I spent today afternoon being desperately bored so I dug out all my old photo albums, school reports and crap and found some IQ test results I’d never seen before, or, at least, never remembered seeing. Actually, I think there were several tests, only one of which measured IQ but anyway. A strange thing I noticed was that my overall score for each section was higher than my average, and my overall score for the test was higher than any mark I’d got for any of the sections. So, uh… why? It makes no sense to me but I’m sure there’s a reason to be found somewhere.
Dunno if this answers it but perhaps it will shed some light on this.
I will try to keep this pretty basic.
IQ scores are normed. That means that the raw scores don’t really mean anything especially since individual questions can be weighted differently. Instead, the final scores are place markers for the person’s position on a normal curve.
Take a look at this normal curve.
Most IQ tests have a mean of 100 and a standard deviation of 15 or 16. This is useful to know because normal curves have mathematical properties that allow you to calculate a percentile score without knowing anything else about the test.
A score of 100 is in the 50th percentile by definition (although this drifts sometimes).
To calculate an IQ score percentile, you use what is called a z-score.
z-score = IQ score - mean (100) / Standard Deviation
Say to have an IQ score of 130. That means that your z-score is (130 - 100) / 15 = 2
If you go to the z-score calculator in the link above and enter a z-score of positive 2 then your percentile score is the 97.7th percentile.
Note that normal curves are symmetrical and an IQ score of 70 = a z-score of negative 2. That puts it at the opposite end with the same area under the curve at 2.3 percentile.
I don’t know what your sub-scores look like but they may just be raw scores and not that meaningful. There are separate curves for sub-tests but it doesn’t sound like they are translated.
The sub-scores were given as percentiles of the general population, just like the overall scores. I would have thought the curves were already applied. I’ll see if I can find it again to show you what I mean.
It has been awhile since I had to deal with IQ tests, but here is my guess. The results for each section can be compared against the population. So you could score higher than say, 75% of the population on a particular section, but that would not be your IQ overall. You IQ is specific to you. That is, when the results of all the sections completed are tabulated, you will have a score. That score is compared against your chronological age to determine your IQ.
Therefore, you may outscore 75% of the population on a particular section, you may even outscore 75% of the population overall. Then when you compare your score against your chronological age, you may only have an IQ of 100. Also, keep in mind that the scores on each individual section are not as important as your IQ. Predictions on personality, aptitude, and potential for deviant behavior can be predicted from the scores on the sections, but are not as meaningful as far as intellegence indicators. (Nor, for that matter, the score on an IQ test IMHO)
Sgt Schwartz
Huh. That could be it. I was 11 (apparently), so there was probably a fair amount of that sort of scaling involved.
I.Q. scores (these days, anyway) are only drawn from comparisons from either just adults or just children of your own age. That means that if you’re a child and given an I.Q. test, the scores for each section are only relevant to children of your age. You wouldn’t be compared to adults or to children of other ages. This hasn’t always been true. It used to be the case that I.Q. scores weren’t normal curves. A child could be given a number of I.Q. tests, each of which was originally intended for children of various ages. If the child was n years old and they scored average on a test for children of age m, the child would be said to have an I.Q. of 100 * n/m. Notice that this is actually a quotient (hence the term “intelligence quotient”), unlike the present-day I.Q. scores, which are not quotients at all.
If a 7-year-old child on the old-style tests took the test for 16-year-olds and scored average on it, their I.Q. would be said to be 100 * (16/7) ~ 228. Marilyn Vos Savant claims to have once scored 228 on an I.Q. test, which presumably means that she did this. Under the present sort of I.Q. tests, it is not longer possible to have an I.Q. score anywhere near this high, since 228 is way too far out on the normal curve.
Excuse me, not “an I.Q. of 100 * n/m”, but “an I.Q. of 100 * m/n”.
It’s the Stanford-Binet IV
In what year were you given the Stanford-Binet IV (both your age and the calendar year when this happened)? I would ignore any I.Q. test you were given as a child, especially if it was one of the old-fashioned ones where the I.Q. score was really a quotient. Only an I.Q. test given to you as an adult (and by a professional, not these crap ones you find online) have any current validity. Incidentally, ignore any scores that claim you have an I.Q. over 160. It’s pretty much impossible to validate any score that far out. The higher (or lower) the score, the larger a group that has to be used to norm the test.
Agreed. I always say that anyone who really has an IQ over 160 would be the first to realize how unlikely a score that high is. Less knowledgeable people tend to add on points to their score to exaggerate without understanding that it is not a linear scale. Tacking on relatively few absolute points can change your claim from being the smartest person in your town to the smartest person in the world. Not likely.
1999, 10, 158, for what it’s worth. I know I said 11; I screwed up. By a real psychologist. Is the Stanford-Binet a quotient? I would really just like to know why the numbers are funny. I found the test again, here is what I mean. There are 4 categories in the test, and each category has sub-categories. For example, the short-term memory category has 4 sub-categories:
Subtests Standard age score Percentile Category
Bead memory 76 99.94th
Sentences 64 96th
Digits 68 99th
Objects 144 99.7th
Short-term memory 154 99.96th Superior
So these are my scores for the 4 categories:
Subtests Standard age score Percentile Category
Verb. reasoning 144 99.7th Very superior
Abstract/Visual 147 99.84th Very superior
Quantitative 148 99.87th Very superior
Short-term Memory 154 99.96th Superior
Test composite score (this is the IQ, right?): 158
Test composite percentile: 99.99th
Test composite category: Very superior
So the questions are:
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Why do the scores shift upwards every time you move up into a larger category? I’m not sure if this makes sense, basically I got 99.96 for short-term memory which I didn’t get for any of the sub-categories, and 99.99 overall which I didn’t get for any of the categories. And if the scores aren’t a mean of the parts then how are they calculated? Scaling according to age could be it but do they need to adjust the score EVERY time?
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Why is it that 99.7 in verbal reasoning is “very superior” while my 99.96 in short-term memory is only “superior”?
Wendell and Shagnasty are right, I’m really not very fussed about my score since it’s probably inaccurate and in any case doesn’t say much. Though it does make a good trump card when someone with a lower score cares a little too much 
I’m just trying to understand the process a little better. The other tests in the same report are pretty straightforward - get a score, which translates to a percentile, and if you get above this percentile you’re in this category, and above this one is this category, and I imagine there’s scaling involved there too… but the Standford-Binet is a lot more hocus-pocus. I don’t get it.
The numbers below 100 are probably just raw scores that haven’t been translated into I.Q. scores. Not knowing how the raw scores are used to figure the I.Q., it’s impossible for us to interpret them. In any case, you’re now 16 (or 17), right? An I.Q. score of 158 when you were 10 means just that you scored near the top of what can be conventionally measured relative to your age. Incidentally, a 160 I.Q. means that you’re about one in 31,000. It would be necessary to give the test to about 100,000 people (who are age 10) to be able to accurately make that claim. An I.Q. test would have to be given to hundreds of millions of people to be able to make the claim that someone had an I.Q. of 180, for instance.
And now that you know your I.Q., you might as well forget it. Anybody who meets you can tell you’re smart without having to ask for your I.Q. Your future path in life will be determined by lots of things - performance on standardized test, course work, work in a job, etc., but nobody is going to care about your I.Q.
But… that’s not what I was asking! I know about the old dodgy tests that use mental age/age and give results of 200+ but I’m not sure if the Stanford-Binet IV, being relatively modern, is one of them, and in any case that’s not what I wanted to know, though it would be nice, and I WAS asking how they arrived at the final figures, and I don’t think something with a name like “percentile” is a raw score, and even if it were, that still doesn’t explain why they CHANGE, and I don’t particularly care that nobody will care about my IQ because that’s not what I was asking either. I hope this makes it clear.