Cobb, M. V., & Hollingworth, L. S. (1925). The regression of siblings of children who test at or above 135 IQ. Journal of Educational Psychology, 16(1), 1.
One of the first ideas I learned in graduate school (psych), was that of the "hypothetical construct". "intelligence" as addressed in psych is one such. The trait is one we infer. Originally I think because Binet set out to find out which people did well in school. what he put together (as set of questions) was predictive. voila--intelligence had its birth. but at heart it is still just an operationalization of an idea. and your off-hand idea that much of psychology is void if such things as intelligence are not ratio scale is profound. To me, the fact that such tests predict so much in the real world (maybe in spite of being non-ratio) is fascinating. I am over the hill at age 78 so it doesn't matter to me except for some curiosity that won't settle down. TY EK.
I thought most anthropometric traits, such as height, weight, body mass index, are better approximated by a log-normal distribution. See 'The limits of normal approximation for adult height'.
> from genetics we know that there is a thing called regression towards the mean.
I don't think this really affects the post, but we shouldn't need to rely on genetics to know about regression to the mean. Regression to the mean must occur wherever measurement errors exist. (...under the assumptions that being closer to the mean is more common than being farther away from it, and that measurement errors are symmetrical.) Offspring will regress to a mean compared to their parents, but individuals will also regress to a mean when compared to themselves, because of measurement error. And we could even say that the reason we expect regression to the mean in inheritance is precisely that the genes of the offspring are those of the parents, plus some sampling error.
This got me curious about how much regression to the mean should be expected "in general". Suppose we take a population with mean height 1700 millimeters, measure a bunch of them using some technique where the error is normally distributed with mean 0mm and standard deviation 2mm, and pick out everyone who's 1800mm or taller. Then we measure our 1800+ population again with the same technique. More people will retest as shorter-than-originally than as taller-than-originally. How much regression to the mean do we expect?
> Given that height is easy to measure accurately, random measurement error is rarely a major cause of RTM for height. The real explanation is that, as a general rule, parents can only transmit their additive genetic effects to their children. Other influences on parents’ own traits, such as non-additive genetic effects and accidents of individual development (e.g., a severe illness contracted early in life), will usually not be transmitted to children for lack of reliable mechanisms for such transmission. If parents have extreme phenotypic values due to other influences than additive genetic ones, those influences cannot be transmitted to their children who therefore tend to be phenotypically less extreme (more average) than their parents.
Granted, if you are stunted by early-life starvation, your children will be taller than would be predicted from your adult height. But I don't think that can explain much of the observed regression between parents and children. Starvation is rare.
On the other hand, a child only gets half of each parent's genes. If you assume that the parent's height is fully determined by additive genetic effects, you'll still see regression to the mean in the height of their children, because there is variation in which of those additive genetic effects are passed on to each child. This is the "sampling error" I referred to above.
Genetic regression to the mean is more a matter of sampling error than it is a matter of "stable, non-transmissible influences".
Numerically, that is quite easy - in your original sample you had individuals who all jumped above 1800mm. Once? Right? Let's say the standard deviation for the measurement error is 30mm. So if someone was really 1799mm, and was clocked at 1800mm you just have to calculate the probability of 2nd error being -2mm, if he was clocked at 1801, the probability of 2nd error being at -3mm and so on. Continue till ..., then you would need to do the same at 1798 etc. If I calculate correctly, you'd end up with 3 summations, so it's numerically intensive, but R will do it for you in seconds.
But that's just regression to the mean over an average of two measurements...
Of course you could also have the situation that someone was really 1801, and was initially clocked correctly at above 1800, but then through a 2nd measurement got underwater... That will happen with a certain probability too.
"Similarly, if you made a test of 3rd grade arithmetic and gave it to some math PhD students, the performance would presumably be nearly perfect and not very normally distributed." Don't be so sure :)
Also, would asking whether interval/ratio like measures that are mediocre proxies of intelligence (i'm thinking of reaction time, coding tests, and other measures of processing speed as well as cortical neuron density, cranial capacity, and other measures of physiological intelligence) are normally distributed, help us answer these questions? What about proxies of low intelligence, like car accident frequency and such?
Brain size is normally distributed, but we cannot necessarily assume that intelligence is a linear function of brain size. Our measures show a linear relationship, however. Such a linear relationship could result if the relationship is nonlinear and our measurements is non-interval, so it is not conclusive, just plausible. I think the other brain variables are also very normal.
I am not sure about the distribution of reaction time medians/means.
One of the studies Jensen probably read.
Cobb, M. V., & Hollingworth, L. S. (1925). The regression of siblings of children who test at or above 135 IQ. Journal of Educational Psychology, 16(1), 1.
https://archive.org/details/sim_journal-of-educational-psychology_1925-01_16_1/mode/2up
One of the first ideas I learned in graduate school (psych), was that of the "hypothetical construct". "intelligence" as addressed in psych is one such. The trait is one we infer. Originally I think because Binet set out to find out which people did well in school. what he put together (as set of questions) was predictive. voila--intelligence had its birth. but at heart it is still just an operationalization of an idea. and your off-hand idea that much of psychology is void if such things as intelligence are not ratio scale is profound. To me, the fact that such tests predict so much in the real world (maybe in spite of being non-ratio) is fascinating. I am over the hill at age 78 so it doesn't matter to me except for some curiosity that won't settle down. TY EK.
I thought most anthropometric traits, such as height, weight, body mass index, are better approximated by a log-normal distribution. See 'The limits of normal approximation for adult height'.
https://pmc.ncbi.nlm.nih.gov/articles/PMC8298501/
If that applies to IQ too how much does that change things?
> from genetics we know that there is a thing called regression towards the mean.
I don't think this really affects the post, but we shouldn't need to rely on genetics to know about regression to the mean. Regression to the mean must occur wherever measurement errors exist. (...under the assumptions that being closer to the mean is more common than being farther away from it, and that measurement errors are symmetrical.) Offspring will regress to a mean compared to their parents, but individuals will also regress to a mean when compared to themselves, because of measurement error. And we could even say that the reason we expect regression to the mean in inheritance is precisely that the genes of the offspring are those of the parents, plus some sampling error.
This got me curious about how much regression to the mean should be expected "in general". Suppose we take a population with mean height 1700 millimeters, measure a bunch of them using some technique where the error is normally distributed with mean 0mm and standard deviation 2mm, and pick out everyone who's 1800mm or taller. Then we measure our 1800+ population again with the same technique. More people will retest as shorter-than-originally than as taller-than-originally. How much regression to the mean do we expect?
There are 3 different variants of RttM, and I am referring to the genetic one here, not the measurement error/sampling error one. Cf. https://humanvarieties.org/2017/07/01/measurement-error-regression-to-the-mean-and-group-differences/
I'm not sure I buy what it says there:
> Given that height is easy to measure accurately, random measurement error is rarely a major cause of RTM for height. The real explanation is that, as a general rule, parents can only transmit their additive genetic effects to their children. Other influences on parents’ own traits, such as non-additive genetic effects and accidents of individual development (e.g., a severe illness contracted early in life), will usually not be transmitted to children for lack of reliable mechanisms for such transmission. If parents have extreme phenotypic values due to other influences than additive genetic ones, those influences cannot be transmitted to their children who therefore tend to be phenotypically less extreme (more average) than their parents.
Granted, if you are stunted by early-life starvation, your children will be taller than would be predicted from your adult height. But I don't think that can explain much of the observed regression between parents and children. Starvation is rare.
On the other hand, a child only gets half of each parent's genes. If you assume that the parent's height is fully determined by additive genetic effects, you'll still see regression to the mean in the height of their children, because there is variation in which of those additive genetic effects are passed on to each child. This is the "sampling error" I referred to above.
Genetic regression to the mean is more a matter of sampling error than it is a matter of "stable, non-transmissible influences".
Numerically, that is quite easy - in your original sample you had individuals who all jumped above 1800mm. Once? Right? Let's say the standard deviation for the measurement error is 30mm. So if someone was really 1799mm, and was clocked at 1800mm you just have to calculate the probability of 2nd error being -2mm, if he was clocked at 1801, the probability of 2nd error being at -3mm and so on. Continue till ..., then you would need to do the same at 1798 etc. If I calculate correctly, you'd end up with 3 summations, so it's numerically intensive, but R will do it for you in seconds.
But that's just regression to the mean over an average of two measurements...
Of course you could also have the situation that someone was really 1801, and was initially clocked correctly at above 1800, but then through a 2nd measurement got underwater... That will happen with a certain probability too.
"Similarly, if you made a test of 3rd grade arithmetic and gave it to some math PhD students, the performance would presumably be nearly perfect and not very normally distributed." Don't be so sure :)
Also, would asking whether interval/ratio like measures that are mediocre proxies of intelligence (i'm thinking of reaction time, coding tests, and other measures of processing speed as well as cortical neuron density, cranial capacity, and other measures of physiological intelligence) are normally distributed, help us answer these questions? What about proxies of low intelligence, like car accident frequency and such?
Brain size is normally distributed, but we cannot necessarily assume that intelligence is a linear function of brain size. Our measures show a linear relationship, however. Such a linear relationship could result if the relationship is nonlinear and our measurements is non-interval, so it is not conclusive, just plausible. I think the other brain variables are also very normal.
I am not sure about the distribution of reaction time medians/means.