What does this IQ score mean (if anything)?

Factual Questions
101

I can’t remember if anyone has posted a link to a graphic, so here’s one. IQ has a more-or-less normal, bell-shaped distribution. WAIS scores from about 85-115 are statistically normal (that is, they fall within one standard deviation of the mean score). Scores in 15 point increments above and below this range are statistically less likely, and account for 32% of scores (16% significantly low, 16% significantly high). Of that 32%, 28% of the overall distribution will be in the 70-85 and 115-130 score ranges (within 2 SDs of the mean). About 4% will fall in the 55-70 and 130-145 ranges, and about .1% (1 person in 1000) will fall below 55 or above 145.

Depending upon the circumstances, you may see more or fewer people in any of these ranges. At a school for the gifted you’ll see more outliers on the high end than at a school for people with developmental disabilities. You may not see more common sense, ability to sing, or kindness, but you will see more of the factors that are measured by IQ tests, which tend to correlate with ability to learn and apply certain domains of knowledge.

102

I do not know what the result from my second grade IQ test was, only that it must have been at least 2-sigma because that was the lower limit for admission to our school district’s so-called “mentally gifted minors” program. I would find taking a modern IQ test interesting only to see what methodology is considered valid these days.

The SAT was originally designed to predict collegiate success, that is, probability of doing well scholastically in college (good grades, basically). Just because your abilities say you have a better chance of succeeding means nothing about how you the individual will do; I, too, was a college “failure” because I failed to apply myself. It wasn’t until law school that I decided to do the work needed to be scholastically successful at the collegiate level. So high SAT/ACT scores for an individual will not necessarily correlate to success in college. However, the College Board claims that their studies show that the correlation between HS grades and college grades increases significantly when SAT scores are factored in.

Ymmv.

103

[QUOTE=What Exit?]
The IQ test in school way back when, was another group class test and did take many hours, but it was not professionally administered, just professionally graded (outside graders). This would be back in the mid-seventies. That was the only time I ever took a “real IQ” test. It sounds like you might be saying that even this should not be considered real. Is that correct? Jim
[/QUOTE]

No, that is not what I am saying. This is why all of these discussions fall into either a clusterfuck or a greasy snakepit of lies. If you had an official, standardized test that claimed to measure IQ, it would most likely give you an approximation of your real IQ score. If one of those gave you an IQ score of 145 then that is perfectly plausible.

The only reason why one is “real” and the other is not is just a matter of definition. You can’t get your “real” IQ score without an individually administered traditional IQ test. In reality, most standardized tests are IQ tests of sorts. You can convert scores from the SAT, ACT, and GRE into IQ scores fairly accurately just based on percentiles. IQ is an invented construct although it is supported statistically. It is just that no one is quite sure what it represents. The major difference between tests that are solely devoted to IQ testing versus the others is a matter of definition. Lots of tests have a high g-loading (general factor of intelligence) but measuring that isn’t their stated purpose so they are not labeled IQ tests.

104

[QUOTE=Shagnasty]
No, that is not what I am saying. This is why all of these discussions fall into either a clusterfuck or a greasy snakepit of lies. If you had an official, standardized test that claimed to measure IQ, it would most likely give you an approximation of your real IQ score. If one of those gave you an IQ score of 145 then that is perfectly plausible.

The only reason why one is “real” and the other is not is just a matter of definition. You can’t get your “real” IQ score without an individually administered traditional IQ test. In reality, most standardized tests are IQ tests of sorts. You can convert scores from the SAT, ACT, and GRE into IQ scores fairly accurately just based on percentiles. IQ is an invented construct although it isn’t baseless statistically. The major difference between tests that are solely devoted to IQ testing versus the others is a matter of definition. Lots of tests have a high g-loading (general factor of intelligence) but measuring that isn’t their stated purpose so they are not labeled IQ tests.
[/QUOTE]

I’m curious now, would you say a 1600 SAT in 1983 would probably equte to a 160 then, or higher? I thought the wildcard was with SATs is that you could study for them. It seems much harder, if not impossible to study for an IQ test.

If you know a rule of thumb for converting, what would a 1370 in 1983 be?

Jim

105

IIRC, the SAT was set up with the scale 200 - 800 intending to mean that the median would be 500, and each 100 pts to the side is intended to represent a standard deviation. Thus, 1600 would be someone who was 3 sigmas above the median in both the verbal and the math portions.

1370 would have to be broken down according to individual results. I’m not certain it’s statistically valid to assume that the combined score also follows a normal distribution, with standard deviations every 200 pts. In any event, it would be quite a different result if you were someone who went 760 verbal, 610 math, or someone who was scored 670 and 660, respectively.

106

[QUOTE=DSYoungEsq]
IIRC, the SAT was set up with the scale 200 - 800 intending to mean that the median would be 500, and each 100 pts to the side is intended to represent a standard deviation. Thus, 1600 would be someone who was 3 sigmas above the median in both the verbal and the math portions.

1370 would have to be broken down according to individual results. I’m not certain it’s statistically valid to assume that the combined score also follows a normal distribution, with standard deviations every 200 pts. In any event, it would be quite a different result if you were someone who went 760 verbal, 610 math, or someone who was scored 670 and 660, respectively.
[/QUOTE]

Ok, so how about a 620 Verbal and 750 math as an example. :wink:

107

[QUOTE=Shagnasty]
I will wait with bated breath your apology as it relates this response. I have no idea where you came up with this vomited up horse shit as it relates to me in this thread. I just commented on the psychometrics of IQ tests and how the normal curve works. I simply mean that anyone that claims to have a a very high IQ better supply some supporting evidence or else that person is most likely lying.

You yourself claimed knowing two students that had an IQ at or above 160 which means that you have almost certainly been taken as well. The traditional tests just don’t work that way.
[/QUOTE]

My, my. The quote I responded to was:

[QUOTE=Shagnasty]

A good rule of thumb is that anyone that claims to have an IQ above 145 is probably lying unless there are some extreme extenuating circumstance like a summa cum laude degree from Harvard.

[/quote]

I don’t think such a degree would tell you anything about whether a person had an IQ of over 145 or not. Perhaps you didn’t mean for this to imply that IQ controls performance, but it sure sounds like it.

I know statistics quite well, thank you, and perhaps you don’t understand clustering. The scores were confirmed by more than one person, and in fact one was confirmed a different year. This happened over 40 years ago, by the way. This school fed the best academic high school in New York, not counting the specialized ones, and people in this class were selected from high achievers in elementary school. Back then New York classes were strictly tracked. One of these people went to Yale, the other to MIT, and both had very high SATs, and were Merit Semifinalists, and one was in Mensa. (The other qualified but wasn’t interested.) One had the second highest Regents Scholarship score in Queens county, and in the top 15 in New York State, and the other had the second highest gpa of a class of 1500.

You are correct that in a random population of students such a thing would be very unlikely, but this population was far from random.

108

[QUOTE=Wendell Wagner]
Voyager writes:

> While I agree in general that some people inflate their scores, I know (from the
> teacher leaving her book open) that two kids in my junior high homeroom had
> IQ scores of 160 and above.

What junior high school was this? Perhaps it would be possible if it was one of those selective all-state ones that chooses by test from everyone in the state of that age and gives them scholarships to allow them to reside at the school, but otherwise it’s absurdly improbable. If your homeroom had 30 kids in it, the probability is only 1 in 1000 that even one child in that homeroom would have an I.Q. of 160. And forget about the I.Q.'s being above 160, because as I pointed out in my last post, honest I.Q. tests don’t measure scores that high.
[/QUOTE]

40 years ago? I’ve seen others above 160. I’m aware that there is a cutoff, but I thought it was around 170.

See above for some details about the school. The homeroom was selective, and the neighborhood had a bunch of smart kids. The grade, btw, had 18 classes of about 30 students each, so it was a very big school, and thus there was more chance of seeing this anomaly at the top. New York schools were quite jammed at the time.

109

[QUOTE=DSYoungEsq]

One of the troubles with the normal IQ test is that, once it starts trying to measure past 2σ, it gets quite difficult to differentiate. Usually, you have to start using tests that are normed over a smaller portion of the population, namely those who’s regular IQ scores were already at the 2σ level or higher. Most people never take such a test, and in my opinion, they have little purpose other than putative bragging rights. :rolleyes:
[/QUOTE]

When I was a kid, every child in New York City (and the state, I assume) took it. I’d guess a lot more kids around the country did also, since this was before there was (quite valid) doubt about the meaning of intelligence tests. The educational philosophy was very different also. After third grade, kids were split based on what passed for intelligence. In my 7th grade there were 6 SP (special progress) classes, 3 of which skipped 8th grade and 3 of which got an enriched 9th grade. There were 12 “regular” classes, and the lower the number the smarter the kids in it. So, there might have been a big enough population to make results beyond 2σ valid.

I don’t know when IQ tests were renormed, but it is possible there was score creep at the time.

As I mentioned, the SAT scores of both of these people were 99% (well over 1500 combined) so that was in keeping. The scores were from 1968, by the way, well before SAT score creep, and before anyone thought about studying for the tests.

110

[QUOTE=Shoshana]

Depending upon the circumstances, you may see more or fewer people in any of these ranges. At a school for the gifted you’ll see more outliers on the high end than at a school for people with developmental disabilities. You may not see more common sense, ability to sing, or kindness, but you will see more of the factors that are measured by IQ tests, which tend to correlate with ability to learn and apply certain domains of knowledge.
[/QUOTE]

Neighborhoods factor into this also, since certain ones will have a higher percentage of well educated residents who will have a relatively higher IQ than others. There is obviously regression to the mean, but a school populated with the children of high achievers will look at least a little bit different from that of a population more average.

111

Let’s say that there were 20,000,000 people in the state of New York at the time you were in junior high school. That would mean there were perhaps 400,000 students in any one grade in all the schools in the state of New York. That would mean you would expect there to be at most 15 people in the same grade as you in every school in the state of New York with an I.Q. of 160 or above. You say that two of them were in your homeroom. That’s . . . interesting.

An I.Q. of 170 is four and two-thirds standard deviations away from the mean. That means that you would expect one or two people in any group of a million people to have an I.Q. that high or higher. That means in your grade among all students in the state of New York, it’s maybe fifty-fifty whether you would find even one person with an I.Q. of 170. That’s why it’s extremely hard to norm an I.Q. test for an I.Q. of 170. You would have to give the test to perhaps 2,000,000 people (of the same age or whatever) to norm it reliably so that you would have about three people with that I.Q. taking the test. Giving the test to just all the students in one given grade in one state in the U.S. would be insufficient. You would have to give the test to perhaps one-quarter of all the students in a given grade in the U.S. to norm the test reliably for an I.Q. of 170. That’s extremely difficult. Everything I’ve read has said that it’s too difficult to norm an I.Q. test for a score above 160. Give me a citation saying that it’s possible to norm it for a score of 170.

112

But you’re assuming that those 160s were evenly distributed. Many communities have schools that attract high-testing or high-performing students.

113

Look just how hopelessly unevenly distributed the 160 I.Q.'s were distributed. There are approximately 400,000 students in that one grade in the state of New York, and only approximately 15 of them have an I.Q. of 160 (or above). Of those fifteen, two of them are in Voyager’s homeroom. That’s extraordinarily concentrated, even if Voyager’s homeroom and school are very selective.

Look, I’m a mathematician. I know how to do this math. Even if Voyager’s homeroom was selected by testing everyone in the state of New York, it would take some work to get two students with I.Q.'s of 160. Voyager said that the students were only from a single school district, even if it was a well-off school district with a very good school. That’s quite unlikely. No, it’s not completely impossible, but it’s quite unlikely.

114

The point here is simple: while it is unlikely, it is possible (anything is possible). What is much more possible, however, is that the reported scores were erroneous, that is, that they resulted from failure to differentiate above the two or three sigma level (the result of answering a single correct versus incorrect question, for example), or they resulted from something that was used as a proxy for an IQ test, such as a standardized screening test taken by the students in a classroom condition (which would not be shocking given the assertion that all students were so tested).

And if all they managed was 1500 plus on the SAT’s, that’s not very strong confirmation of their putative IQs because after all, that’s only 2.5 sigmas above median, and we’d expect them to have pegged out at 1600 without trouble if they were 160 plus in IQ. And Merit semifinalists, well, hell, I was one of those, and I assure you, I’m nothing special that way in an IQ test (Merit Scholarship semifinalists would have been based on their PSAT/NMSQT test results, and 160 plus would expect to peg that one out, too).

All of which shows simply how silly the whole business is. They sound like they were scholastically successful, and if so, who cares if they were 130, 145, or 160? :rolleyes:

115

Any obtained IQ score is understood to fall into a “true score” range. The numbers reported may have been the top of those ranges, or the obtained scores may have been high expressions within that range for those individuals.

116

[QUOTE=Wendell Wagner]
Look just how hopelessly unevenly distributed the 160 I.Q.'s were distributed. There are approximately 400,000 students in that one grade in the state of New York, and only approximately 15 of them have an I.Q. of 160 (or above). Of those fifteen, two of them are in Voyager’s homeroom. That’s extraordinarily concentrated, even if Voyager’s homeroom and school are very selective.

Look, I’m a mathematician. I know how to do this math. Even if Voyager’s homeroom was selected by testing everyone in the state of New York, it would take some work to get two students with I.Q.'s of 160. Voyager said that the students were only from a single school district, even if it was a well-off school district with a very good school. That’s quite unlikely. No, it’s not completely impossible, but it’s quite unlikely.
[/QUOTE]

In my work I see the clustering of supposedly random defects all the time. When you see a result that seems extremely unlikely under the assumption of randomness, you sometimes must reject that assumption.

As another datapoint, Stephen Jay Gould graduated from the same junior high ten years before us. I don’t know what his IQ was, I suspect higher than mine.

I’m not rejecting the possibility that the New York school system made a mistake (though not that big a one, considering the future performance of these people) or that IQs normed when my class got tested were high before being renormed. However, this discovery made quite a stir, and the scores were confirmed later, as I said, and not by either of the students involved.

Since I would have shut up if this hadn’t happened, when computing the odds you’d need to compute how likely would it be to never happen - at least over the population of Dopers. I can tell you anecdotes of my wife hitting slot jackpots on one pull just as leaving - low probability, but I’m not telling you the times she didn’t hit.

As pTerry says, million to one shots happen nine times out of ten.

117

[QUOTE=DSYoungEsq]
The point here is simple: while it is unlikely, it is possible (anything is possible). What is much more possible, however, is that the reported scores were erroneous, that is, that they resulted from failure to differentiate above the two or three sigma level (the result of answering a single correct versus incorrect question, for example), or they resulted from something that was used as a proxy for an IQ test, such as a standardized screening test taken by the students in a classroom condition (which would not be shocking given the assertion that all students were so tested).

[/quote]

That may well be true. I have no recollection of ever taking an IQ test in elementary school, but then I doubt they would have told us what they were doing. I also don’t know the methodology used to compute scores. I have no time this week, but I’ll try to see if I can find something. However, this was the New York City school system, not Podunk, so I think they could afford a decent psychologist to run this program. As I said, this was during a time of rampant IQism, no doubt more than made sense.

Well above 1500. I wonder what a 1550 in 1970, say, translates to today. (When I was in high school we had to write SATs using chisels on rock.) The point I was making was that there is at least some evidence that two random kids weren’t assigned high scores.

Of course. No one ever gets hired based on IQ, accomplishments are everything. However, it is not always the case that anyone claiming an IQ of over 145 is lying or deluded. 185, sure. But there are certain environments where the IQ distribution is going to be skewed way high.

118

[QUOTE=Shoshana]
Any obtained IQ score is understood to fall into a “true score” range. The numbers reported may have been the top of those ranges, or the obtained scores may have been high expressions within that range for those individuals.
[/QUOTE]

That sounds plausible. I doubt the test was designed to differentiate at the three or four sigma level, so there would have to be quite a range. There is of course a random factor, in that a test taker might get a question wrong by accident, which would have a big impact.

119

[QUOTE=Voyager]
That may well be true. I have no recollection of ever taking an IQ test in elementary school, but then I doubt they would have told us what they were doing.
[/QUOTE]

How sure are you that the scores you saw in a teacher’s book were IQ scores? Wouldn’t that information be kept confidential, with only the psychologist having access to it? It’s not like the teacher would be able to adjust his/her teaching style/lesson plan to accomodate a 160 IQ vs, say, a 155 IQ, so there’s not much point in giving the teacher the scores in the first place.

120

I scored a 138, which is about in-line with most unofficial IQ tests I’ve taken (never taken an official one): generally between 135 and 145 with outliers at 116 and 160. All of which is to say, I’m pretty good at online IQ tests. Yippee.