it is not necessarily. it is an assumption based on CLT >In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
https://en.wikipedia.org/wiki/Central_limit_theorem
I bet that in practice there are fat tails for which a Gaussian distribution is a bad fit.
I don't think that's using the CLT correctly. CLT says that the mean/sum of variables tend to be normal, not the variables themselves.
https://i.imgur.com/LYrDATv.jpg
why is iq normally distributed?
A lot of things in nature are normally distributed. This is likely just the natural tendency for the middle values to be more common, and the more "extreme" values to be less likely.
Intelligence test scores are normal distributed. That doesn’t mean intelligence is normal distributed.
I would guess tests are designed to cover a large range of intelligence, such as have many questions, and the score is some large sum over individual questions. The normal distribution then applies to the scores, not the intelligence.
it is an obsolete science from the last century used to measure the intelligence of humans.
to truly measure a human's intelligence, it takes more than a simple test.
another reason it's a failed metric.
Intelligence test scores are normal distributed. That doesn’t mean intelligence is normal distributed.
I would guess tests are designed to cover a large range of intelligence, such as have many questions, and the score is some large sum over individual questions. The normal distribution then applies to the scores, not the intelligence.
wrong >A lot of things in nature are normally distributed.
it is an obsolete science from the last century used to measure the intelligence of humans.
to truly measure a human's intelligence, it takes more than a simple test.
Because it’s defined to be. The tester generates, in order: >number of points you got on various parts >a raw percentile score compared yo other test takers >a z-score assuming normal distribution >an IQ score using [math]mu=100[/math] and [math]sigma=[/math] 15 or 16 depending on which IQ test youve taken
Because the normal distribution is highly efficient. You should study it more, it's a very beautiful distribution.
Anyway, it's because there a many different noises that affect IQ, like anything. Many different little random events coming from countless distributions. When many different distributions interact, in a summation, you typically get a normal distribution due to the CLT.
Noise is typically normal in shape or at least bell like. There may be specific groups of people who have different distributions of course, but like height, there are so many environmental (and random genetic) impacts that everything looks bell shaped.
Of course, IQ is not actually normal. It's probably more close to the distribution you get when rolling many different dice and taking their sums. It's shape is just modelled very well by the normal distribution, but the reality is, humans have limits on their IQs from both ends. You can't ever have a negative IQ for example, so you already know it's not a 'typical' normal distribution.
And ignore all these morons on this thread, anon. The real reason intelligence is distributed on a gaussian is because intelligence alleles are additive in nature, with each allele having two options/forms of being and with those alleles being basically independent. This makes variance of intelligence essentially a consequence of a very high amount of "coinflips"(allele form switches), which is a binomial distribution in a discrete case and a gaussian in a continuous case(assuming "infinite coinflips"). The amount of alleles is so large alongside the error and environmental effects that we just take the continuous case as properly representative.
Look at this video:
Imagine that ball is the prediction or progression of one's intelligence as we know more information or genes express themselves more. We start assuming the average. On each bolt/peg the ball can either fall left or right, therefore representing two potential options, same way an allele can be in two forms. Just imagine all forms of alleles affecting intelligence in the favorable direction are the ball rolling right and all forms of alleles negatively affecting intelligence are the ball rolling left. Then each floor of pegs is an allele affecting intelligence and we have an uncanny amount of those. This of course has some large assumption, such as each allele being the same effect size.
(cont.)
Additionally, please note this exception: > An interesting exception involves severe intellectual disability (IQ < 70), which DF extremes analysis suggests is etiologically distinct from the normal distribution of intelligence (Reichenberg et al., in press).
If we include those, then the distribution will become left-skewed. This phenomenon arises because a single ill mutation may annihilate your entire brain, but there is no such mutation for being a genius. Statistically-speaking the skew is the consequence of large size effects in one direction and not the other.
You know every distribution is ultimately a binomial distribution right? The reason binomials add up to a normal shape is the same reason every distribution does.
The world of statistical noise tends to be bellshaped and symmetric because so many different random variables are at play, many drawing from the same or similar distributions
Philosophy, history, and IQ are the three things the academic humanities have. The rest is garbage. IQ research is also tightly related to essentially all research everywhere by proxy of p-value to the extent of phenomena like Higgs-Boson. You really sure you wanna take the high way on this on, anon?
2 years ago
Anonymous
Give up, IQ is not real, the variance in the same subject can be as high as 30%, in the same subject. You expect anyone to take a metric that can measure someones IQ at 130 one day and like 100 the next seriously?
That metric also coming out of a field of study that is infamous for not being able to replicate well over three fourths of all studies ever conducted? Give it up.
Psychology is a joke.
2 years ago
Anonymous
low IQ cope. Psychology is trash, but not because of IQ. It's the other way around, the very first inch we made towards understanding humans, everyone got offended and now we're stuck administering antipsychotics to unruly children and meth to children that don't pay attention.
Additionally: > > with reproducibility being generally stronger in studies and journals representing cognitive psychology than social psychology topics,[214] and the subfields of differential psychology (including general intelligence and Big Five personality traits research),[215][216] behavioral genetics (except for candidate gene and candidate gene-by-environment interaction research on behavior and mental illness),[217][218] and the related field of behavioral economics being largely unaffected by the replication crisis.[219]
> You expect anyone to take a metric that can measure someones IQ at 130 one day and like 100 the next seriously?
Buzzfeed tier testing.
it is not necessarily. it is an assumption based on CLT
>In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
https://en.wikipedia.org/wiki/Central_limit_theorem
I bet that in practice there are fat tails for which a Gaussian distribution is a bad fit.
I don't think that's using the CLT correctly. CLT says that the mean/sum of variables tend to be normal, not the variables themselves.
A lot of things in nature are normally distributed. This is likely just the natural tendency for the middle values to be more common, and the more "extreme" values to be less likely.
Intelligence test scores are normal distributed. That doesn’t mean intelligence is normal distributed.
I would guess tests are designed to cover a large range of intelligence, such as have many questions, and the score is some large sum over individual questions. The normal distribution then applies to the scores, not the intelligence.
wrong
>A lot of things in nature are normally distributed.
that's an excuse not an reason.
bicause its an intrinsic qualia of chance.
it is an obsolete science from the last century used to measure the intelligence of humans.
to truly measure a human's intelligence, it takes more than a simple test.
another reason it's a failed metric.
It's normally distributed by definition. Same reason the mean is 100.
https://www.youtube.com/shorts/Vo9Esp1yaC8
bicause its a intrinsic quality of chance.
Because it’s defined to be. The tester generates, in order:
>number of points you got on various parts
>a raw percentile score compared yo other test takers
>a z-score assuming normal distribution
>an IQ score using [math]mu=100[/math] and [math]sigma=[/math] 15 or 16 depending on which IQ test youve taken
Because the normal distribution is highly efficient. You should study it more, it's a very beautiful distribution.
Anyway, it's because there a many different noises that affect IQ, like anything. Many different little random events coming from countless distributions. When many different distributions interact, in a summation, you typically get a normal distribution due to the CLT.
Noise is typically normal in shape or at least bell like. There may be specific groups of people who have different distributions of course, but like height, there are so many environmental (and random genetic) impacts that everything looks bell shaped.
Of course, IQ is not actually normal. It's probably more close to the distribution you get when rolling many different dice and taking their sums. It's shape is just modelled very well by the normal distribution, but the reality is, humans have limits on their IQs from both ends. You can't ever have a negative IQ for example, so you already know it's not a 'typical' normal distribution.
Read this: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4739500/
And ignore all these morons on this thread, anon. The real reason intelligence is distributed on a gaussian is because intelligence alleles are additive in nature, with each allele having two options/forms of being and with those alleles being basically independent. This makes variance of intelligence essentially a consequence of a very high amount of "coinflips"(allele form switches), which is a binomial distribution in a discrete case and a gaussian in a continuous case(assuming "infinite coinflips"). The amount of alleles is so large alongside the error and environmental effects that we just take the continuous case as properly representative.
Look at this video:
Imagine that ball is the prediction or progression of one's intelligence as we know more information or genes express themselves more. We start assuming the average. On each bolt/peg the ball can either fall left or right, therefore representing two potential options, same way an allele can be in two forms. Just imagine all forms of alleles affecting intelligence in the favorable direction are the ball rolling right and all forms of alleles negatively affecting intelligence are the ball rolling left. Then each floor of pegs is an allele affecting intelligence and we have an uncanny amount of those. This of course has some large assumption, such as each allele being the same effect size.
(cont.)
Forgot video: https://www.youtube.com/watch?v=3m4bxse2JEQ
Additionally, please note this exception:
> An interesting exception involves severe intellectual disability (IQ < 70), which DF extremes analysis suggests is etiologically distinct from the normal distribution of intelligence (Reichenberg et al., in press).
If we include those, then the distribution will become left-skewed. This phenomenon arises because a single ill mutation may annihilate your entire brain, but there is no such mutation for being a genius. Statistically-speaking the skew is the consequence of large size effects in one direction and not the other.
*sorry that video is a bit confusing this one is a bit better: https://www.youtube.com/watch?v=4HpvBZnHOVI
You know every distribution is ultimately a binomial distribution right? The reason binomials add up to a normal shape is the same reason every distribution does.
The world of statistical noise tends to be bellshaped and symmetric because so many different random variables are at play, many drawing from the same or similar distributions
IQ isn’t normally distributed since it’s fat tailed
On the left maybe. lmfao
Midwit cope to the max, there is no magical excess of geniuses.
https://medium.com/incerto/iq-is-largely-a-pseudoscientific-swindle-f131c101ba39
Philosophy, history, and IQ are the three things the academic humanities have. The rest is garbage. IQ research is also tightly related to essentially all research everywhere by proxy of p-value to the extent of phenomena like Higgs-Boson. You really sure you wanna take the high way on this on, anon?
Give up, IQ is not real, the variance in the same subject can be as high as 30%, in the same subject. You expect anyone to take a metric that can measure someones IQ at 130 one day and like 100 the next seriously?
That metric also coming out of a field of study that is infamous for not being able to replicate well over three fourths of all studies ever conducted? Give it up.
Psychology is a joke.
low IQ cope. Psychology is trash, but not because of IQ. It's the other way around, the very first inch we made towards understanding humans, everyone got offended and now we're stuck administering antipsychotics to unruly children and meth to children that don't pay attention.
Additionally:
> > with reproducibility being generally stronger in studies and journals representing cognitive psychology than social psychology topics,[214] and the subfields of differential psychology (including general intelligence and Big Five personality traits research),[215][216] behavioral genetics (except for candidate gene and candidate gene-by-environment interaction research on behavior and mental illness),[217][218] and the related field of behavioral economics being largely unaffected by the replication crisis.[219]
> You expect anyone to take a metric that can measure someones IQ at 130 one day and like 100 the next seriously?
Buzzfeed tier testing.