily life experiences? That’s the goal of the test. The assumption is that the more absorbtion and retention, the more intelligent. Of course there are other opperative factors in such a process. Differences in education, nutrition, social environment, etc will all impinge upon one’s absorbtion and retention of information and, therefore, effect one’s performance on such tests. When the test goes through the long and arduous process of standardization these differences in life experiences and opportunities is taken into account. At least the test makers try to do so, but it’s not fool proof. So our measrument of intellect is affected by those other factors. Intelligence is not measureable in any other fashion.
This should not make the results of IQ testing invalid nor useless. The problems with the IQ results is more a matter of how such information is used and understood. I say it in that order because unfortunately that information is often used before it is fully understood and by people who have limited understanding of the testing and measurement process. It’s a test of learning. It is subject to error. On the whole it does a pretty good job of distinguishing between people of similar social backgrounds and experiences. Should IQ be used to make significant decisions about an individual’s oppotunities? Not at all. The tests were not developed for that purpose.
One additional and salient point. If you belong to Mensa and think that you’re special you’re an ass. If you think that you know your IQ score and that it gives you certain rights and priviledges over those who have lower scores you’re yet a bigger ass and an ignorant fool.
Buff,
Bruce can’t bait me. Remember that I live in Cambridge Massachusetts which is one of the premier cities of enlightenment in the United State while Bruce lives I believe somewhere in Little Hope California.
Also, the way the liberals work the problem is they say to be enlightened is good and if you follow us on points A, B, and C we will label you an enlightened one. But then you’ve let other people dictate your beliefs with threats of peer pressure. That not enlightenment and most liberal that agree with a checklist are anything but enlightened.
***According to the Wikipedia entry, the scores are *defined to be* normalized. Deviations from normality would come from errors in the normalization sample.***
I’m no expert on this, but I believe that the old way of doing things (Ratio IQ) assigned a mental age. Unintelligent people had mental ages lower — maybe substantially lower — than their calendar ages. IQ was computed as mental age divided by calendar age. The newer — distribution method — computes IQ directly based on the assumption that IQ is normally distributed and given the mean value for the individual’s age group. I don’t think either I or Wikipedia are all that clear. Try this link. http://www.iqcomparisonsite.com/IQBasics.aspx
Anyway, the important point here is that the distribution method computation assumes that IQs distribute normally, it doesn’t dictate that they distribute normally.
I could be wrong. As I said, I’m no expert.
***Given a normalized definition, we would expect to see the difference between 80 and 81, however, be equal to (in some sense) the difference between 119 and 120***
There is a catagorization scheme for data by Stevens in 1946. Ordinal and Interval are two of his data types. Although it might look like IQ is Interval data (evenly spaced) it’s quite clear that the inputs are ordinal — ordered, but not necessarily evenly spaced. It might be possible to somehow convert ordinal data to interval data in some cases, but I doubt this is one of them. As with distribution method IQs, a normal distribution seems to be assumed, not dictated. Philosophically, I think this is erroneous, but pragmatically, it may be good enough for government work.
Again, I’m no expert.
http://en.wikipedia.org/wiki/Level_of_measurement
=============================
It’s common practice to assume normal distributions even for data that is obviously not normally distributed. IQ looks to me to be far closer to normality than a lot of stuff that folks are whipping out Standard Deviations, etc for.
It would be nice to have a wicked high IQ but you have to live with what nature gives you.
*** The newer — distribution method — computes IQ directly based on the assumption that IQ is normally distributed and given the mean value for the individual’s age group. ***
Yes, the designers of the test are assuming that some underlying parametric property of human beings is distributed normally. As I read the description, the designers give the test to a random sample, and correlate the raw scores to an assumed random distribution. Presumably the raw scores are not distributed normally, so in cases where one raw score value (or small range) is over-represented, it’s mapped to a relatively narrower range of the normal distribution.
The point being that IQ (the measurement) cannot be anything but normally distributed, and because IQ is so defined we cannot infer anything from IQ about the distribution of “intelligence” (the underlying parameter).
Hey, Cantab, that’s the first comment that you’ve made that I couldn’t find any fault with. What is the world coming to when we agree on a concept?
***The point being that IQ (the measurement) cannot be anything but normally distributed, and because IQ is so defined***
You’re free to believe that. I’m pretty sure that reality is that the raw IQ test results are input to a transformation that is supposed to result in a normal distribution. If the raw IQ test results don’t have whatever distribution is assumed for them (and this being the real world, they probably won’t), the result after transformation will not be Gaussian.
***we cannot infer anything from IQ about the distribution of “intelligence” (the underlying parameter).***
Not wrong exactly, but I think you missed the point. Robert and Razib are discussing a finding that there is an 11 IQ point difference between the IQs of very liberal and very conservative individuals. That’s the comparison of the means of two different populations. It’s permissable and legitimate to compare two different normally distributed populations if you want to and have any fairth in the underlying data and the transformations performed on it.
*** I’m pretty sure that reality is that the raw IQ test results are input to a transformation that is supposed to result in a normal distribution. If the raw IQ test results don’t have whatever distribution is assumed for them (and this being the real world, they probably won’t), the result after transformation will not be Gaussian. ***
I would imagine that the distribution of the raw scores is *measured* (from a sample), not assumed. Of course, there are all sorts of biases and problems inherent in this procedure, but again I would imagine that there are a few competent statisticians in the mix.
*** Robert and Razib are discussing a finding… ***
I’m not discussing R&R’s findings; I more or less agree with Robert. I’m curious as to the accuracy of Robert’s statement that I originally mentioned, ” IQ scores … are not normally distributed. IQ scores have a fat upper tail.” That doesn’t seem correct.
In other words, it appears that IQ scores are *by definition* normally distributed, to the limits of error in measuring the sample distribution.
***IQ scores have a fat upper tail.” That doesn’t seem correct.***
You might be right. Urban legend says that IQ scores have way to many outliers = approach zero slower than exponentially (and don’t push me on that, I barely understood it when I was younger and smarter) = fat tails. But it’s possible that is a hangover from the days of ratio method IQ scores. It appears that ratio method scoring resulted in a distribution with a Gaussian looking middle, but genuine fat tails with too many outliers.
OTOH, it may just be that there is no way to coerce distribution method IQ data into a perfect fit to a Gaussian curve and that the best possible result is near Gaussian with fat tails.
Jack,
I think it would be a fun to have an IO of 180. So our record is intact, we still don’t agree on anything.
One thing about the “lefitst/intelligent” argument that gets missed I think is what gets you defined as a leftist in todays political environment. Another is the matter that a person who is intellectually curious, studies matters and sees the fallacy of many of the rights positions often times is described as someone who was a “leftist” first and has been indoctrinated into an anti freedom cult of closet Stalinists that is self perpetuating at universities.
Today your likely to be labeled a leftist if you “believe” in evolution, question the authenticity of biblical stories, truly consider that man is in fact negatively affecting our environment with our continued output of hydrocarbons and wonder if war is worth the enormous costs. This would place many 60s and 70s conservatives way to the left of the spectrum in the minds of too many Americans today.
Just because you score high on an IQ test doesnt mean you have the willingness to explore the proper questions which are relevant to our day. I work with many high IQ people who are well versed in many subjects but absolutely lack intellectual curiosity about too many important ideas. They have been convinced by Fox News that they already KNOW all the answers to the relevant questions. They cling to 18th century notions of America, 1st century notions of the bible and are lovin’ them some 21st century notions of how to kill people with turbans.
Cantab,
That’s a rather peculiar response, but consistent with your past performance, which is what psychological measurement is often all about. Note that I haven’t stated any opinion regarding what level of IQ it might be fun to be able to demonstrate. And that’s another important point. Having the high IQ is only a measure of a brief performace. Being able to demonstrate behavior that would be expected to coincide with a high IQ is another story. One that not many do consistently and you seem not to do at all.
One other thing. If we were to judge the intelligence of the average conservative by extrapolating from Cantab’s demonstrated behavior on this blog then we would have to conclude that Khan has a point, though I would have generally agree with Waldman’s analysis.
Jack,
It’s only a peculiar response to you and I believe everyone else here would find it a kick to have their same inner core beliefs but add the processing power of a 180 IQ brain. I define intellect as a combination of character and processing power, character is your soul and processing power represented in IQ stands alone. For myself I think I’m way above average in the former and about average in the latter. I have no idea how high your IQ is but since you’re a black hearted misanthrope you potential for intellect is pretty low.
Here is an example. You said the following above:
If you think that you know your IQ score and that it gives you certain rights and privileges over those who have lower scores you’re yet a bigger ass and an ignorant fool.
This statement is idiotic. Rdan already told us that high IQ is a good predictor educational achievement. IQ does not give you any “rights or privileges” in any field nor does athletic ability gives you the “rights or privileges” to be a professional basketball player. But some people are genetically superior otherwise Danny Devito would have the same chance become a professional basketball player as Michael Jordon. And Joe the Plumber would have the same chance of winning the Nobel Prize as Einstein. So IQ in inself is an absolute good and gift and not something to be sneered at.
So the bottom line is your dependence on ideology and lack of character forces you say one stupid thing after another. And then you blow your top when I point it out to you. Go figure. And by the way, you won’t see me lining up with conseratives on religion, choice, or the two types of music: country, and western.
Jack,
It’s only a peculiar response to you and I believe everyone else here would find it a kick to have their same inner core beliefs but add the processing power of a 180 IQ brain. I define intellect as a combination of character and processing power, character is your soul and processing power represented in IQ stands alone. For myself I think I’m way above average in the former and about average in the latter. I have no idea how high your IQ is but since you’re a black hearted misanthrope you potential for intellect is pretty low.
Here is an example. You said the following above:
If you think that you know your IQ score and that it gives you certain rights and privileges over those who have lower scores you’re yet a bigger ass and an ignorant fool.
This statement is idiotic. Rdan already told us that high IQ is a good predictor educational achievement. IQ does not give you any “rights or privileges” in any field nor does athletic ability gives you the “rights or privileges” to be a professional basketball player. But some people are genetically superior otherwise Danny Devito would have the same chance to have been a professional basketball player as Michael Jordon. And Joe the Plumber would have the same chance of winning the Nobel Prize as Einstein did. So IQ in inself is an absolute good and gift and not something to be sneered at.
So the bottom line is your dependence on ideology and lack of character forces you say one stupid thing after another. And then you blow your top when I point it out to you. Go figure. And by the way, you won’t see me lining up with conseratives on religion, choice, or the two types of music: country, and western.
Cantab,
Your intellectual and social immaturity speaks for itself. You are self evident and none too convincing as you continuously try desperately to reinterpret waht I and others have to say in order to either defend yourself or criticize what has not been suggested.
Jack,
Get lost. You cant hang with me.
Cantab
Jack,
Get lost. You cant hang with me.
Yet another concrete example of your immaturity of mind and the limitation of your ability to discuss anything with other than simplistic slogans and canned talking points. You sem to have no original ideas.
buffpilot, if you “knew” the data, you wouldn’t cite demonstrably untrue things about it.
Cantab last I heard being a yahoo in a bar in Cambridge didn’t qualify you for Academic honors. Plus I have two degrees from Berkeley which apart from being a leftist hell-hole also has a certain reputation for academic quality, particularly in the fields in which I studied where the two grad departments (Comp Lit and History) that I studied in consistently scored in the top two in the country. Plus you goof if you had any reading comprehension and memory whatsoever you would know I currently live north of Seattle. Not exactly the least wired city in the country.
Plus I doubt you could identify the Enlightenment with a blowtorch and the Encyclopedia Britannica opened to the right page.
I have a wicked high IQ (according to that childhood Stanford-Binet test), but have to live with what nature brought me, in this case Cantab. Man that tradeoff sucks.
Cantab you are here by sufferance. Want to be vanished? Keep being a jerk.
You are the very last person in the world to be telling anyone at AB to “get lost”, given that your formal banning has never in fact been lifted. And no the asymmetry doesn’t bother me, I don’t have to be on my best behavior, you do.
Bruce,
You don’t matter here. You really ought to take your game to the daily kos where they’re more like you. Take jack with you.
Bruce,
I don’t hang out in bars in Cambridge, but I do take take classes from time to time from one of our better local colleges and even cobbled enough of them together to get a graduate certificate that adds window dressing to my masters degree. So I both live in an acedemic town and take advantage of the opportunities it offers. So like always you’re wrong again.
The problem with you is that you have a little town inferiority complex that you carry through life as a chip on your shoulder. Russians call this being from the villiage. You’re not a liberal minded person inside rather you’re that person with a chip on his shoulder and this does not go away when you join the leftwing and spout their ideology.
Bruce,
Another trashy post from you.
Jack,
You’re projecting yourself again. It was you resorting to slogans with your attack on the IQ measure. And calling people proud of their high IQ scores asses was pulled from the cliche jar.
It is truly amazing that you out do yourself on the scale of ignorant and baseless statement. I did not attack the IQ measure. I instead provided a reasonable laymen’s explanation of the score. I did note that any one who goes around with a self satisfied attitude based on a simple measure of one time performance is a self satisfied fool. Given that most measurements of IQ are done in childhood, and with less than the best measurement scales, most people’s belief of what their own score may be is usually subject to significant error. On the other hand, your commentary is indicative of a limited ability to see beyond your own beliefs about the world you live in. An inability to accept alternative explanations and ideas is indicative of limited intellectual functioning. Voila!!
The Cantanabrian.
Though I suspect that you may be a reasonably intelligent peerson who is only suffering a significant delay of social development. Your performance on AB is at best facetious and never informative. It is often very obvious that you have no intent other than to obfuscate the discussions here through misrepresentation of real events and actual comments from others.
Jack,
I’m still disappointed that you did not make good on your histrionic temper tantrum when you said you were going to leave this site. You sent your emails, fired your silver bullet, but failed. So why are you still here?
IQs can be done at any age and were they are predictors of academic performance they not substitutes for it. When a high school student applies to college he or she generally sends along transcripts, SAT scores, an essay, and other records of achievement or indicators that the student would contribute to a college or university. I’ve never heard of a college asking for an IQ score. Anyway, academic achievement is based on training and a person with low academic achievement may be highly intelligent and more intelligent then someone that’s earned a doctorate from a university. I don’t have a problem with them proving it by joining a group like Mensa, and I don’t see the basis for calling them asses because they are proud to be in an exclusive group. Do you really think full professors at universities don’t see themselves as the elite. How about the editorial opinion writers at the New York Times.
The notion that IQ is just another stochastic variable could hardly be more groundless. It’s not as though IQ is measuring something that has a clear, independent meaning, such as height or weight. It’s a manufactured measurement, and its distributions are basically a logical consequence of the conventions assumed in the definition of the measurement.
More here:
http://scienceblogs.com/gnxp/2010/03/intelligence_politics_religion.php#comment-2327920
I’d say it’s total nonsense to make an assumption which you know to be false. It didn’t seem to be very hard to use the actual distribution. The only way you can argue that it is an OK approximation is to do the correct calculation and note it isn’t hugely different. Therefore nothing is gained by considering the normal. Making a false assumption which is not needed is not excusable.
You are still assuming that the fraction of atheists with IQ’s above say 130 is equal to the fraction in the general population with IQ’s above 230 the average IQ among atheists.
In your original post, you assumed, not only, that IQ is distributed normally but that it is additively seperable in atheism and other factors. Just as you think it is OK to assume that a random variable which is definitely not normally distributed is normally distributed, you think it is OK to assume that random variables can be decomposed into an expected value based on an observed variable plus a random variable which is independent of that observed variable. This is valid if, for example, all random variables are jointly normal. It is true in other cases as well. It is generally false.
The only way to determine what fraction of atheists have IQs over 130 without making assumptions which are probably false is, uhm, well to ask people if they are atheists and give them IQ tests and count the fraction who score over 130. The raw data used to caculate the average IQ of atheists can be used this way. If the sample size of atheists is so small that this approach does not give usefully precise estimates of the fraction of atheists with IQs over 130, then a usefully precise answer is not in the data set. That is not a reason to pretend that it is based on assumptions which are made because then you can get conclusions.
So what am I so upset about ? Well I think a reasonable case can be made that the economy was destroyed in large part by the Gaussian Copula, that is the assumption that all continuous random variables are jointly normal.
“The ratios” does not explain the calculation. Is that the ratio of an estimate of the empirical density to the normal density or of the fraction say 3 standard deviations above the mean to 1-Phi(1.3).
Is “the normal” the normal density, the cumulative normal or one minus the cumulative normal. Which do you mean ? I take it from your last sentence that it is not the normal density or the cumulative normal. “normal” is a technical term in statistics. It has two definitions. You are using neither.
Oh a question for information. What score is given to people who answer all of the questions correctly ? How about for an IQ test with 20 questions ?
Look up thread. Razib (you know the guy who assumed normality) notes that IQ has a fat upper tail. One could take measured IQ then apply a monotonic function so the resulting variable is normally distributed. However, this is not what is done. Scores are normalized by adding a constant and multiplying by a constant to set the mean and the standard deviation. They are not transformed so that they are normal.
It is certainly possible to coerce any variable in any sample to have any distribution which is desired. You have N observations of a test score x. if x is the mth score from the bottom make f(x) = (M-1)/N. Make g(f(x)) = invPhi(f(x)) where invPhi is the inverse of the cumulative normal. g(f(x)) is normally distributed.
I don’t think Yglesias is numerically illiterate. As far as I can tell, he handles numbers very well. It is true that he types homonyms. That would be illiterate maybe, but not innumerate.
well bbartlog, IQ could be a better indicator of class background than the indicators used as controls. It might just be a symptom, not a measurement of the root cause of income. That is, given the data, it is possible that a better predictor would drive the apparent effect of IQ to zero and that this better indicator is clearly not related to cognative ability.
I’m really just saying that evidence can’t ever amount to absolute proof of a really interesting claim. Note I didn’t say “in the human sciences.” This is also true in the narural sciences.