I think the confusion is that IQ is not an objective measurement. It’s subjective.
Its not like say, height, where you can have a normal distribution and then a statistical outlier.
The IQ point isnt a constant, tangeable unit of measure, like an inch. Intelligence isn’t something you can put a ruler up to and say, oh that’s weird, this person has an IQ of 300 and is a statistical outlier.
IQ is defined statistically. You use some method of claiming that each person has a certain ranking of intelligence. Then you use a defined mean and SD to determine what IQ value that corresponds to, in the context of everyone else in the population.
Yes, a ranking. Ideally the same test for the whole population.
Then you use a defined mean and SD to determine …
Here is your error. Limiting the description of the population distribution to only 2 parameters severely restricts the range of distributions that can be selected. Forcing the population distribution to be Normal is done for arithmetic convenience only. Not because intelligence must be normally distributed.
I’m not saying intelligence is a normal distribution. I’m saying that IQ scores are a normal distribution.
The metric, IQ is a normal distribution because that’s how the metric is defined.
I’d like to hear your explanation how an IQ of above 200 is possible and what that would actually mean.
Its only possible if there are about 10x more humans. With a population of around 80 billion, the smartest one person would have a z score of roughly 6.6 and an IQ of roughly 200. This is calculated from a mean of 100 and a standard deviation of 15, which is how it’s defined.
Here’s a reference from Wikipedia for you, which, itself, references many scientific journals:
"
IQ scales are ordinally scaled.[81][82][83][84][85] The raw score of the norming sample is usually (rank order) transformed to a normal distribution with mean 100 and standard deviation 15.[3] While one standard deviation is 15 points, and two SDs are 30 points, and so on, this does not imply that mental ability is linearly related to IQ, such that IQ 50 would mean half the cognitive ability of IQ 100. In particular, IQ points are not percentage points
"
So, as I’ve been saying, you just put everyone’s test scores in order from worst to best, calculate the z score of the person you’re interested in, multiply by the SD (15) and add the mean.
It is also the case that for populations over 80 billion, you can have negative IQ scores, using the same logic that was used for a person with an IQ of >=200.
I’d like to hear your explanation how an IQ of above 200 is possible and what that would actually mean.
It means that the mean and standard distribution have been calibrated to a population, but that the population kurtosis is significantly non-normal
Its only possible if there are about 10x more humans.
Incorrect. It’s also possible if human intelligence isn’t normally distributed.
With a population of around 80 billion, the smartest one person would have a z score of roughly 6.6 and an IQ of roughly 200. This is calculated from a mean of 100 and a standard deviation of 15, which is how it’s defined.
Only if intelligence of the human population is normally distributed.
So, as I’ve been saying, you just put everyone’s test scores in order from worst to best,
No you don’t. You have invented this unnecessary step.
calculate the z score of the person you’re interested in, multiply by the SD (15) and add the mean.
No, because the “person” and the z score have no link.
It is also the case that for populations over 80 billion, you can have negative IQ scores, using the same logic that was used for a person with an IQ of >=200.
If a rock has zero intelligence, how can something score lower? Negative intelligence is impossible.
Look, I’m saying the same thing that I also found on Wikipedia. You just put the scores in order and then you fit them to a normal curve. This is what it means to scale them ordinally and then fit this to a normal distribution.
Its clear that we aren’t going to agree on any of this, so I’m going to stop replying.
Additonally, you seem to incorrectly think that an IQ of 0 would mean zero intelligence when I have explained exactly what an IQ of zero would mean.
I linked to a list of many examples
Only if normal distributions are assumed. Clearly this assumption is incorrect.
But we do agree that a negative IQ is impossible?
You provided a link to reader’s digest. It’s not the most credible reference.
A negative IQ score and an IQ score above 200 would be possible with larger populations.
A 200+ IQ is possible with a small population. Normal distributions are not a physical law.
I’m struggling to see how a negative IQ can be practically assessed.
I think the confusion is that IQ is not an objective measurement. It’s subjective.
Its not like say, height, where you can have a normal distribution and then a statistical outlier.
The IQ point isnt a constant, tangeable unit of measure, like an inch. Intelligence isn’t something you can put a ruler up to and say, oh that’s weird, this person has an IQ of 300 and is a statistical outlier.
IQ is defined statistically. You use some method of claiming that each person has a certain ranking of intelligence. Then you use a defined mean and SD to determine what IQ value that corresponds to, in the context of everyone else in the population.
Yes, a ranking. Ideally the same test for the whole population.
Here is your error. Limiting the description of the population distribution to only 2 parameters severely restricts the range of distributions that can be selected. Forcing the population distribution to be Normal is done for arithmetic convenience only. Not because intelligence must be normally distributed.
I’m not saying intelligence is a normal distribution. I’m saying that IQ scores are a normal distribution.
The metric, IQ is a normal distribution because that’s how the metric is defined.
I’d like to hear your explanation how an IQ of above 200 is possible and what that would actually mean.
Its only possible if there are about 10x more humans. With a population of around 80 billion, the smartest one person would have a z score of roughly 6.6 and an IQ of roughly 200. This is calculated from a mean of 100 and a standard deviation of 15, which is how it’s defined.
Here’s a reference from Wikipedia for you, which, itself, references many scientific journals:
" IQ scales are ordinally scaled.[81][82][83][84][85] The raw score of the norming sample is usually (rank order) transformed to a normal distribution with mean 100 and standard deviation 15.[3] While one standard deviation is 15 points, and two SDs are 30 points, and so on, this does not imply that mental ability is linearly related to IQ, such that IQ 50 would mean half the cognitive ability of IQ 100. In particular, IQ points are not percentage points "
So, as I’ve been saying, you just put everyone’s test scores in order from worst to best, calculate the z score of the person you’re interested in, multiply by the SD (15) and add the mean.
It is also the case that for populations over 80 billion, you can have negative IQ scores, using the same logic that was used for a person with an IQ of >=200.
It means that the mean and standard distribution have been calibrated to a population, but that the population kurtosis is significantly non-normal
Incorrect. It’s also possible if human intelligence isn’t normally distributed.
Only if intelligence of the human population is normally distributed.
No you don’t. You have invented this unnecessary step.
No, because the “person” and the z score have no link.
If a rock has zero intelligence, how can something score lower? Negative intelligence is impossible.
Look, I’m saying the same thing that I also found on Wikipedia. You just put the scores in order and then you fit them to a normal curve. This is what it means to scale them ordinally and then fit this to a normal distribution.
Its clear that we aren’t going to agree on any of this, so I’m going to stop replying.
Additonally, you seem to incorrectly think that an IQ of 0 would mean zero intelligence when I have explained exactly what an IQ of zero would mean.
It’s pretty obvious that a rock can’t have an IQ of anything but zero.