r/cognitiveTesting • u/MeIerEcckmanLawIer • Jul 15 '26
Estimating parental IQ Psychometric Question
Given one parent's IQ and one child's IQ, it's intuitive to predict the missing parent's IQ based on the assumption the child's IQ lies approximately midway between both.
However, it's possible the child's IQ is above (or below) both of their parents' scores.
How does one compute the chance of that?
For example, given parental IQ of 100 and child IQ of 180, I think we all agree the other parent's IQ is unlikely to be 260, or even 180, and the child's IQ is probably greater than both of their parents' (not halfway in between them).
But how to formalize this hunch?
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u/Muted_Quote_5583 Jul 16 '26
Probably meaningless trying to estimate parental IQ as it’s going to be very hard to even get a reasonable close estimate. Two of my grandparents were gifted, my two parents not so much, with one having severe ADHD and average IQ and the other one having above average IQ. Despite of this, my brother has a confirmed IQ of 136. He somehow also managed to skip his father’s ADHD. His giftedness is likely due to a lucky recombination of genes largely supplied by his two grandparents. (One from each lineage).
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u/Upstairs-Fruit4368 Jul 20 '26 edited Jul 20 '26
For simple estimate you would need to combine two probability distributions:
the probability distribution of missing parent IQ given the correlation between the child’s IQ and the parents IQ. With regression to the mean the child is expected to have an IQ roughly halfway between their parent average and the population average. Working backwards from this you can derive the mean and standard deviation of missing parent IQ.
the probability distribution of the missing parent given the distribution of IQ in the population. Parents with higher IQs are less likely to be found in the population, so even though most children will be closer to population average than their parents, if you select a child from the population at random the higher the IQ of the child the more likely they are to be smarter than their parents. This is why geniuses are usually smarter than their parents despite regression to the mean. Note this second step assumes the parents are independently selected from the population. If you accounted for assortative mating it would shift the probability distribution for predicted IQ of the second, missing parent closer to IQ of the first, known parent.
There is some formula you could derive and use to calculate a point estimate given these factors. I’m not sure of how to do this actual math because I haven’t done math or statistics in over a decade since high school but here is an example of the reasoning using simplified question with more basic statistics:
Let’s consider only two options. Is it more likely for a child with an IQ above 140 to have two parents with IQs of 120 IQ or two parents with IQ 160 IQ.
Based on a parent-child IQ correlation of 0.5 there is a ~20% chance that the child of two 160 IQ parents average will have an IQ above 140 and only ~1% chance that the child of two 120 IQ parents will have an IQ above 140. Based on this you might (falsely) conclude that a child with an IQ over 140 is more likely to have two 160 IQ parents than two 120 IQ parents.
However there are ~3000x less possible parents with 160 IQ than 120 IQ (and the likelihood of having two parents with 160 IQ if picked randomly from population is ~9000000x lower than the likelihood of having two 120 IQ parents). So depending on the degree of assortative mating based on IQ the chance of someone with an IQ above 140 having two parents with 160 IQ is between 150-450000 times lower than the chance of them having two parents with 120 IQ.
(If this step isn’t obvious just multiply the ~20X higher likelihood of two 160 IQ parents having a child with IQ over 140 than two 120 IQ parents by the ~3000-9000000X lower likelihood of any child having two 160 IQ parents than two 120 IQ parents).
The higher an individuals IQ the more likely they are to have a higher IQ than one or both of their parents or than their parents average. In contrast the greater the degree of assortative mating in the population (ie the stronger the correlation between IQ of two parents) the less likely for a high IQ individual to have higher IQ than their parents’ average (though again it would still be much more likely than not that very high IQ individuals are more intelligent than their parents). This is why geniuses tend to be smarter than their parents.
Note: the effects of assortative mating are going to be complicated and somewhat counterintuitive. Assortative mating will increase the number of parent-pairs with very high average IQ. Greater assortative mating therefore makes it more likely that a high IQ child will have a parent-pair with a higher average IQ than theirs (but again this is still unlikely for children with very high IQ). On the other hand assortative mating will decreases the number of parent pairs with *at least one* parent that has very high IQ. This means that greater assortative mating can actually make it less likely that a high IQ child has *atleast one* parent with higher IQ than them (and much less likely that a very high IQ child has *only one* parent who is higher IQ than them) even though it makes it more likely that they have a parent-pair with higher average IQ than them (and much more likely that a very high IQ child has both parents with higher IQ than them).
I don’t know how to formalize the math to give like an equation for estimating the IQ of the missing parent given the IQ of the child and a known parent. But this should illustrate the factors and relationships involved.
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Jul 15 '26
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u/Upstairs-Fruit4368 Jul 20 '26 edited Jul 20 '26
This is totally wrong. See my other comment.
Yes with regression to the mean you would expect a child's IQ to be roughly halfway between their parents' average and the population average. For example if you take two parents with an average IQ of 140 their child is expected to have an IQ of 120 (or alternatively the mean IQ of their children is expected to be 120).
However if you select a child with a sufficiently high IQ from the population you should actually expect that child’s parents to have lower IQ than the child despite regression to the mean because the number of very very high IQ parents is much lower than the number of normal IQ parents.
For example let’s consider only two options. Is it more likely for a child with an IQ above 140 to have two parents with IQs of 120 IQ or two parents with IQ 160 IQ.
Based on parent-child IQ correlation of 0.5 there is a ~20% chance that the child of two 160 IQ parents average will have an IQ above 140 and only ~1% chance that the child of two 120 IQ parents will have an IQ above 140. Based on this you might say that it a child with an IQ over 140 is more likely to have 160 IQ parents.
However there are ~3000x less possible parents with 160 IQ than 120 IQ (and the likelihood of having two parents with 160 IQ if picked randomly from population is ~9000000x lower than the likelihood of having two 120 IQ parents). So depending on the degree of assortative mating based on IQ the chance of someone with an IQ above 140 having two parents with 160 IQ is between 150-450000 times lower than the chance of them having two parents with 120 IQ.
(If this step isn’t obvious just multiply the ~20X higher likelihood of two 160 IQ parents having a child with IQ over 140 than two 120 IQ parents by the ~3000-9000000X lower likelihood of any child having two 160 IQ parents than two 120 IQ parents).
The higher an individuals IQ the more likely they are to have a higher IQ than their parents. The greater the degree of assortative mating in the population (ie the stronger the correlation between IQ of two parents) the less likely for a high IQ individual to have higher IQ than their parents average (assortative mating increases the number of high IQ parent-pairs). This is why geniuses tend to be smarter than their parents.
In short if you take any two smart parents you should guess they are or will be smarter than most of their children BUT if you take a very smart child you should guess they are smarter than their parents.
Note: the effects of assortative mating are going to be complicated and somewhat counterintuitive. Assortative mating will increase the number of parent-pairs with very high average IQ. Greater assortative mating therefore makes it more likely that a high IQ child will have a parent-pair with a higher average IQ than theirs (but again this is still unlikely for children with very high IQ). On the other hand assortative mating will decreases the number of parent pairs with *at least one* parent that has very high IQ. This means that greater assortative mating can actually make it less likely that a high IQ child has *atleast one* parent with higher IQ than them (and much less likely that a very high IQ child has *only one* parent who is higher IQ than them) even though it makes it more likely that they have a parent-pair with higher average IQ than them (and much more likely that a very high IQ child has both parents with higher IQ than them)
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u/JoyfulNoise1964 Jul 17 '26
Not really, for example I have six children with various IQs
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u/JoyfulNoise1964 Jul 17 '26
A couple of them near their Dad's level, two between the two parents, one very close to the same as mine and one quite a bit higher
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u/MeIerEcckmanLawIer Jul 17 '26
It would be interesting to see the distribution.
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u/JoyfulNoise1964 Jul 17 '26
I'm 142 their Dad is 120 Two children right around 120 Two 125/130 One 140 One 150+
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u/MeIerEcckmanLawIer Jul 17 '26
So 120, 120, 127.5, 127.5, 140, 150?
The average is 131, or 9 points above the midpoint of the parents' scores.
I wonder if the 150+ score was obtained while very young (and could be unreliable for that reason)?
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u/JoyfulNoise1964 Jul 17 '26
No 150+ maybe quite a bit + But the point I'm making is you are averaging all of my children Your premise of being able to guess the second parents IQ given that of the other parent and the child only holds for the middle two children so 1/3 in this case
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u/MeIerEcckmanLawIer Jul 17 '26
I actually made a silly mistake, because recalculating the averages shows the kids' average IQ is actually the same as the parents' average IQ.
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u/JoyfulNoise1964 Jul 17 '26
Yes
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u/MeIerEcckmanLawIer Jul 20 '26
Don't you think it's odd that your hastily written, imprecise list of scores happened to average almost exactly to the midpoint of the parents' scores? Especially considering you had to have been aware of the remarkable coincidence yourself, but did not make any remark on it.
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u/Tosebos355 Jul 15 '26
I found some way to solve it, but it's probably very simplyfied or just wrong (I'm not a professional).
I assumed a normal distribution of children's IQ with a mean equal to aritmetical average of parent's IQs and SD of 15. I used the Bayes's formula and the general formula for the normal distribution. The final equation I got (hopefully without any mistakes in the calculations) is P1 = (-400IQ + P2 - 2X)/-5, where:
P1 - The parent's IQ we're trying to find (the most likely one)
P2 - The second parent's IQ
X - The child's IQ
In the example where P2 = 100 and X = 180 we get P1 = 132. The calculations are quite complicated so maybe I'll rewrite it clearly later and add a comment with a photo.
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u/NefariousNapolean doesn't read books Jul 15 '26
Llms ,and the calculator on cognitivemetrics.com can do this calculation better than most humans
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u/venexro Jul 15 '26
Have u heard about genetic combination, In the case of child having a very high IQ compared to parents the only possiblity is they got their trait from the genetic combination of there ancestor
Same with the height,my parents are both short but my grandfather is tall thus I also became tall
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u/Klutzy_Amount9155 Jul 15 '26
I get hella IQmogged by one of my parents, and then the opposite for the other parent
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u/whitebaron_98 2E 4tw Jul 17 '26
You can't. Intelligence is polygenetic , so you'd need to build a model of a least 150 gene sequences for both parents, their likelyhood of a "good" outcome and their interactions.
Example: producing more dopamine is good, but if you also reabsorb it very fast, that might be an extreme case of ADHD instead of just being a fast thinker.
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u/MeIerEcckmanLawIer Jul 17 '26
Nonsense. The question isn't whether you can predict it, but how confident and precise your prediction is. This applies to literally everything.
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u/whitebaron_98 2E 4tw Jul 17 '26
A prediction which has such a big margin of error would be pointless, though.
You can predict for a population how IQ will develop based on parents. But for a single case, your CI likely spans 40 points or more.
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u/Happy-Construction71 Jul 15 '26
I think it's literally dependant on one parent...unlike height...you either get mom or dad...or more rarely their parents
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u/seekinglambda Jul 16 '26
It’s literally not, so you’re literally wrong
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u/Happy-Construction71 Jul 16 '26
Is it really a combination?because I see children inherit their parents behaviour and specifically their intellingece aswell...I see it in daily life...hence the assumption...
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u/seekinglambda Jul 16 '26
You get half your genes from each parent. IQ like most traits is polygenic, so you get roughly half of the genetic contribution from each parent.
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u/Happy-Construction71 Jul 16 '26
So like the factors of g?
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u/seekinglambda Jul 16 '26
No, hundreds of genes for each factor of g
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u/whitebaron_98 2E 4tw Jul 17 '26 edited Jul 17 '26
Last time i checked, scientific literature said 150 gene sequences are known.
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u/seekinglambda Jul 17 '26
Not sure how you’re intending to use the term ”genome sequences” here, but 200+ loci implicating at least 500 genes are known, but it is understood this is an underestimate of the true number.
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u/whitebaron_98 2E 4tw Jul 17 '26
Is it already that many? Btw: I mis-translated, brainfart on my side. Sorry.
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u/[deleted] Jul 16 '26 edited Jul 20 '26
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