People have to stop resorting to the brain size fallacy when comparing individual differences for three reasons:
1) Brain size is a weak predictor of intelligence. A 2014 meta-anaylsis found brain size only explains 6 % of variance in intelligence among a group of 8000 participants. A 2015 study found brain size only explains 12 % of variance in intelligence in another group.
https://www.researchgate.net/publication/282703216_Meta-Analysis_of_Associations_Between_Human_Brain_Volume_And_Intelligence_Differences_How_Strong_Are_They_and_What_Do_They_Mean
http://www.sciencedirect.com/science/article/pii/S0160289615000616
[b]2) If brain size was a large indicator of intelligence then whales would be the smartest beings on the planet since the long-finned pilot whale neocortex has approximately 37.2 × 109 neurons, which is almost twice as many as humans, and 127 × 109 glial cells. It's not brain to body ratio either since certain types of mice have the same as humans as well.[b]
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4244864/
3) It's brain function that determines intelligence. How the brain functions as result of it's processing and integration efficiency or in other words the way it is wired.
Is there anyone who still believes in the Brain size fallacy?
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You should probably stop using percent of variance as an effect size measure, since it is misleading to non-experts. What matters is the correlation-type measure.
For total brain volume, the correlation from the meta-analysis is about .24 (the exact number depends on which studies one includes in the best subset). Assuming measurement reliability of .94 (around the true value for WAIS), this means an estimated true correlation of .26 or so. Ritchie et al found a correlation of about .35 (not sure if this was corrected for measurement error or not).
So we may conclude that the total volume probably has an effect somewhere in the region of .20 to .45, when accounting for various statistical artifacts (note that these tend to decrease the effect size, cf. Hunter and Schmidt's work).
--
Next you try to use total brain volume in a cross species comparison, which is not the same as the within species comparison where we know that it is relevant. You then use raw brain volume, a measure that pretty much no one thinks is useful (i.e. strawman).
You then add a comment about ratio of brain to body size. Still, as you would know from a cursory look into this topic, this metric is also too simple because it does not account for differential allometry. The main proposed replacement metric is the encephalization quotient, which does try to adjust for differential allometry. https://en.wikipedia.org/wiki/Encephalization_quotient
Of course, this one also has problems.
--
You then claim that it's brain function that determines cognitive ability. Determines is not a good word to use (it is too categorical and tends to upset the people who are confused about determinism in general). Now, since you already argued that total brain volume has some effect, the total effect cannot be functional factors.
Well, you are attacking a strawman. I have not heard of any scholar who has claimed that all individual differences are due to total brain volume. Ritchie et al is a case in point of a set of scholars explicitly looking for more than just total volume.
In my unfinished draft paper, I mentioned the following other reported correlates:
Brain evoked potentials: habituation time (Jensen, 1998:155)
Brain evoked potentials: complexity of waveform (Deary and Carol, 1997)
Brain intracellular pH-level (Jensen, 1998:162)
Brain size: total and brain regions (Jung and Haier, 2007)
Of the above, grey matter and white matter separate
Cortical thickness (Deary et al, 2010)
Cortical development (Shaw, P. et al. 2006)
Nerve conduction velocity (Deary and Carol, 1997)
Brain wave (EEG) coherence (Jensen, 2002)
Event related desynchronization of brain waves (Jensen, 2002)
White matter lesions (Turken et al, 2008)
Concentrations of N-acetyl aspartate (Jung, et al. 2009)
Water diffusion parameters (Deary et al, 2010)
White matter integrity (Deary et al, 2010)
White matter network efficiency (Li et al. 2009)
Cortical glucose metabolic rate during mental activity / Neural efficiency (Neubauer et al, 2009)
Uric acid level (Jensen, 1998:162)
Density of various regions (Frangou et al 2004)
White matter fractional anisotropy (Navas‐Sánchez et al 2014; Kim et al 2014)
Reliable responding to changing inputs (Euler et al, 2015)
--
Now I take it that you are done with this strawman? :) (Crosses fingers)
For total brain volume, the correlation from the meta-analysis is about .24 (the exact number depends on which studies one includes in the best subset). Assuming measurement reliability of .94 (around the true value for WAIS), this means an estimated true correlation of .26 or so. Ritchie et al found a correlation of about .35 (not sure if this was corrected for measurement error or not).
So we may conclude that the total volume probably has an effect somewhere in the region of .20 to .45, when accounting for various statistical artifacts (note that these tend to decrease the effect size, cf. Hunter and Schmidt's work).
--
Next you try to use total brain volume in a cross species comparison, which is not the same as the within species comparison where we know that it is relevant. You then use raw brain volume, a measure that pretty much no one thinks is useful (i.e. strawman).
You then add a comment about ratio of brain to body size. Still, as you would know from a cursory look into this topic, this metric is also too simple because it does not account for differential allometry. The main proposed replacement metric is the encephalization quotient, which does try to adjust for differential allometry. https://en.wikipedia.org/wiki/Encephalization_quotient
Of course, this one also has problems.
--
You then claim that it's brain function that determines cognitive ability. Determines is not a good word to use (it is too categorical and tends to upset the people who are confused about determinism in general). Now, since you already argued that total brain volume has some effect, the total effect cannot be functional factors.
Well, you are attacking a strawman. I have not heard of any scholar who has claimed that all individual differences are due to total brain volume. Ritchie et al is a case in point of a set of scholars explicitly looking for more than just total volume.
In my unfinished draft paper, I mentioned the following other reported correlates:
Brain evoked potentials: habituation time (Jensen, 1998:155)
Brain evoked potentials: complexity of waveform (Deary and Carol, 1997)
Brain intracellular pH-level (Jensen, 1998:162)
Brain size: total and brain regions (Jung and Haier, 2007)
Of the above, grey matter and white matter separate
Cortical thickness (Deary et al, 2010)
Cortical development (Shaw, P. et al. 2006)
Nerve conduction velocity (Deary and Carol, 1997)
Brain wave (EEG) coherence (Jensen, 2002)
Event related desynchronization of brain waves (Jensen, 2002)
White matter lesions (Turken et al, 2008)
Concentrations of N-acetyl aspartate (Jung, et al. 2009)
Water diffusion parameters (Deary et al, 2010)
White matter integrity (Deary et al, 2010)
White matter network efficiency (Li et al. 2009)
Cortical glucose metabolic rate during mental activity / Neural efficiency (Neubauer et al, 2009)
Uric acid level (Jensen, 1998:162)
Density of various regions (Frangou et al 2004)
White matter fractional anisotropy (Navas‐Sánchez et al 2014; Kim et al 2014)
Reliable responding to changing inputs (Euler et al, 2015)
--
Now I take it that you are done with this strawman? :) (Crosses fingers)
Actually I don't think so. Correlation just means relation. A statistical number of 0.45 simply means that brain size has 45 percent relation to intelligence similar to how one can say muscle density has whatever percent relation to athleticism. It means there IS some sort of positive relation with size not that 45 % implies size explains away half of individual differences in intelligence. It doesn't mean much, nor can it be used it any way to explain individual differences in skill nor intelligence (especially of entire groups). One can simply assume brain size places a part in processing capacity which is why one might find that correlation similar to how muscle density might play a part in athletic coordination. Again, on average muscle density cannot be used to explain individual differences in athleticism either.
Variance is definitely more important than correlation. Variance explains magnitude of differences within a population and the studies I quoted demonstrates that brain size can only explain 6-12 % of such differences within a population. Therefore it is obvious that there are SIGNIFICANTLY other neurobiological factors that play in creating individual differences in cognitive processing efficiency, brain function and cognitive abilities (intelligence).
I don't know what related studies you quoted buy you do realize that cortical thickness, white matter integrity and brain networks are NOT indicators of brain size right? Brain size refers to the total gray matter volume of the brain either measured raw or after controlling for body size.
Variance is definitely more important than correlation. Variance explains magnitude of differences within a population and the studies I quoted demonstrates that brain size can only explain 6-12 % of such differences within a population. Therefore it is obvious that there are SIGNIFICANTLY other neurobiological factors that play in creating individual differences in cognitive processing efficiency, brain function and cognitive abilities (intelligence).
I don't know what related studies you quoted buy you do realize that cortical thickness, white matter integrity and brain networks are NOT indicators of brain size right? Brain size refers to the total gray matter volume of the brain either measured raw or after controlling for body size.
Variance is definitely more important than correlation. Variance explains magnitude of differences within a population and the studies I quoted demonstrates that brain size can only explain 6-12 % of such differences within a population.
Telling people, "Don't touch! That plate is a burning hot 300 degrees (kelvin)!" invites a little confusion when people are used to thinking in terms of Fahrenheit.
Effect size r ~ r^2 (variance explained)
Small 0.10 ~ 0.01
Medium 0.30 ~ 0.09
Large 0.50 ~ 0.25
"Same, same" as they say in Thailand.
On correlation, r, and r-squared
The ballpark is ten miles away, but a friend gives you a ride for the first five miles. You’re halfway there, right? Nope, you’re actually only one quarter of the way there.
That’s according to traditional regression analysis, which bases some of its conclusions on the square of the distance, not the distance itself. You had ten times ten, or 100 miles squared to go – your buddy gave you a ride of five times five, or 25 miles squared. So you’re really only 25% of the way there.
This makes no sense in real life, but, if this were a regression, the "r-squared" (which is sometimes called the "coefficient of determination") would indeed be 0.25, and statisticians would say the ride "explains 25% of the variance." There are good mathematical reasons why they say this, but they mean "explains" in the mathematical sense, not in the real-life sense.
For real-life, you can also use "r". That’s the correlation coefficient, which is the square root of 0.25, or 0.5. In this example, obviously the r=0.5 is the value which makes the most sense in the context of getting to the ballpark. Because you really are, in the real life sense, halfway there.
r is usually the value you use to draw real life conclusions from a regression. According to "The Hidden Game of Baseball," if you regress Runs Scored against Winning Percentage, you get an r of .737, which is an r-squared of .543. A statistician might use the r-squared to say that runs "explains 54.3% of the variation in winning percentage." Which is true if you are concerned with the sums of the squares of the differences – and only a statistician cares about those
No I smell confirmation bias from you. The fact is even the author in that meta-analysis has said that researchers overestimate the significance of brain size to intelligence. If brain size only explains 6 percent of the variance then it suggests size alone means nothing. It's could simply be that bigger brain size is masking bigger specific brain regions which may be the true mediator of individual differences and hence confused past researchers. Bigger specific regions can be a better explanatory factor for the variance in intelligence and NOT the global brain volume in itself.
No I smell confirmation bias from you. The fact is even the author in that meta-analysis has said that researchers overestimate the significance of brain size to intelligence. If brain size only explains 6 percent of the variance then it suggests size alone means nothing. It's could simply be that bigger brain size is masking bigger specific brain regions which may be the true mediator of individual differences and hence confused past researchers. Bigger specific regions can be a better explanatory factor for the variance in intelligence and NOT the global brain volume in itself.
SQRT(r^2 =0.06) = r = 0.24. Yes, that's at the low end of the range of estimates. So at minimal, an increase of 0.24 SD IQ per an increase of 1 SD brain size. Consider that the variance explained by all environmental factors which vary in the Black and White American populations is no more than ~ 0.20, thus r = 0.40. Is that 20% variance 3.33*nothing = zip? What are we disagreeing about, again?
SQRT(r^2 =0.06) = r = 0.24. Yes, that's at the low end of the range of estimates. So at minimal, an increase of 0.24 SD IQ per an increase of 1 SD brain size. Consider that the variance explained by all environmental factors which vary in the Black and White American populations is no more than ~ 0.20, thus r = 0.40. Is that 20% variance 3.33*nothing = zip? What are we disagreeing about, again?
I'm not arguing that 6% of the variance is a lot. But rather that it is what it is. I would prefer if people were consistent with their interpretations, though. The US B/W income, years of education, poverty and occupation prestige differences -- which the media tells me are massive -- come out, last I checked, to a between group variance -- in the sense of r^2 -- of about 6% (Cohen's d ~ 0.5). Is this practically non-existent/ of no interest? Well, I, for one, will not try to convince you otherwise!
Too much math I'm not familiar with. Like I said, that brain size may merely mask specific structure size which may be the main cause of individual differences. It is too simplistic to assume a large global size is the main cause of intelligence because in that case why isn't someone like Pat Robertson a genius? The man has a huge cranium (an indication of brain size) yet spends most of his time talking about religious nonsense and magical thinking. ( https://www.youtube.com/watch?v=_WToin3NbYY) Why did Einstein have an average brain size? His post-mortem size was below average but after controlling for age it was exactly average. How about Bill Gates and OJ Simpson? Simpson has a cranium that is 2-3 times as large as the popular billionaire, yet where is his intellectual superiority? So no, essentially the brain's capability cannot be credited to it's size (or else whales would the smartest) but rather it's function, organization and network efficiency. It's quality not quantity. I think most scientists would agree that brain size plays a role alongside cortical thickness and complexity, but obviously functional efficiency plays the biggest factor in individual differences.
If you don't understand introductory statistics, I recommend that you read a stats textbook before commenting further. If you cannot understand intro level statistics, you cannot understand this topic. Compare: If you cannot understand algebra and trigonometry, you cannot understand Newtonian mechanics.
This one is decent and free:
http://health.adelaide.edu.au/psychology/ccs/teaching/lsr/
Otherwise, one can find lots of other choices. A popular choice is Andy Field's book. The strength of it is that it comes made for different statistical software, including R and SPSS. It's on libgen:
http://gen.lib.rus.ec/search.php?req=discovering+statistics&open=0&view=simple&phrase=1&column=def
This one is decent and free:
http://health.adelaide.edu.au/psychology/ccs/teaching/lsr/
Otherwise, one can find lots of other choices. A popular choice is Andy Field's book. The strength of it is that it comes made for different statistical software, including R and SPSS. It's on libgen:
http://gen.lib.rus.ec/search.php?req=discovering+statistics&open=0&view=simple&phrase=1&column=def
Emil, I did something better. I emailed Stuart Ritchie for his own professional opinion on this matter and got a reply. Quote:
Brain size and intelligence
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Hi,
I’m not Dr. Pietschnig, but his recent paper (attached here) is the best evidence that brain size matters for intelligence. It shows that the correlation between brain size and intelligence is not strong, but it is consistently found across brain imaging studies. So brain size is a factor, just not a huge one, in explaining individual differences in intelligence.
Hope that helps,
Stuart
Which proves everything I have been saying. Plays a role in intelligence, not a strong factor and therefore cannot be used to measure individual differences.
Brain size and intelligence
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Hi,
I’m not Dr. Pietschnig, but his recent paper (attached here) is the best evidence that brain size matters for intelligence. It shows that the correlation between brain size and intelligence is not strong, but it is consistently found across brain imaging studies. So brain size is a factor, just not a huge one, in explaining individual differences in intelligence.
Hope that helps,
Stuart
Which proves everything I have been saying. Plays a role in intelligence, not a strong factor and therefore cannot be used to measure individual differences.
So no, essentially the brain's capability cannot be credited to it's size (or else whales would the smartest) but rather it's function, organization and network efficiency.
https://www.youtube.com/watch?v=kkbHi2eT5_U
Which is why humans are smarter than whales because of our brain functions such as cortical organization....
Which is why humans are smarter than whales because of our brain functions such as cortical organization....
What measure of intelligence did you have in mind when it comes to interspecies comparisons?
Emil, this one's for you from Dr. Jakob Pietschnig.
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******** 21/01/2016
To: jakob.pietschnig@univie.ac.at
Dear Dr.Pietschnig,
Is brain size a strong factor in explaining individual differences in intelligence?I have also read that instead of using variance among individuals, correlation is a better factor in interpreting data that links brain size to intelligence. Is that true?
RESPONSE:
Dear *********,
simply put: no, it is not a good predictor (I attached a paper which might clarify things for you). Moreover, you must have misunderstood the concept of correlation. Correlation is a method which describes the strength of associations and which may be used to express the amount of explained variance.
Best regards,
Mag. Dr. Jakob Pietschnig, FHEA
Department for Applied Psychology: Health, Development, Enhancement and Intervention
Faculty of Psychology
University of Vienna
Liebiggasse 5, A-1010 Vienna
Austria
Email: jakob.pietschnig@univie.ac.at
Phone: +43 1 4277 47237
Actions
******** 21/01/2016
To: jakob.pietschnig@univie.ac.at
Dear Dr.Pietschnig,
Is brain size a strong factor in explaining individual differences in intelligence?I have also read that instead of using variance among individuals, correlation is a better factor in interpreting data that links brain size to intelligence. Is that true?
RESPONSE:
Dear *********,
simply put: no, it is not a good predictor (I attached a paper which might clarify things for you). Moreover, you must have misunderstood the concept of correlation. Correlation is a method which describes the strength of associations and which may be used to express the amount of explained variance.
Best regards,
Mag. Dr. Jakob Pietschnig, FHEA
Department for Applied Psychology: Health, Development, Enhancement and Intervention
Faculty of Psychology
University of Vienna
Liebiggasse 5, A-1010 Vienna
Austria
Email: jakob.pietschnig@univie.ac.at
Phone: +43 1 4277 47237
edited. had the wrong numbers before.
Don't be a bird brain. :o)
"Correlation is a method which describes the strength of associations and which may be used to express the amount of explained variance."
This means that the square of r (correlation) = r^2 (variance). Same same. If you are interested in unit increase in X per unit increase in Y, which most people are, then use r, which is what we have been saying.
"simply put: no, it is not a good predictor."
Let's get the matter straight. At one time, the correlation was estimated to be 0.38 (not corrected for range restriction, weighted). A new meta-analysis came out and put the correlation at 0.26 (for healthy subjects, not corrected for range restriction, with missing data filled in with 0 due to the author's conservative approach, weighted). The latter correlation isn't horribly different from the traditional 0.38 value. Either way, we are not dealing with a good predictor.
Presumably what happened is that you saw the .38 correlation that is frequently discussed. And then you saw the 6% variance. And you thought, "6% = 0.06 is a lot lower than 0.38 -- these brain size guys were all wrong!" And so you posted here. But in fact we are not talking about very different values.
Don't be a bird brain. :o)
"Correlation is a method which describes the strength of associations and which may be used to express the amount of explained variance."
This means that the square of r (correlation) = r^2 (variance). Same same. If you are interested in unit increase in X per unit increase in Y, which most people are, then use r, which is what we have been saying.
"simply put: no, it is not a good predictor."
Let's get the matter straight. At one time, the correlation was estimated to be 0.38 (not corrected for range restriction, weighted). A new meta-analysis came out and put the correlation at 0.26 (for healthy subjects, not corrected for range restriction, with missing data filled in with 0 due to the author's conservative approach, weighted). The latter correlation isn't horribly different from the traditional 0.38 value. Either way, we are not dealing with a good predictor.
Presumably what happened is that you saw the .38 correlation that is frequently discussed. And then you saw the 6% variance. And you thought, "6% = 0.06 is a lot lower than 0.38 -- these brain size guys were all wrong!" And so you posted here. But in fact we are not talking about very different values.
Did you even read any of my posts? Both Dr.Pietschnig and Stuart Richie have stated that brain size is NOT a good predictor. I have already posted their email responses on this thread....it's a fact whether you like it or not.
Did you even read any of my posts? Both Dr.Pietschnig and Stuart Richie have stated that brain size is NOT a good predictor. I have already posted their email responses on this thread....it's a fact whether you like it or not.
:op
No one here is disagreeing with the reported effect sizes or with the claim that brain size is NOT a "good" predictor.
The original disagreement was with your claim that:
"Variance is definitely more important than correlation."
[Different ways of expressing the same effect size!]
&
"If brain size only explains 6 percent of the variance then it suggests size alone means nothing"
[Misunderstanding of r^2!]
&
"Which proves everything I have been saying. Plays a role in intelligence, not a strong factor and therefore cannot be used to measure individual differences."
But you originally said "size alone means nothing" -- now you have changed the claim to size alone is "not a strong factor".
So we agree that:
1.The association between brain size and IQ is moderate; thus, brain size is not a GOOD predictor.
2.The association was previously overestimated (0.38 versus 0.26, weighted healthy subjects).
3.The "true" association would be higher were corrections for range restriction made.
4.Correlation and variance explained (as r-squared) are just two different ways of looking at the same effect.
You can't just set aside variance and use correlation as a indicator for it's association with intelligence. Of course variance matters! If brain size as a factor explains very little of variance between individual scores then it's simply is not a good predictor. It simply means brain size has no causal role in intelligence and that may merely share latent traits such as memory capacity with higher order g. The problem as to why many racialists like you fear this is because now you no longer have arm chair logic in explaining racial differences in intelligence. You actually have to go do the work.
You can't just set aside variance and use correlation as a indicator for it's association with intelligence. Of course variance matters! If brain size as a factor explains very little of variance between individual scores then it's simply is not a good predictor. It simply means brain size has no causal role in intelligence and that may merely share latent traits such as memory capacity with higher order g.
Are you just a moron? r= SQRT(r^2).
"You can't just set aside feet and use inches as a indicator for height. While that tarantula may be three inches high, it's only 1/4th of a foot."
Would someone please ban this clown?
This is exactly why your papers get nowhere. Good luck publishing your low quality garbage on sites like these while getting rejected by peer reviewed journals year after year.
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