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Fred (anonymous) meinte am 22. Sep, 21:32:
Mensa test
I took the Mensa tests in 1982. I was between jobs, bored, and curious. So, the choices were go take the Mensa tests or try some experiments with explosives.

I, too, have a top 1% IQ. That was the first shock. The second was reviewing the IQ materials included and noting the bell curve for IQ distribution. To create that symmetry I must have a soul mate as far off the mean on the downside as I am on the upside. In my life I have known some of them.

In actuality the IQ curve is skewed at the lower end because low IQ is associated with severe medical problems and survival is less likely. 
Mahalanobis antwortete am 22. Sep, 23:35:
Same here.
I've been studying for too long and now I badly need a regime change... which includes having a girlfriend. Hedgefundguy immediately saw through my sinister plans:

HFG: Impregnate a 160 IQ chick and create an Uber-Stastny who will conquer the world with his evil genius (and buy you a nice house in the Alps).

Me: Was that so obvious?

HFG: I watch a lot of cartoons.
In actuality the IQ curve is skewed at the lower end because low IQ is associated with severe medical problems and survival is less likely.
What I'd like to know: What are the implications of constructing test such that scores follow a normal distribution? My gut feeling is that intelligence follows a bimodal distribution. But I'm not going to elaborate on this ;-D. 
Anon (anonymous) antwortete am 23. Sep, 18:51:
If the distribution of IQ test scores is gaussian, then there should be a positive (although small) probability of getting a negative score, which makes no sense. So, the fitted gaussian distribution must be a misspecification. Ok, one could use a truncated gaussian distribution instead, but it lacks motivation as it's not the exact limit given by the CLT, which I guess is the main reason of using the bell curve.

Those tail probabilities are of course very sensitive to the specification of the distribution... 
Mahalanobis antwortete am 24. Sep, 00:30:
Truncated Gaussian
I was told that on standard IQ tests (with sd = 15) one can't receive a score lower than 70 (~ 2nd percentile), i.e. one has to use a special test for severely mentally retarded people anyway.

Btw, assuming that the world is populated by 6.5 billion people and using a test with mean = 100 and sd = 15, only 0.085 people are expected to have an IQ below zero ;D 
Anon (anonymous) antwortete am 24. Sep, 17:32:
Yes, it's true, the probability is negligible. (maybe I should've done some calculations before claiming anything...)

On the other hand, the relevant Wikipedia article suggests that sd=24 is used too (where do they get these figures from?), and it gives:

R> pnorm(0, mean=100, sd=24)
[1] 1.545430e-05

so, approximately 1.55 in every 10000, which, admittedly, doesn't seem much, but in the full population it gives

> 6.5e9 * 1.545430e-05
[1] 100452.9 
Hedgehog (anonymous) antwortete am 25. Sep, 02:39:
Wikipedia is a minefield of errors
Wikipedia is full of errors (some of them benign and some, more serious, seem to have been planted there deliberately). Sd=24 in standard IQ tests is apparently one of that type. Unfortunately, many of those errors are hard to spot unless you already know the subject very well (in which case most probably you won't need to search for the info in Wikipedia). I learned by my own experience that it's worth the effort to double-check everything that you read in Wikipedia as long as it is of any importance to you.
However, I have to admit that Wikipedia is a great place to start when you have no idea where else you can get the relevant information. Wiki also contains many good (and mostly authoritative) links which can be used (among other things) to verify the information that you read. 
Mahalanobis antwortete am 25. Sep, 03:19:
AFAIK
Wechsler scale: sd = 15
Stanford-Binet scale: sd = 16
Cattell scale*: sd = 24

The "World Intelligence Network" (...) agrees.

*Cattell IIIB and the Raven´s Advanced Progressive Matrices (old form) 
Hedgehog (anonymous) antwortete am 25. Sep, 05:55:
Truncation of normal from below is likely to occur well above zero
Wow, the "World Intelligence Network" link that you gave looks quite impressive! And I was not aware about the Cattell scale (which shows that my knowledge of the subject is limited).
On a related matter, it seems like we can never observe extremely low IQ scores simply because it is impossible to collect ANY meaningful experimental data with regular IQ tests from the people who are severely mentally retarded. Even if an alternative methodology can be applied to test those people, it isn't clear whether the mapping of scores obtained by that methodology to those obtained by standard IQ testing would make much sense. In some sense, the truncation from below occurs naturally, at a level much higher than zero. 

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