It is a common misconception that IQ follows the normal distribution. In fact, at the extreme tails there are far more than the normal distribution would predict.
With regard to collegedad13’s post #438, pittsburghscribe posted a comment that some research has indicated that the adjustment difficulties for severely gifted people tend to be greatest between the ages of 4 and 9. I think the difficulties probably taper off, but are not gone, up to age 15 or 16, maybe even older. The comment about golf in #438 indicates social adjustments that can be made by teens and adults. A few 4 year olds do play golf (Tiger Woods), but that’s a very small group.
hebegebe is right from what I have read, that the IQ’s in the 165+ range do not follow a normal distribution, and there are many more such people than one would predict from a normal distribution.
If this is true, then I am curious what precise definition of “IQ” the people who develop these tests and scoring scales think they are using.
I was taught that it was an ordinal ranking that is wrassled down and converted at gun-point to a normal distribution (mean = 100, sigma = 15/16), but if what you are saying is right then this must be incorrect or perhaps (as I suspect) it’s simply that these testing scales are not well calibrated in the tails.
(The archaic definition as “mental age / physical age” could give non-normal distributions, but this was never made rigorous and is at least 70 years out of date.)
I have no doubt that they center IQ with a mean of100 and a standard deviation of 15. Both are easy enough to calculate and fit. And the distributions appear to visually match, so that is the reason for the widely held belief.
However, lots of things which appear to visually fit a normal distribution have fatter extreme tails than expected, including height, stock returns, and IQ. This is known as kurtosis.
Yes, but a person’s height has a precise definition that involves using an engraved platinum meter stick shipped direct from the NIST plus some painful medieval torture device to hold their spine straight. The population distribution is whatever it is … approximately normal but not truly so.
Similarly, once we are given a set of prices, stock returns also have an exact definition as (final price / initial price - 1). Their distribution is whatever it is … as you point out, it is kurtotic, heteroskedastic, etc.
There has to be a precise (cardinal) definition of IQ in order to even have the statement “IQ isn’t distributed normally” not be meaningless.
I know that I’m not in the profoundly gifted category because I can no longer follow the tail of this thread. Have never heard of kurosis, etc.
In my many years of testing for gifted kids, I only came across one little 5 y.o. Who was well above the norm. He loved the testing, flew thru it, and was engaging. I wish I knew what happened to him.
For the record, I always tell parents I need to test over two sessions. This boy didn’t want to stop.
I read “kurtosis” as turtle head. In stead of a normal bell as a turtle with 2 tails, we have a turtle with the PG kids as the head. So, 250 PG kids a year rather than 25? Also, are we thinking of PG kids as someone 8+ feet tall who have problems playing basketball with the rest of us?
When I moved in theoretical physics circles I just sort of assumed most of the players were really, really smart. But I don’t think most of them had actually gone through the full testing process to determine their exact IQ. With my one kid who is somewhere on the gifted scale, I have not. I am making sure her needs are met and I don’t see the value in rather expensive testing at this point.
Lots of things do not follow a normal distribution. I had heard that the trend in statistics was to not assume a distribution but to make conclusions by using the sample and using computer simulation to run experiments against the sample tens of thousands of times.
Vicki,
In my state, you need a certain score to move into the gifted program. I don’t think $250 was expensive. Now, they added so many more tests to the mixture, prices have doubled.
In our district all kids are given the CogApt test in 3rd grade, free of charge. One of mine scored high enough for GATE program and one didn’t.
But if a standard IQ test shows a high IQ, you really have to take another test that focuses on higher IQ to say that you have an IQ of 160 or 170.
For example, my GATE kid didn’t miss any questions on the spatial or quantitative sections. So that test wasn’t hard enough to narrow down where she is, other than to place her in the “gifted” category. Which I had known she would be in from the time she was a toddler, so no surprises there for me.
I could pay for more testing, but didn’t see the point. I suspect most gifted people don’t go through that sort of testing either due to expense, access or lack of interest.