I need to point out that IQ isn’t a score. It’s a quotient. There are literally not enough people on earth for anyone to have an IQ of 210. There aren’t even enough for a single person to have an IQ of 202.
if it’s based on an approximated normal distribution, then it is entirely possible to have people well into the tail ends. Regardless of the current population of humanity.
Say you have a test with 100 questions and the mean score is 76, but the standard deviation is super low like 3, then getting a perfect score would put you at a z-score of 8, which would be roughly a 1 in 803.7 Trillion rarity.
You don’t need 803.7 Trillion people to take the test to reach this conclusion. In fact (if I’ve done my math correctly) you would only need a sample size of 65 people (including the outlier), to get this though that’s under perfect conditions assuming everyone else got exactly 76. (You’d need a lot more samples in different places to be confident in that result)
Anyway, that’s a super idealized example, but the principle of the Central Limit Theorem is sound and does allow for crazy seeming probabilities. It’s not comparing your score to everyone who has taken the test for quartiles, it’s telling you how you’d compare to everyone who could possibly ever take the test.
The statistical approach is sound; however the test and sampling is not. IQ score tests are just biased, inaccurate, not really scientific, not useful and typically only serve to give people ego boosts.
I never debate the ability of IQ tests to measure what they say they do. That’s a position of automatic loss.
However I will debate any claim of an IQ over 201.
You proposed a test with an absurdly low SD. Can you find one that is respected (maybe MENSA qualifying) that meets that criteria. We can create math problems to invent a hypothetical test that makes getting an IQ over 201 but the second step is to confirm that one not only exists but is credible within the sloppy credibility standards that exist within the industry.
This is describing a defective test. Any test that allows for an IQ above the population limit is a defective test.
My example may have been idealized, but it doesn’t apparently matter. Looks like the raw scores for modern IQ tests are transformed to fit a normal distribution with mean 100 and standard deviation 15. (Meaning they basically subtract the average score from raw scores, divide by the deviation of the raw score, multiply by 15, and add 100. Basically they just scale the data from every test so number of questions doesn’t really matter. This also might reduce bias from people in a given location or who took a specific test if those are the groups for normalization).
The only real question for confidence in the scale is then the number of people who have taken the test. So let’s say we want to be 8sigma sure (likelyhood were wrong is about 1x10^-15) that a person’s IQ is correct to ±1 point.
For this confidence interval we have 8 as the critical z value and 15 as the standard deviation. A 1 point error in score means we’d only need a sample size of 14,400 people.
In other words, you only need to have 14,400 people take the test (or an equivalent one with the same normalization) in order to dettermine with ~99.999999999999999% confidence that someone’s score is between 200 and 202.
I’d imagine that’s not an unreasonable number of samples for MENSA or WAIS. Ergo IQ scores of extraordinarily high values are not necessarily signs of defects in the math of the test.
Given the world population there is zero reason to go to sigma 8. That’s more than 12000x the population of earth.
But, anyway. If the theoretical limit to IQ for the current population is 201 and a test even has the potential to give a result of 202 the test is defective. And people that make IQ tests have to know that because any result outside of theoretical limits is going to get them laughed out of town.
You mentioned Wikipedia earlier. The test that gave the 210 result is known to be defective.
The sigma 8 was for our confidence interval of the point estimate, not a score that would give you sigma 8 results.
Furthermore as your picture points out, that test was defective because it gave a standard deviation higher than it said. The modern ones normalize the distribution to avoid that problem.
There is no theoretical limit to IQ. If you gave an arbitrarily long enough test it would be possible (though incredibly unlikely) that you could get IQ values in the thousands.
I think you are getting confused by what the meaning of the score is supposed to be. It has nothing to do with the number of people in existence.
The test is assuming that humans have an IQ that follows a normal distribution. They then sample humans and normalize the scores of each sample population. This is not a “you are smarter than x people” test. It assumes that IQ is an inherent property of humanity and gives you a probability of people (any amount of them) having a lower score than you.
Sure, at a certain point that basically means you’re likely to be smarter than everyone alive currently. And yeah if we get multiple scores like that it means it is likely (though not guaranteed) that our metrics are not effective.
As a counter example of why multiple crazy high scores don’t necessarily mean the scales are broken here’s a thought experiment:
Imagine you did this test over a million years or just that you actually sampled an absurd number of people like 4quadrillion. There are going to be people who ranked the highest on that set. So the chance of a person being in the top 4 is about 1 in a quadrillion.
Now if we make the assumption that IQ is unaffected by time, it is entirely possible that two of those people might be alive at the same time or even all 4 of them.
These people would have IQ scores placing them wayyy above the population of their current time period, but that wouldn’t change the fact those scores are still in fact accurate.
The scores have nothing to do with the current living population of humanity; those scores are supposed to be relative to general human intelligence regardless of time or place. Ergo, if we assume intelligence is not limited and that humanity survives indefinitely (and that IQ tests actually mean something) then there is a nonzero chance of getting any arbitrary score in the natural numbers. 400, 8000, 10^23, who cares.
As long as you can write tests long enough and you keep testing humans long enough you’ll eventually find someone who scores at those levels without your test being defective. That’s how probability works.
If you still don’t get what I’m saying or what a normal distribution is, I suggest you go to YouTube or peertube to look it up. Chances are they’ll be able to explain it better than me lol
Originally, IQ was a score obtained by dividing a person’s estimated mental age, obtained by administering an intelligence test, by the person’s chronological age. The resulting fraction (quotient) was multiplied by 100 to obtain the IQ score.
“Originally” because that’s not the case for modern IQ tests because now we fit the data to a normal distribution, giving us a much more reliable and repeatable experiment.
Furthermore, even if that was quotient formula was still used, the average score of others your age is still a population parameter (something you cannot measure the true value of) that you can only sample and estimate for the possibly indefinite population. Your confidence in your estimate of the average depends on the number of samples; the actual parameter does not because it is (supposedly) an inherent quality of the class of things you’re sampling.
Please just go through a statistics crash course I don’t know how to explain this better.
Kim Ung-Yong (Korean: 김웅용; born March 8, 1962)[1] is a South Korean civil engineer and university professor. During his youth, he was recognized as a child prodigy with the highest recorded IQ on record, having scored above 210 on the Stanford–Binet Intelligence Scale.
Ah in that case … I’m not really good at maths but … why don’t you go on and correct the wikipedi article, and the one in the Guinnes book … so that people like me, i. e. not that good as maths, won’t be fooled anymore by those articles?
Guinness sets their own standards and they are considered valid source by Wikipedia.
I’d recommend somebody who actually has experience editing take care of that edit. My only edit was to remove a bogus citation for fake ethnic identity used by white supremacists on the page of a pornstar. And that page no longer exists.
That’s not it. Your IQ isn’t the score on the test. It’s the score divided by the score of every in your age group multiplied by 100. It’s upper limit isn’t based on how well you did. It’s based on the population. That’s why it’s an IQ, Intelligence Quotient, not an IS, Intelligence Score.
It is mathematically impossible to get an IQ over 201 given the population of the planet. And that’s using the generous 16 point deviation most use the 15 point SD. That one allows for a maximum score of 195 with the current population.
To add to this, above a given level of intellectual ability, the tests are not capable of measuring. If we both get every question correct, we do not necessarily have the same intellectual ability even though the test will say we both deviated from the mean by the same amount.
That is not some redditor but one person, who impressed the Guinness book of world record staff. And before you go on, that they too don’t impress you … I neither bother if that person had such an IQ or not, nor do I bother by you being impressed or not.
I need to point out that IQ isn’t a score. It’s a quotient. There are literally not enough people on earth for anyone to have an IQ of 210. There aren’t even enough for a single person to have an IQ of 202.
if it’s based on an approximated normal distribution, then it is entirely possible to have people well into the tail ends. Regardless of the current population of humanity.
Say you have a test with 100 questions and the mean score is 76, but the standard deviation is super low like 3, then getting a perfect score would put you at a z-score of 8, which would be roughly a 1 in 803.7 Trillion rarity.
You don’t need 803.7 Trillion people to take the test to reach this conclusion. In fact (if I’ve done my math correctly) you would only need a sample size of 65 people (including the outlier), to get this though that’s under perfect conditions assuming everyone else got exactly 76. (You’d need a lot more samples in different places to be confident in that result)
Anyway, that’s a super idealized example, but the principle of the Central Limit Theorem is sound and does allow for crazy seeming probabilities. It’s not comparing your score to everyone who has taken the test for quartiles, it’s telling you how you’d compare to everyone who could possibly ever take the test.
The statistical approach is sound; however the test and sampling is not. IQ score tests are just biased, inaccurate, not really scientific, not useful and typically only serve to give people ego boosts.
I never debate the ability of IQ tests to measure what they say they do. That’s a position of automatic loss.
However I will debate any claim of an IQ over 201. You proposed a test with an absurdly low SD. Can you find one that is respected (maybe MENSA qualifying) that meets that criteria. We can create math problems to invent a hypothetical test that makes getting an IQ over 201 but the second step is to confirm that one not only exists but is credible within the sloppy credibility standards that exist within the industry.
This is describing a defective test. Any test that allows for an IQ above the population limit is a defective test.
My example may have been idealized, but it doesn’t apparently matter. Looks like the raw scores for modern IQ tests are transformed to fit a normal distribution with mean 100 and standard deviation 15. (Meaning they basically subtract the average score from raw scores, divide by the deviation of the raw score, multiply by 15, and add 100. Basically they just scale the data from every test so number of questions doesn’t really matter. This also might reduce bias from people in a given location or who took a specific test if those are the groups for normalization).
The only real question for confidence in the scale is then the number of people who have taken the test. So let’s say we want to be 8sigma sure (likelyhood were wrong is about 1x10^-15) that a person’s IQ is correct to ±1 point.
For this confidence interval we have 8 as the critical z value and 15 as the standard deviation. A 1 point error in score means we’d only need a sample size of 14,400 people.
In other words, you only need to have 14,400 people take the test (or an equivalent one with the same normalization) in order to dettermine with ~99.999999999999999% confidence that someone’s score is between 200 and 202.
I’d imagine that’s not an unreasonable number of samples for MENSA or WAIS. Ergo IQ scores of extraordinarily high values are not necessarily signs of defects in the math of the test.
Given the world population there is zero reason to go to sigma 8. That’s more than 12000x the population of earth.
But, anyway. If the theoretical limit to IQ for the current population is 201 and a test even has the potential to give a result of 202 the test is defective. And people that make IQ tests have to know that because any result outside of theoretical limits is going to get them laughed out of town.
You mentioned Wikipedia earlier. The test that gave the 210 result is known to be defective.
The sigma 8 was for our confidence interval of the point estimate, not a score that would give you sigma 8 results.
Furthermore as your picture points out, that test was defective because it gave a standard deviation higher than it said. The modern ones normalize the distribution to avoid that problem.
There is no theoretical limit to IQ. If you gave an arbitrarily long enough test it would be possible (though incredibly unlikely) that you could get IQ values in the thousands.
I think you are getting confused by what the meaning of the score is supposed to be. It has nothing to do with the number of people in existence.
The test is assuming that humans have an IQ that follows a normal distribution. They then sample humans and normalize the scores of each sample population. This is not a “you are smarter than x people” test. It assumes that IQ is an inherent property of humanity and gives you a probability of people (any amount of them) having a lower score than you.
Sure, at a certain point that basically means you’re likely to be smarter than everyone alive currently. And yeah if we get multiple scores like that it means it is likely (though not guaranteed) that our metrics are not effective.
As a counter example of why multiple crazy high scores don’t necessarily mean the scales are broken here’s a thought experiment:
Imagine you did this test over a million years or just that you actually sampled an absurd number of people like 4quadrillion. There are going to be people who ranked the highest on that set. So the chance of a person being in the top 4 is about 1 in a quadrillion.
Now if we make the assumption that IQ is unaffected by time, it is entirely possible that two of those people might be alive at the same time or even all 4 of them.
These people would have IQ scores placing them wayyy above the population of their current time period, but that wouldn’t change the fact those scores are still in fact accurate.
The scores have nothing to do with the current living population of humanity; those scores are supposed to be relative to general human intelligence regardless of time or place. Ergo, if we assume intelligence is not limited and that humanity survives indefinitely (and that IQ tests actually mean something) then there is a nonzero chance of getting any arbitrary score in the natural numbers. 400, 8000, 10^23, who cares.
As long as you can write tests long enough and you keep testing humans long enough you’ll eventually find someone who scores at those levels without your test being defective. That’s how probability works.
If you still don’t get what I’m saying or what a normal distribution is, I suggest you go to YouTube or peertube to look it up. Chances are they’ll be able to explain it better than me lol
There is a limit. A limit based on population. Because, again, it’s not a score. It’s a quotient.
(Mental Age / Chronological Age) X 100.
Chronological age is the average score of others your age. If you aren’t comparing to the population then you aren’t calculating an IQ.
“Originally” because that’s not the case for modern IQ tests because now we fit the data to a normal distribution, giving us a much more reliable and repeatable experiment.
Furthermore, even if that was quotient formula was still used, the average score of others your age is still a population parameter (something you cannot measure the true value of) that you can only sample and estimate for the possibly indefinite population. Your confidence in your estimate of the average depends on the number of samples; the actual parameter does not because it is (supposedly) an inherent quality of the class of things you’re sampling.
Please just go through a statistics crash course I don’t know how to explain this better.
Sure? 🙂
Yes I’m sure because that’s how math works.
Ah in that case … I’m not really good at maths but … why don’t you go on and correct the wikipedi article, and the one in the Guinnes book … so that people like me, i. e. not that good as maths, won’t be fooled anymore by those articles?
Guinness sets their own standards and they are considered valid source by Wikipedia.
I’d recommend somebody who actually has experience editing take care of that edit. My only edit was to remove a bogus citation for fake ethnic identity used by white supremacists on the page of a pornstar. And that page no longer exists.
The alternative is that the test isn’t trustworthy in the upper and lower ranges (or at all), but that’s unpossible.
That’s not it. Your IQ isn’t the score on the test. It’s the score divided by the score of every in your age group multiplied by 100. It’s upper limit isn’t based on how well you did. It’s based on the population. That’s why it’s an IQ, Intelligence Quotient, not an IS, Intelligence Score.
It is mathematically impossible to get an IQ over 201 given the population of the planet. And that’s using the generous 16 point deviation most use the 15 point SD. That one allows for a maximum score of 195 with the current population.
To add to this, above a given level of intellectual ability, the tests are not capable of measuring. If we both get every question correct, we do not necessarily have the same intellectual ability even though the test will say we both deviated from the mean by the same amount.
You can find plenty of Redditors who tell you they’re over 300, I’m not impressed
That is not some redditor but one person, who impressed the Guinness book of world record staff. And before you go on, that they too don’t impress you … I neither bother if that person had such an IQ or not, nor do I bother by you being impressed or not.
😒 this guy doesn’t have a 400 IQ like me