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A Critique of Brain Size versus Test
Scores
Dear Raymond,
If you think this will damage your reputation, then it will
definitely will not be posted it to the usenet. The only objective is to get out of
the ad hominem stage and onto the discourse stage. If you would like to modify it or
as you suggested before add a counter-point, then we can post it, but only if you
say to. There are 2 million Signatories to the Fathers' Manifesto who are following
this fairly closely who are more interested in facts than invective.
I'd rather not get into a shooting match. It would be pointless and perhaps bloody.
The material I am giving you below this paragraph may be posted if you like. It is my
professional opinion (albeit preliminary). However, if you print it, you must print it in
its entirety, without comment. You may, in a section afterward, comment with quotes and
your own annotations, provided that they are fair and relevant. However, before you post,
you must present to me your comments and additions before posting, along with the
opportunity to respond to any of your concerns with my analysis. I will not require any of
your comments to be deleted. Simply that I have the right to post additional comments, and
that afterward the post be made without further comment. As a professional providing an
opinion, I must insist that these conditions be strictly held to. Agreed?
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You may also find the following page interesting. Your
math expertise could be useful if you're interested in serious discourse:
http://millennium.fortunecity.com/redwood/547/grebrainsize.htm
Sincerely,
John Knight
As a gesture of good-will (but not agreement with your conclusions), I have examined
and will further look at the page and links provided. However I have a few concerns that
need to voiced. This is from a brief read and preliminary analysis of some of the data and
supporting statements.
I am afraid that the data presented does not convince me of the claim that brain mass and
intelligence are significantly correlated. The secondary claim, that intelligence levels
are differentiated by race (unstated, but present), is also AFAIAC, unsubstantiated.
Group means may indeed be compared. But if you correlate averages against averages, you
may get a mess of rather meaningless stuff. Even if the results are more or less ball-park
type accurate (but probably less, far less!), you are going to be contested on the
results. There are a number of objections, including (but not limited to) the fact that
the individuals contributing brain mass data are not the same as the individuals
contributing the test score data. Further frustrating the analysis is the fact that the
"average brain mass data" is for adults, yet some of the data it is being
correlated against on the basis of ethnic origin is from juvenile subjects.
In my opinion, no competent statistical analyst would take much stock in the grouped data
(brain sizes v. test scores, grouped by ethnicity) as it is presented in the page you
referenced (http://millennium.fortunecity.com/redwood/547/grebrainsize.htm). Yes, I know
some analysts have done work using such grouped (and questionably linked) data, but such
work is subject to justifiable criticism. Yes, some of the people who do such work may
hold respectable positions. It makes little difference. The data itself is questionably
linked, so all analyses done with it must be suspect.
Furthermore, even *if* the data could be compared with confidence, it only tells a small
part of the story.
There are also several battles being run about the validity and reliability of educational
testing and the results being reported. These battles are being fought on several fronts,
with the people who put the *most* stock in the comparative validity of grouped scores
being the politicians and the relatively naive populace. The statistical experts almost
always warn that comparisons between groups require tightly controlled conditions -- which
this data does not appear to have provided. For example, it is noted that states with the
highest SAT scores have achieved those scores in part by restricting testing to those who
are immediately college-bound, while states with lower scores usually require all students
at a particular grade level to be tested, college-bound or not. Such discrepancies in
testing methodologies can cause significant difficulties in accurate analysis.
As a possible explanations regarding the apparent lower brain mass of and lower test
scores in the black ethnic group, I suggest the following. Lower brain mass is an
insufficient explanation of lower test scores. Poverty is more rampant in the black
communities than, say, in the white communitites (for a wide variety of reasons, none of
which I will get into an argument about). Poor nutrition contributes to poor physical
development, as well as to poor educational attainments. Add to this a demonstrated lower
educational opportunity, education systems which have systematically put minorities into
the lower-performing groups rather than seeking remediation for any skills that were
lacking, as well as other social barriers to performance, and you have a mixture of things
that will contribute to a class of people performing lower as a group.
I performed a tests of means between black and white on the GRE verbal scores for 1997-98
and found a significant difference between the means. Although black scores as averages
were below that of other groups (according to the table
http://millennium.fortunecity.com/redwood/547/grebrainsize8.gif), the standard deviations
of all ethnic groups show that the scores of all groups present significant overlaps with
each other.
These kinds of studies are really unreliable for judging whether one "race" or
ethnic group is superior to another "race" or ethnic group. They may be more
valuable in proving discrimination, or perhaps bias present in the test(s).
The best data is point data. Take a *large* number of students and track them
longitudinally. At each stage, take head measurements (although you cannot take brain mass
measures, obviously, unless you do an MRI) along with any other physical measures you
wish, and record their ages, test scores, etc. Also include relevant socioeconomic factors
for comparison purposes. Include in the socioeconomic factors such things as family
income, the type of family group, number of siblings, access level to technology, an
evaluation level of the school the subject goes to, the subject's GPA, weight, average
number of calories consumed per day, etc. The longitudinal scores will provide continuity
and add strength to the measurements. The other measures provide a more complete picture
of the individual and contribute to the overall group picture you must develop in order to
run a complete analysis.
It *must* also be noted that socioeconomic distinctions were not taken into account here
in the data. Assertions without data were given concerning socioeconomic analysis in the
link to "Race, Intelligence, and the Brain". Even there, the correlation given
(0.24) is so low as to be nearly without meaning.
It *must* be noted that group results even if
accurate (and I do *not* find this to be the case based on the
quality of the data presented), do *not* translate to the
individual.
I noted in one of the links a reference to IQ and brain size correlate at the 0.40 level.
However, correlation is not causality (a first-course
emphasis in statistics). Furthermore, a 0.40 correlation means that only 16% of the
variation in the data is explained by the model. Other correlations were even lower. A
correlation of 0.40 is not very useful. Correlations quoted of 0.24, 0.15, and 0.21 are
getting pretty close to useless. A correlation of 0.15 means that only 2.25% of the
variation in IQ is explained by the linear relationship with brain size -- a worthless
comparison.
It is to be expected that cranial size and brain mass are positively correlated. But even
at a correlation of 0.60, that means that only 36% of the variation of brain sizes can be
explained by cranial size. While this is a significant amount, it shows that there is a
great deal that is unexplained, and probably there are better measures that can more
adequately explain the differences (even if we do not know what they are).
I would enjoy having access to the original data sets and experimental conditions given to
create the data referenced in your link
(http://www.lrainc.com/swtaboo/stalkers/jpr_gould_paid.html). I would then be able to
judge things more accurately. However, it is appropriate to note that many of the studies
purporting to find differences between the "races" start out with unstated
assumptions and innate biases, and these may well color the authors' perceptions as they
do the study. A well designed study will note the possible areas that bias could influence
it, and design measures to eliminate the bias.
It is very tempting for someone with a point to prove to find support for it any way they
can. Unfortunately the popular understandings of probability and statistics are so poor as
to make the general public susceptible to emotional manipulation based on bad math and
analysis with a priori assumptions.
To summarize: the data as presented provides no proof that brain size and intelligence are
significantly related in human beings, much less does it show any cause and effect
relationship. The data as presented provides no proof that a smaller brain size in a human
being of any race will produce an "inferior" intelligence. The data presented
needs to be seriously reexamined for its origins, applicability, replicability and
suitability for drawing conclusions.
Sincerely,
Raymond E. Griffith
Thanks for that feedback. Following are my comments.
The secondary claim, that intelligence levels are differentiated by race
(unstated, but present), is also AFAIAC, unsubstantiated
"Intelligence" implies IQ tests, but the test which is of most interest is
GRE Quantitative, and this shows the closest correlation, for some of the reasons you
mention below. The other test scores are provided as a cross check to the GRE
scores.
the individuals contributing brain mass data are not the same as the individuals
contributing the test score data
This makes the assumption that somebody is interested in comparing individuals.
This is not the case. The objective is to compare average test scores of races
and sexes to their average cranial capacities. There are of course deviations from
the average, but it makes no sense to compare the lowest scoring individual of one
race to the highest scoring individual of another race. That would in
fact invalidate the inquiry.
Further frustrating the analysis is the fact that the
"average brain mass data" is for adults, yet some of the data it is being
correlated against on the basis of ethnic origin is from juvenile subjects.
Those who take the Graduate Record Examination are full grown adults, usually over 21
years of age. There is no evidence that test scores increase after that age, and
much evidence that they decrease, for all groups. Cranial capacity doesn't change
after that age. This factor may account for some of the lower correlations,
like on the IAEP which is administered to 13 year olds, but again the interest and
focus should be on the GRE Quantitative scores.
The data itself is questionably linked, so all analyses done with it must be
suspect.
What do you mean by "questionably linked"? Are you referring back to
your argument about individuals' test scores and cranial capacities?
There are also several battles being run about the validity and reliability of
educational testing and the results being reported
Almost all valid standardized tests correlate very well with parents' family income,
college grades, and expected future income, so it's not clear why there could be any
legitimate battles about it. If they didn't, there would be no demand nor
requirement for the tests. My experience as an employer shows that test
scores are much better at predicting employees' future probability of success
than college grades, high school grades, or letters of recommendation.
The statistical
experts almost always warn that comparisons between groups require tightly controlled
conditions -- which this data does not appear to have provided. For example, it is noted
that states with the highest SAT scores have achieved those scores in part by restricting
testing to those who are immediately college-bound, while states with lower scores usually
require all students at a particular grade level to be tested, college-bound or not. Such
discrepancies in testing methodologies can cause significant difficulties in accurate
analysis.
That's why most people are interested in looking at more than just one
test. The above example is not such a good one, though, because NAEP is a genuine
random sampling of the same students who take the SAT, and it shows a pattern between
states which is similar to the SAT. It's not exact for the reason you point out
above, but the fact that SAT provides the data regarding the percentage of students in
each state who take the test enables that to be taken into account.
Lower brain mass is an insufficient explanation of lower test scores. Poverty is
more rampant in the black communities than, say, in the white communitites (for a wide
variety of reasons, none of which I will get into an argument about). Poor nutrition
contributes to poor physical development, as well as to poor educational attainments.
There is zero statistical evidence that poverty causes low test scores or even more
poverty. Poverty is the result of poor academic and motor skills. The lower
"brain mass" [read: cranial capacity] is about the only explanation for why
friends of mine in Tanzania earn a whopping $50 per year and are very worried
about what is going to happen to their country now that the British are gone. As bad a
reputation as we may think the British had in their colonies, I have yet to meet even one
individual who didn't appreciate the great efforts they made in so many countries around
the world to build schools, teach English and math, spread Christianity, build roads
and sewers, and establish functional governments.
If money was the answer to education or reducing poverty or crime, then the schools in
Washington, DC, which cost 6 times as much per as the average Catholic school and 4
times as much as those in Iowa, would be producing the best students in the world.
Instead, Washington, DC, scores dead last on every test they take, whereas Catholic
schools and Iowa score at the top.
Poverty is more rampant in the black communities than, say, in the white
communitites (for a wide variety of reasons, none of which I will get into an argument
about).
You are diverging from the issue, but to reply to your point, it's immoral to throw
money at the black community and think it will improve something. All that happened
is that black women received a 22% pay increase by throwing the father of their children
out of the house so she could go on welfare, which left three quarters of black men
without fathers. One of the authors of the Fathers' Manifesto is one of those black
fathers in East Los Angeles, and he KNOWS that every man in his church detests what
welfare did to their community.
Poor nutrition
contributes to poor physical development, as well as to poor educational attainments. Add
to this a demonstrated lower educational opportunity, education systems which have
systematically put minorities into the lower-performing groups rather than seeking
remediation for any skills that were lacking, as well as other social barriers to
performance, and you have a mixture of things that will contribute to a class of people
performing lower as a group.
Black Americans have the best nutrition the world could offer, and don't score even one
point higher than black Africans. The British set up an education system in
Tanzania which made them probably the best educated blacks in the world (far better than
American blacks), yet you cannot even imagine how little food you can buy for
$50 per year, even in Tanzania. The least nourished people in the world (at least
from our perspective) are Koreans, yet they scored second from the top in the TIMSS,
scoring 107 points higher than us. Until this discovery about their larger cranial
capacity, I was at a complete loss to explain why. They spend almost no public
money for education, eat like birds, have 60 kids per classroom, are mistreated for
centuries by the Japanese and now by us, yet are able to educate their children FAR better
than we can. They are such small people that it's really hard to believe
they actually have a larger cranial capacity than we do, but if they really do, then it
all fits.
I performed a tests of means between black and white on the GRE verbal scores for
1997-98 and found a significant difference between the means. Although black scores as
averages were below that of other groups (according to the table
http://millennium.fortunecity.com/redwood/547/grebrainsize8.gif), the standard deviations
of all ethnic groups show that the scores of all groups present significant overlaps with
each other.
With black women scoring 338 and a standard deviation of 88, and white men scoring
512 with a standard deviation of 105, I would argue that this is not a "significant
overlap". Nevertheless, the higher standard deviation of white men means that
the 174 point gap in median scores becomes a 208 point gap at the upper 95th
percentile. The gap in median scores is even bigger in quantitative, at 182.
These kinds of studies are really unreliable for judging whether one
"race" or ethnic group is superior to another "race" or ethnic group.
They may be more valuable in proving discrimination, or perhaps bias present in the
test(s).
This depends on your definition of "superior". Tanzanians could care
less what you believe is "superior", and in fact detest American blacks because
they've given blacks around the world a bad rep. Much of what most white Americans
know about blacks comes from the totally distorted and immoral "mainstream
media" which paints a completely unrealistic picture of American blacks.
By ignoring a possible factor in the differences between the races, we are DESTROYING
the black family, which is literally destroying American blacks. Do you really want
that to continue?
It *must* also be noted that socioeconomic distinctions were not taken into
account here in the data. Assertions without data were given concerning socioeconomic
analysis in the link to "Race, Intelligence, and the Brain". Even there, the
correlation given (0.24) is so low as to be nearly without meaning.
It seems here that you want to adjust the data for precisely what we want to know--what
is the relationship between cranial capacity and socioeconomic condition. It
appears that you want to adjust pygmies for height and thus announce that pygmies are no
shorter than normal people. Please correct me if I'm wrong.
It *must* be noted that group results even
if accurate (and I do *not* find this to be the case based on the
quality of the data presented), do *not* translate to the
individual.
That's because we don't want it to. We want to know the median and the standard
deviation. To attempt to alleviate such concerns, an additional graph has been
added based on the standard deviations noted on Rushton's page:
I noted in one of the links a reference to IQ and brain size correlate at the 0.40
level. However, correlation is not causality (a
first-course emphasis in statistics). Furthermore, a 0.40 correlation means that only 16%
of the variation in the data is explained by the model. Other correlations were even
lower. A correlation of 0.40 is not very useful. Correlations quoted of 0.24, 0.15, and
0.21 are getting pretty close to useless. A correlation of 0.15 means that only 2.25% of
the variation in IQ is explained by the linear relationship with brain size -- a worthless
comparison
IQ tests have been too politicized to be able to provide a clear picture.
The .88 correlation with GRE Quantitative is what needs to be analyzed.
Considering that all of the different measurements of cranial capacity and brain mass
by race and sex on Rushton's site are consistent with each other, it seems clear that the
Asian cranial capacity is significantly larger than that for Caucasians. It
would be nice to know if that is specifically true for Koreans, because my own
[unscientific] observations don't seem to support this--though eyeballing may not be
the best way to judge this );
It is to be
expected that cranial size and brain mass are positively correlated. But even at a
correlation of 0.60, that means that only 36% of the variation of brain sizes can be
explained by cranial size. While this is a significant amount, it shows that there is a
great deal that is unexplained, and probably there are better measures that can more
adequately explain the differences (even if we do not know what they are).
With a correlation between cranial capacity and GRE quantitative of .88, it seems that
cranial capacity rather than brain mass is what counts. What would prove this is if
the correlation between brain mass and GRE Quantitative were to be lower than
.88. If the above is correct, then this is most likely true, in which event the
determining factor is cranial capacity.
A well designed study will note the possible areas
that bias could influence it, and design measures to eliminate the bias.
Agreed, but probably for a different reason. The Army study adjusted for
sex, height, weight, body area, and even rank. That will confuse the issue. If
you take a female captain who's 6 feet tall and weighs 180 pounds and compare her cranial
capacity to that of a male captain who's the same height and weight, you are comparing the
upper 1/2 percentile of women to the median men, which is meaningless for most
purposes. This is ok if you want to know if, per height and weight, there is a
difference in brain mass by sex, but this is an obscure case. If the differences in
cranial capacity by race and sex and the standard deviations are correct, then there is as
little overlap here as there is in the GRE Quantitative scores.
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