HTB:
If we’re talking about the correlation factor for a linear regression with 400 data points, then .58 is an indication of pretty high correlation. Check your statistics book.
Doesn’t say anything about the “non-std” IQ test, but don’t be fooled by what might appear to be a relatively low correlation factor.
Around here? A lot, I suspect.
Bush’s SAT scores are not all that impressive. Nor is the IQ estimate based on those scores. They are better than average, but certainly not awe-inspiring. Many of the people I know, and certainly many people on this board, could boast of higher scores. Heck, if these numbers are taken as an accurate reflection of intelligence then I myself must be much smarter than Bush.
But as I said before, I don’t think Bush is an idiot or anything. He’s probably of somewhat better than average intelligence, and certainly not below average. It’s just unfortunate that simply being of at least average intelligence isn’t all it takes to be a good president.
** Hentor the Barbarian** – First, the sample isn’t that small. Second, while a sample of 400 would not be as accurate as a sample of 4,000 there probably isn’t that much difference in the results. The biggest difference is that the occasional individual anomalies have less opportunity to be averaged out.
But more important - not only is +.58 a pretty high correlation, that correlation was reported as “spuriously low” in the quote you provided from the link.
The restricted range of “this sample” was also stated in the link as --–
“In this group: Otis Gamma mean = 117, SD = 7.2; SAT mean = 980, SD = 126. – That is, these were all college students with a mean IQ of 117 with a standard deviation of only 7.2! The standard deviation in the overall population is 15.6. Yet they use the “standard error of estimate” for the SAT total score which was 102 and “the standard error of estimate” for the Otis which was 5.8.
Hence we have the quote you refer to ----
“This correlation of 0.58 gives a * spuriously low* [My emphasis] impression of the correlation between the SAT and the Otis due to restriction in the range of ability in this sample.”
The posters on this board, whatever their take on the issue presented, have in general put forth interesting arguments.
There has been relatively little of the sort of “argument by assertion” that one often encounters on BBs, and people have generally striven to back up their formulations by refererring to the record, such as it is. In short, I would be hesitant to characterize most of those who have posted here as “stupid”. And, in all fairness, I have seen lots of weapons-grade “unintelligent” on other boards. I have a particular fondness for one fellow on another BB who argued for some proposition or other pertaining to the Middle East, and was then confronted with a link to an article by Johns Hopkins Prof. Fouad Ajami, certainly one of the leading Muslim intellectuals in the western world, which ran entirely contrary to his position. This fellow responded by posting that Ajami was a “moron.”
So in any event, even given the generally high level of discourse here, I have noted that some of the people complaining about Bush’s poor syntax and weak communications skills have themselves tripped over the intricacies of the language, and/or fallen prey to common spelling errors… as we all do from time to time. To rehash just a few here:
Do these minor errors betoken stupidity? I suggest not. Might they, if more egregious and present in profusion? Perhaps.
Much more difficult, of course, to speak extemporaneously, often in a hostile or at least adversarial environment, than to compose posts in the relative luxury of one’s home.
Bush isn’t Daniel Webster, but then again very few people in this age really are. In my view he is an effective communicator, though certainly not one who reaches heights of rhetorical brilliance. I am hesitant to extrapolate too much about his intelligence from those circumstances in and of themselves. His academic record and test scores seem to speak to the issue more directly and in my view do suggest that Bush is a man of far above average intelligence.
HTB –
In addition – not only is the correlation “spuriously low” – the actual correlation for the pre-1994 test to the WAIS is +.80. This is higher than some IQ tests have with each other as shown in the quote below. This quote is concerning the pre-1994 SAT. Note the correlations given –
Here’s the link -
http://members.cox.net/sidelock/pages/Telicom090299.html
I would maintain that there is a huge difference between the grammatical errors you cited and the incredible flubs that Bush spews even in his carefully planned and rehearsed speeches. And that’s not just because I’m the author of one of those flubs. I write about as fast as I can type on these boards, and my grammatical errors are much more like speech flubs than anything else, as I suspect is the case with the others. My feeling is, you want perfect grammar and spelling from me, show me some cash. So long as I’m doing this recreationally, I’m not gonna sweat the small stuff. Huge difference also between casually posting to a board and speaking as President of the USA.
Much more difficult, of course, to speak extemporaneously, often in a hostile or at least adversarial environment, than to compose posts in the relative luxury of one’s home.
Actually, I’m sure Bush has people to help him prep his speeches, and most importantly, who write his speeches for him. Who writes your posts for you?
**I am hesitant to extrapolate too much about his intelligence from those circumstances in and of themselves. His academic record and test scores seem to speak to the issue more directly and in my view do suggest that Bush is a man of far above average intelligence. **
Piffle. All of the assertions of the ‘Bush smart’ crew on this thread are to the effect that we are to ignore the clearly evident words and deeds of Bush and focus instead on his credentials or on his “achievements” as a politician. Whenever one is being asked to ignore ones own direct observations in favor of what is essentially a paper trail, one should ALWAYS be suspicious. And I am.
Stupid is as stupid does. Anybody catch Letterman Monday night? They showed a clip of Bush talking about the Department of Homeland Security on September 10:
If he in fact is not an idiot, he is doing his best to hide it.
John Mace, how embarrassing that you would be smug while simultaneously revealing that you do not know what you are talking about.
“The correlation factor from a linear regression?” You mean the coefficient, or the beta weight, for the Otis IQ term in the regression equation? I have 12 stats books sitting next to me. Which book would I check that would tell me that .58 is a “pretty high correlation?” In some circumstances, that might be true, but here, where you are attempting to suggest that you can determine the relationship between an unrelated data point (Bush’s SAT) and a predicted y value of his purported IQ, this is wholly insufficient. A correlation of .58 means that only about 36% of the variance in Otis scores is explained by SAT scores, and that roughly two-thirds is explained by other factors – a huge amount of error for the application you are trying to put the equation to. Perhaps if you or Tigers2B1 could show me the 95% confidence interval for Bush’s score, that would help things out.
For this purpose, the sample is very small, particularly because it is so unrepresentative of the populations about which you are trying to make conclusions. If you sampled 4,000 people, your results would be exceptionally different. You speak of occasional anomalies, and then go on to talk about the existent range restriction in the sample. I am flummoxed.
Exactly why this data sample is entirely unable to do anything like what you are trying to do with it, and why I cannot fathom how you could refer to this as “occasional anomalies.” The entire sample is anomalous. Its distribution of scores is very different from the population. Further, given that this is the only data with Otis scores and SAT scores, the correlation is what it is. Whether or not it is “spurious” is speculative based on how we expect distributions to act when they are not skewed. You are saying that this sample is not even sufficient to tell us the true correlation between scores in this sample – how can you turn around and argue that it is sufficient for determining the IQ score of an unrelated person at a different time and place with a different SAT score?
Don’t be fooled by it? I am trying not to be. It is what it is. See above.
From Tigers2B1
And? This has no information regarding the correlation between the Otis and the SAT, which is the issue at hand.
Replication is hugely important in making any conclusions regarding relationships between variables. Yes, inferential statistics help to account for individual differences, but they are still subject to error, especially when the error is inflated by the nature of the sample. Furthermore, even when testing someone directly using the WAIS, I still must give the error band around their own score. So, Tigers2B1 or John Mace, or Sam Stone, since you can give me the score of 129 for Bush’s IQ, surely you can give me the error bands around that score.
I get it. The board scores, the college and grad school grades, that all means nothing. We can just throw all of that away because a bunch of visceral Bush-haters want to portray a Yale undergrad and Harvard Business School grad as an idiot. That’s fine.
I think of a Polish gentleman named Karol Wojtyla, whom some people believe to be Catholic. I love the guy. And I’m absolutely certain he’s Jewish. Ignore that past history and that stuff about the College of Cardinals and their choice of a pope. I mean, there are records of it, but that’s just a paper trail, isn’t it? Let’s consider the objective evidence. Mr. Wojtyla sometimes wears a head covering that looks suspciously like a yarmulke. In his public pronouncements he has articulated a decided eceumenicism and warm feelings to those of the Jewish faith. He grew up in Wadowice, which had a heavily Jewish population, in pre-WWII Poland, which itself had a prominent Jewish minority. He was not happy when Bashar Assad launched into an anti-Jewish tirade in his presence. The first audience he gave upon stepping into the proverbial shoes of the fisherman was to a Jewish guy-- his closest childhood friend.
It’s as simple as that. Bush dumb; Pope Jewish.
Straw man irrelevant.
Unfortunately the Pope hasnt been showing signs of his jewishness… so we didnt know about his jewish blood before you told us. 
Now if a guy with extremely high SAT and IQ starts attacking other countries…get bogged in Iraq… doesnt try diplomacy… gets ordered around by his aides… shows lack of curiosity… speaks badly even when the speeches are written for him… thinks creationism is scientific… keeps saying silly quotes and has over 2/3 of the world pissed at him… etc… etc… Do you call him stupid or a genius ? If you still think we call him stupid because we hate him… its your view on it. We hate 'em AND think he is stupid. (I think he is average to low actually… but point made).
HTB –
“unrepresentative of the population”?? Really? How so. Isn’t the “population” those who take SAT tests? The “population” who plans to attend college? And better – explain to me how this invalidates whatever you seem to think it invalidates – since I’m still not sure what you think that is specifically.
The “results would be exceptionally different” ?? “Exceptionally different?” Really? How do you arrive at your unsupported conclusion? I really suspect that you don’t know what you’re talking about. If, in fact, you “have 12 stats books sitting next to [you]” – now is the time to pick one or two up and explain why the results would be “exceptionally different.” Look - if you take a sample of 400 SAT scores or 400 IQ scores you’re going to get a curve very similar to the one you would with a sample of 4,000. Even the numerical results would probably only be different when you extend out a couple of decimal places. In any event – I have to call you on your assertion that the results would be “exceptionally different.” That’s simply not the case – and its contrary to common sense here –
Please HTB – Look – I understand you don’t like Bush. And that’s fine. But please make real world requests! This isn’t an IQ score from an actual standardized IQ test - And who said that it was? So why are you asking for the margin of error as if there is an industry out there that converts SAT to IQ? — what’s your point? This has always been presented for what it is – Bush made a 1206 on his SAT – pre-1994 SAT scores correlate with IQ results – which indicates an IQ of about 129. Where did you get the notation there would be “error bands” out there?
Well this is just getting silly. I mean – aren’t you the same guy who was using the +.58 correlation when the quote you provided expressly stated that it was “spuriously low?” Now I have to ask you whether YOU read the linked information. The linked summary indicates that the “The designers of the SAT benchmarked it against the Otis” Yet, I have a feeling that’s not going to be satisfactory. And so - taking measures again your next objection — No – I’m not going to go find the primary sources or the raw numbers for you– the link provided is heavily footnoted and you can do that for yourself if you’re inclined.
Wow Tiger2B1, have you had any education or training in statistics whatsoever?
Yes. Presuming that the IQ scores of the Otis are supposed to be normally distributed, they should have a mean of 100. This sample is a full standard deviation above the mean. They are therefore more extreme than most people, and unrepresentative of the population you are trying to extend the conclusions to (everybody else, apparently). Many common inferential statistics are based on a normal distribution of scores, which is violated here. Furthermore, the more atypical a sample is, the less external validity the conclusions drawn from that sample have. Because they are not normally distributed, you can hardly make conclusions about the relationships between variables within the study, let alone extend results to other samples (such as to George Bush). What this invalidates is the notion that you can use the scores of these guys to determine what the scores of other guys would be. You yourself have highlighted the problem of range restriction in this sample. Yet, you are now asking how this sample is unrepresentative. I can only conclude that you do not know what these terms mean. “Range restriction” means that the range between the lowest and highest scores here is restricted, or smaller than, it should be compared to the larger population. “Extreme” means that the sample tends toward one or the other end of the distribution more than you’d expect.
Common sense must mean something very different to you. Again, you have cited evidence that this sample is atypical: the mean is greater and the standard deviation is smaller than should be expected for these scores. You haven’t just taken 400 IQ scores and SAT scores, you’ve taken 400 people who walked into a Georgia technical institution, with IQ scores higher than the mean. By sampling 10 times as many people, you are going to go a long way to making the distribution look a little more like the normal distribution. Your range will be less restricted, and less extreme.
As far as books, I will have to go back to the rudiments for you, but let’s choose McCall’s (1990) Fundamental Statistics for Behavioral Sciences, 5th ed..
Error bands are not determined by industry. It would be an interesting and humorous excursion to understand where you got this idea (as a hint, it sounds as ludicrous as saying that “there is no industry to provide the mean of the Otis scores” in the study you cite). From the data, you should be able to determine the confidence interval (commonly taken as 95%) that your estimate falls within a certain range. Given the descriptive stats of the sample, those putting forth a conversion should be able to provide confidence intervals for their estimates. The CI around which WAIS and WISC scores are banded are based upon normative samples, not by a captain of industry. You should be able to give that CI, or you should drop your assertion that Bush’s IQ score is 129.
You made it silly long ago. There is no transitive property for correlations. You cannot assume that because X correlates with Y at r1 and Y correlates with Z at r2 that X will correlate with Z in any way. I don’t know what the assertion that the SAT was “benchmarked against the Otis” is. If you are unwilling to explain it, why provide it? Surely you could just provide the correlations that were part of that benchmarking process? You pre-empt because you are mindlessly reading from someone else’s (apparently dubious) site, without understanding a thing about what you are saying.
Look, this is the problem. If I sample five grocery stores in an affluent section of Georgia in 1960, and find how peach prices are correlated with egg prices, I still have no way of saying that the price of a peach in Hawaii is going to be Y given the value of X for eggs there. My sample just is not capable of doing that well. I invite any others with any statistical knowledge to try to help Tigers2B1, John Mace or Sam Stone understand this.
The “paper trail” shows that Bush Jr. has achieved some above-average academic credentials. Point taken – although I’m willing to consider that his family connections had the potential to aid him somewhat in this area.
But these were in his early adulthood.
But consider this: From his college days until he was 40, he drank heavily. This is a fact that he has candidly admitted, and his supporters know of this. On numerous occasions, he has credited his wife for getting him sober and keeping him off the hootch. I also believe that Bush indulged in cocaine on one or more occasions in his youth, but he has been successful in covering this up.
Anyway, on to the $64,000 question: Is the paper trail evidence of above-average intellectual achievement of Bush relevant to his intellectual abilities now? Have the millions or billions of brain cells he has killed through his chemical abuse lowered his intelligence? I think the answer is definitely yes, but as to how much, nobody really knows.
What would he score on an IQ test today? What would a test of his critical thinking abilities show today?
Hentor,
My apologies in advance if I’ve misunderstood you, as I admit not having followed much of your exchange regarding the correlation of the various intelligence measures. But I did read your latest post, and unless I’ve misunderstood you, I believe you are in error in your assertions.
Most significantly, your statement that “Presuming that the IQ scores of the Otis are supposed to be normally distributed, they should have a mean of 100” is a fundamental error. There is nothing magical about the number 100 - it just happens to be the mean of a regular population. A more intelligent population will have a mean that is higher than 100, but that does not imply that the distribution of this population is not normal around its own mean - I don’t know what might have made you think otherwise. So there’s nothing that prevents you from drawing conclusions about this population from the same type of analysis that you might do to any other population.
What is true is that you cannot necessarily extrapolate from this population to other populations, including the “regular” population. This is the point made by the author of the statistics textbook that you quote. But his point, again, is only that the r score of the extreme population will be invalid if it is used for non-extreme populations - not that the r score is invalid if it is used for the population from whose data it was developed.
As applied here, if someone has developed a correlation coefficient (for SAT-IQ) for the group that takes SAT tests, that confident is valid for members of that group. You would be correct that it would not be valid for non-members of the group. But if discussing members of the group, it is valid.
But again, I may have misunderstood you, and if so I apologize.
HTB –
Sorry but that’s just not the case ---- Not if you’re sampling 10 times as many college SAT test takers. The “population” here will be have to be those who take the SAT IF you want to talk SAT to IQ conversation. The average college grad has an IQ of about 115 – not very different than the ‘mean’ IQ of 117 of the 400 students. They’re not extreme groups for crying out loud. The scores of the “population” we are looking at are therefore shifted over with the average being 115 rather than 100. 400 test scores using 115 would create the same curve that 400 test scores with an average of 100. Why is there a problem with that?
And neither is intentionally misrepresenting the intent of what I said.
I did go look on the internet, suspecting there just might be to see if there was a score comparison, with “error bands,” one that converted the vintage SAT taken by Bush - to IQ. While I didn’t make any time consuming search – I didn’t find any using the SAT taken by Bush. If you’re aware of one - feel free to provide that
This link shows the cut-off at the 98th percentile for various tests – including the Otis tests and the WAIS (a prior link indicates a +.80 correlation of WAIS and SAT) The WAIS score is 130 at the 98th percentile. The Otis-Gamma test score is 131 at the 98th percentile. This is presented to show that the WAIS and Otis scores do not vary widely near 129 – and to, in part, respond to your idea that an actual Otis to SAT correlation should be found. (despite the fact that the SAT was benchmarked using the Otis) - And you’re right – I’m not going out an mine the data that supports that. As I stated “the link provided is heavily footnoted and you can do that for yourself if you’re inclined.”
http://www.us.mensa.org/join_mensa/testscores.php3
Linked is another “IQ converter” which indicates a conversion of a “pre-1994” SAT score of 1206 to a score of 125 on the WAIS, a 127 on the Stanford-Binet, and a 141 on the Cattell. No – I don’t know how this was calculated since no information was provided. Nor have I made any attempt to go back and mine the raw data myself. ---- Anyway - this “converter” shows a 125 on the WAIS for Bush and another link indicates a +.80 correlation of WAIS and SAT. It’s provided mostly to show that these scores do not differ by much from the previously linked SAT-IQ converter — the one based on the 400 college students -
http://www.davidpbrown.co.uk/psychology/iq-conversion.html
So -------
Bush can’t be THAT stupid. He gets to ride around on Air Force One while we all have to sit in traffic!
Not In Anger said:
Reagan was NOT stupid. We’ve gone through this debate several times too. Reagan was very intelligent, widely read, wrote many of his own speeches. There is a new book coming out called, “Reagan: a life in letters” - Reagan wrote over 5,000 letters to various people, in his own hand, which survive today. I haven’t read the book yet, but the early reviews say it shows a man who was not only intelligent, but very, very ‘hands-on’ with his administration, contrary to the picture of a doddering old figurehead painted by his opponents.
When are you guys going to learn to stop calling Republicans stupid just because they disagree with you? It’s getting tiresome.
From IzzyR:
While I would differ with your characterization of the “fundamental” nature of the error, you are right that the way I ended up writing that makes it inaccurate. Absolutely, a distribution can have a mean that differs from the larger population, yet still show a normal distribution. However, in this case, this is not even true. The sample is both extreme, and non-normal. What I was trying to convey is that if one wanted to make conclusions about unknown IQ scores (in this case Otis IQ scores, which I presume have a normal distribution centered on 100) one needs to begin with a sample that represents that population.
I agree that the correlation for this sample is the correlation, but if by group you want to argue that this correlation will apply to other putatively related samples, you are going to start treading on thin ice with your first step out of the immediate sample of 400. By the time you get to predicting the specific score of George Bush from his SAT score, you may as well have drawn numbers from a random numbers generator. You appear to be suggesting that this group would be “people that take the SAT,” and I would suggest that this would be most of the population. However, you know that this group is not representative of most of the population, nor is it even normally distributed, leading to the author of the site that was linked to talking about “spuriously low correlations” within this data set itself.
I took no offense at anything you wrote, so no apology necessary. But I ask you, do you feel that this sample was sufficient to be able to predict Bush’s IQ score? If so, why are you not concerned about generalizing from such a specialized and relatively small sample? Further, if so, do you at least agree that the estimate should be presented with error bands?
From Tigers2B1
Are you saying that all SAT takers are college students? Further, unless you are sampling clones, you will absolutely “regress to the mean” or come closer and closer to the mean as you increase your sample size.
It is extreme relative to the general population, which you better be aware of in your creation of an equation to translate SAT scores. Notwithstanding the fact that this sample isn’t one of college grads, isn’t one of typical college students, and isn’t randomly selected.
That isn’t even true. Your own cite says that this sample of 400 scores with a mean of approximately 115 did not “create the same curve.” It says that the standard deviation of this sample is smaller than the normal distribution would be! Gaaa.
The error bands are going to be determined by the sample! You won’t find them on the internet – they should be provided by your source for the assertion that Bush has a translated IQ of 129.
How is pointing out the invalidity of your claim that you can translate Bush’s SAT to an IQ score “ignoring everything?” I’m actually paying close attention – I have read your cite and am suggesting in detail how it is insufficient. You clearly don’t understand it. That apparently can’t be helped. If you want to say that Bush has such and such an SAT score, and that isn’t too bad, great. But you can’t make any claim about a specific predicted score based on what you have - at least, not without giving us an idea of how much error there is in that estimate.
I am arguing that your “Bush has an IQ of 129” claim is not valid. Coming and posting to the thread is not stupid. Arguing for the validity of an assertion because you saw it on the internet, but don’t really understand it…well, that may not indicate stupidity either, but it isn’t very smart.