Always great to see this discussed. IQ is less like height and more like mountains - rarefied tall outliers skew the average height up, obscuring the many minute foothills. Similar writings by Nassim Taleb, and which align with my own experience, suggests a skew even more extreme than presented here.
I am wondering if the level of kurtosis of a group, ideally measured with multiple highly heritable variables, could be a decent proxy for the groups genetic load. This could be used on sufficiently large datasets without genetic data, and potentially validated on datasets with genetic data, or perhaps ones that have a variable on the age of parents.
I'm sorry but this article has made me completely confused, to the point where I now question whether I understand IQ at all:
I have always read that the IQ scale is FORCED to be normal, by making an arbitrarily complex mapping from raw score to IQ points. So a score of 130 always mean that you are at the 98th percentile, exactly because the raw score matching 98th percentile is always mapped exactly to IQ 130, the median in raw points are mapped to IQ 100, the 99.9th percentile to 145... etc.
So if there is some skewness it must necessarily mean that there has been some error in the mapping from raw score to IQ. By definition the normed IQ of a sample must be normal, even if the raw points are skewed as the tower of Pisa.
>I have always read that the IQ scale is FORCED to be normal, by making an arbitrarily complex mapping from raw score to IQ points. So a score of 130 always mean that you are at the 98th percentile, exactly because the raw score matching 98th percentile is always mapped exactly to IQ 130, the median in raw points are mapped to IQ 100, the 99.9th percentile to 145... etc.
Yes.
>So if there is some skewness it must necessarily mean that there has been some error in the mapping from raw score to IQ. By definition the normed IQ of a sample must be normal, even if the raw points are skewed as the tower of Pisa.
That is correct. IQs scored in real life (not on computers) will not perfectly map to intelligence for several reasons, but violations in normality will make it so that an IQ score of 130 is more distant from 100 than 160 in "true intelligence".
Thanks for the reply. But what do we mean here by 'true intelligence'?
Let us say that you have a test with 50 questions. You give it to 1000 people.
500 people get 37 or fewer correct answes, so we map 37 points to IQ 100.
840 people get 42 or fewer points, so we map 42 to IQ 115.
980 people get less than 48 correct, so we map a score of 48 to IQ 130. There is a single person in the sample who gets 49 correct, so we map 49 points to IQ 145 (99.9th percentile). Since not a single person got 50 points we can't really map that anywhere.
In what sense can we then say that the distance from 42 correct answers to 48 correct answers is shorter or longer than the distance from 48 to 49 correct answers?
Always great to see this discussed. IQ is less like height and more like mountains - rarefied tall outliers skew the average height up, obscuring the many minute foothills. Similar writings by Nassim Taleb, and which align with my own experience, suggests a skew even more extreme than presented here.
The left tail theory is supported by the iq distributions of siblings and co-twins when one has mild vs severe ID(the large swedish and israeli studies were posted by cremieux on twitter). It's just the case that most severe ID(and to some extent mild) cases are the result of a developmental issue in a gentile white american population. And the frequency is roughly the same in populations, so I wonder if differences in the standard deviation can be explained by that. But I'm not sure this explains SLODR, if anything mentally disabled individuals have a lower g loading/measurement non-invariance(https://www.research.unipd.it/bitstream/11577/3196682/1/Giofr%C3%A8%2C%20D.%2C%20%26%20Cornoldi%2C%20C.%20(2015).%20The%20structure%20of%20intelligence%20in%20children%20with%20specific%20learning%20disabilities%20is%20different%20as%20compared%20to%20typically%20development%20children.%20Intelligen.pdf). Height has roughly the same distribution as intelligence with a left tail, and similarly rare cases of gigantism/savants have minimal impact on the distribution.
So, how many less people in 140+ range in the US white population than the estimation that uses the normal distribution?
Seems the left-tailedness could be completely explained by some participants not putting in full effort on the tests.
I am wondering if the level of kurtosis of a group, ideally measured with multiple highly heritable variables, could be a decent proxy for the groups genetic load. This could be used on sufficiently large datasets without genetic data, and potentially validated on datasets with genetic data, or perhaps ones that have a variable on the age of parents.
I'm sorry but this article has made me completely confused, to the point where I now question whether I understand IQ at all:
I have always read that the IQ scale is FORCED to be normal, by making an arbitrarily complex mapping from raw score to IQ points. So a score of 130 always mean that you are at the 98th percentile, exactly because the raw score matching 98th percentile is always mapped exactly to IQ 130, the median in raw points are mapped to IQ 100, the 99.9th percentile to 145... etc.
So if there is some skewness it must necessarily mean that there has been some error in the mapping from raw score to IQ. By definition the normed IQ of a sample must be normal, even if the raw points are skewed as the tower of Pisa.
Have I completely misunderstood this concept?
>I have always read that the IQ scale is FORCED to be normal, by making an arbitrarily complex mapping from raw score to IQ points. So a score of 130 always mean that you are at the 98th percentile, exactly because the raw score matching 98th percentile is always mapped exactly to IQ 130, the median in raw points are mapped to IQ 100, the 99.9th percentile to 145... etc.
Yes.
>So if there is some skewness it must necessarily mean that there has been some error in the mapping from raw score to IQ. By definition the normed IQ of a sample must be normal, even if the raw points are skewed as the tower of Pisa.
That is correct. IQs scored in real life (not on computers) will not perfectly map to intelligence for several reasons, but violations in normality will make it so that an IQ score of 130 is more distant from 100 than 160 in "true intelligence".
Thanks for the reply. But what do we mean here by 'true intelligence'?
Let us say that you have a test with 50 questions. You give it to 1000 people.
500 people get 37 or fewer correct answes, so we map 37 points to IQ 100.
840 people get 42 or fewer points, so we map 42 to IQ 115.
980 people get less than 48 correct, so we map a score of 48 to IQ 130. There is a single person in the sample who gets 49 correct, so we map 49 points to IQ 145 (99.9th percentile). Since not a single person got 50 points we can't really map that anywhere.
In what sense can we then say that the distance from 42 correct answers to 48 correct answers is shorter or longer than the distance from 48 to 49 correct answers?
Is this Trend found in the WAIS-IV as well ?
I’m confused and a bit lazy today. How does the “Central Limit Theory” apply to your posting today?
https://substack.com/@stevestewartwilliams/note/c-72405437?r=2kr9ga
Threshold hypothesis =/= SLODR =/= distribution of intelligence
Related ideas and concepts but do not describe the same essence.
Yeah I didn't remember exactly what steve had posted,just thought it was related to your article
I recently read a paper Steve Stewart williams restacked debunking slodr
Which one? I cannot find it.
When I looked at SLODR using UK CAT tests it held up for a ~70 IQ sample versus the general population.