Here Jensen replies to some of the commentaries you have read. Delte now
if not interested.
(two messages rolled into one and several screenfulls)
mike
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Subject: psyc.00.11.082.intelligence-g-factor.19.jensen (153 lines)
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Status: R
psycoloquy.00.11.082.intelligence-g-factor.19.jensen Fri Dec 31 1999
ISSN 1055-0143 (5 para, 5 refs, 0 figs, 0 notes, 153 lines)
PSYCOLOQUY is sponsored by the American Psychological Association (APA)
Copyright 1999 Arthur R. Jensen
CORRELATED VECTORS, g, AND THE "JENSEN EFFECT"
Reply to Rushton on Jensen on Intelligence-g-Factor
Arthur R. Jensen
Educational Psychology
School of Education
University of California
Berkeley, CA 94720-1670
nesnejanda@aol.com
ABSTRACT: The "method of correlated vectors," which Rushton (1999)
has dubbed the "Jensen Effect," was devised as one method for
discovering non-psychometric correlates of psychometric g. It plays
an important role in my book and could probably be applied even
more extensively to data analyses already reported in the
psychological literature.
1. Rushton (1999) is right: My main interest is in the understanding of
g as a scientific construct. From a purely scientific standpoint,
understanding the nature of g seems primary, not only because it is the
basis of the practical validity of the psychometric tests of mental
ability used in schools, in employment, and in selection for college
and for training programs in industry and the Armed Forces, but because
it also plays a central role in our attempts to understand the various
educational, social, and economic problems that exist in every
increasingly technological and information-intensive society.
2. The g factor is usually the largest single source of variance in a
battery of diverse psychometric tests, and although it is only one of
many linearly independent factors that can be extracted from these
tests, it has larger correlations with a wider variety of psychometric
variables than any other factor. The method of correlated vectors is an
efficient and precise method for screening the g factor's (or other
factors') relevance to other, non-psychometric variables. What Rushton
has named the "Jensen Effect" (to obviate having to repeatedly describe
in detail the methodology for the resulting phenomenon) occurs when the
column vector consisting of the g loadings of the n subtests in a
battery is highly and significantly correlated with the corresponding
column vector of those n subtests' correlations with some directly
measurable non-psychometric variable. As Rushton points out, the
"Jensen Effect" has been found for a considerable number of such
variables, including those related to the heritability of the tests,
the effects of inbreeding depression, and various physiological brain
correlates of diverse tests. Although correlations are, of course, not
necessarily causal, they do afford the best clues we can obtain of
where to look for the causal mechanisms using other methods of
investigation. The "Jensen Effect" is not at all inevitable and does
not materialize for certain variables, for example, the variable known
as "inspection time" (IT), or the exposure time required by a person to
make a simple sensory discrimination, such as detecting the difference
between two parallel straight lines that differ in length by a ratio of
2 to 1. Although IT performance is correlated with IQ and with the g
factor, it has a stronger association with a lower-order perceptual
speed factor (Deary & Crawford, 1998).
3. Here Rushton's exposition of the "Jensen Effect" may risk confusing
readers by not emphasising the clear distinction between the simple or
direct correlation between two variables and the "Jensen Effect," which
is the correlation between two vectors each compsed of n elements. If
one wanted the simple correlation between g and, say, brain size, to
use Rushton's example, one would simply correlate a number of
individuals' g factor scores with their brain-size measurements. But g
factor scores are not factor pure; they also have some small proportion
of variance from all of the lower-order factors in the test battery.
The method of correlated vectors allows one to see which unadulterated
factors in the test battery are the most clearly related to the
external variable of interest. The g factor scores (but not the g
factor loadings) are the most vulnerable to some degree of
contamination by other, non-g factors in the matrix; other non-g factor
scores derived by regression methods are purer measures of their
factors than are g factor scores (which are just a g-weighted average
of the individual's standardized scores on the various tests'). But
actually the most valuable advantage of the method of correlated
vectors is its meta- analytic property -- it can be applied to data
obtained from different published studies and different subject
samples. For example, Study A shows the correlations of, say, brain
intracellular pH with each of the 12 subtests of the Wechsler
Intelligence Scale for Children (WISC), but does not give the g
loadings of the subtests or the correlation matrix that would permit
the extraction of the g factor. We can use the g loadings derived from
the WISC standardisation sample of the same age group as was used in
the pH study. For example, the correlated vectors between g and pH in a
study of brain pH undertaken at Cambridge University gave a correlation
of r = +.63, while the simple correlation between the WISC Full Scale
IQ and pH was r = +.52 (Rae et al., 1996). The g loadings were derived
from the standardisation sample, which is much larger and hence yields
a more reliable g than the subject sample used in the measurement of pH
levels. The correlated vectors analysis indicates that g, rather than
other psychometric factors, is the chief source of covariance in the
correlation between individual differences in IQ and in pH levels.
4. The standardised magnitudes of the White-Black differences on a wide
variety of tests consistently shows a strong "Jensen Effect" in over
twenty independent studies. Other factors independent of g contribute
comparatively little to the difference, only a spatial reasoning factor
showing a consistent but relatively small effect. The subtests of IQ
batteries are not at all homogeneous in their contributions to the
overall W-B difference in IQ; nearly all of the difference is
contributed by g, the one factor common to all cognitive tests. This
seems to me an important discovery, not because it proves anything
about causation, which correlation alone cannot do in any case, but
because it narrows and focuses the phenomenon in need of explanation.
Rushton seems to appreciate this value of my investigation as some
other reviewers of "The g Factor" apparently have not.
5. One new application of correlated vectors that was not included in
"The g Factor" (Jensen, 1998, 1999) is in the study of children's
mental growth trends on a large battery of diverse tests, a research
project now in preparation for publication. The vector of the tests' g
loadings is highly correlated with the vector of standardised test
score differences between age groups of school children that differ by
one to two years. It appears that mental growth is manifested most
strongly in those tests with the largest g loading. Moreover, it is
found that the pattern of age-group differences (of 2-years) within
either the White or the Black samples is statistically
indistinguishable from the pattern of W-B test-score differences in W
and B groups of the same age. The mental growth trajectories of W and B
children on a set of diverse tests have essentially the same pattern of
g loadings and the age-to-age mean subtest scores differ only in their
slopes and asymptotes. To explain this finding solely in terms of test
bias and cultural differences would mean that these racial-cultural
influences perfectly simulate chronological age differences in test
scores within each racial group.
REFERENCES
Deary, I. J., & Crawford, J. R. (1998). A triarchic theory of
Jensenism: Persistent conservative reductionism. Intelligence, 26,
273-282.
Rae, C., Scott, R. B., Thompson, C. H., Kemp, G. J., Dumughn, I.,
Styles, P., Tracy, I, & Radda, G. K. (1996). Is pH a biochemical marker
of IQ? Proceedings of the Royal Society (London), 263, 1061-1064.
Jensen, A. (1998). The g Factor: The Science of Mental Ability. Praeger
Jensen, A. (1999). Precis of: "The g Factor: The Science of Mental
Ability" PSYCOLOQUY 10(23).
ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/
psyc.99.10.023.intelligence-g-factor.1.jensen
http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.023
Rushton, J.P. (1999). The "Jensen Effect" and G Vector Analysis.
PSYCOLOQUY 10(44)
ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/
psyc.99.10.044.intelligence-g-factor.3.rushton
http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.044
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>From: PSYCOLOQUY <journal@princeton.edu>
Subject: psyc.99.10.083.intelligence-g-factor.20.jensen (251 lines)
To: PSYC@PUCC.PRINCETON.EDU
Status: R
psycoloquy.99.10.083.intelligence-g-factor.20.jensen Fri Dec 31 1999
ISSN 1055-0143 (10 para, 4 refs, 251 lines)
PSYCOLOQUY is sponsored by the American Psychological Association (APA)
Copyright 1999 Arthur R Jensen
THE GALTON-SPEARMAN PARADIGM AS A PROGRESSIVE RESEARCH PROGRAM
Reply to Buckhalt on Jensen on Intelligence-g-Factor
Arthur R. Jensen
Educational Psychology
School of Education
University of California
Berkeley, CA 94720-1670
nesnejanda@aol.com
ABSTRACT: All roads in the scientific study of human abilities lead
back to Galton and Spearman. Buckhalt (1999) has clearly identified
the main elements of the research programme that they originated,
referring to these as the 'central dogma' of psychometrics. This
long-running research programme has generated more established
facts about human abilities and by far more practically useful
applications of its methods than any other efforts in the study of
human variation in mental traits. It has emerged theoretically,
methodologically, and empirically as the most coherent, clearly
articulated, and progressive research program in the development of
a true science of mental abilities.
1. As a researcher and a professor in the fields of applied psychology
and school psychology, Buckhalt (1999) perhaps has a better
appreciation of psychometrics, individual differences, and particularly
the dominance of g in the schooling process than do many academicians,
whose experience of individual differences is largely confined to
college students who are mostly in the restricted range of the top
quartile of the IQ bell curve. We also know that abilities are more
differentiated in this region of the distribution, that is, at higher
levels of g there is also a greater development of group factors,
talents, and specialised abilities that constitute the total variance
in individual differences, so it is easier to perceive "multiple
intelligences" among persons in the upper than in the lower quartile of
the g distribution. (Appendix A in Jensen, 1998, reviews the evidence
for this phenomenon, discovered by Spearman and more thoroughly studied
in recent years.) Analogously, rich people spend their money on a
greater variety of things than poor people do.
2. While Buckhalt expresses little doubt about the psychometric basis
of g and its behavioural and social correlates, he believes that the
evidence for its biological and evolutionary foundations is "less
strong." This may be true, since this is the most recently investigated
and the least consolidated or fully explicated aspect of the field. Yet
I think two lines of evidence make it virtually certain that g is
essentially biological, although the mechanisms through which its
biological basis operate to produce behavioural differences among
people are only beginning to be understood.
3. First, it is important to realise that "intelligence" and "g" do not
stand for the same thing. They are very different concepts and
confusing them in the least only leads to unnecessary arguments. One
way to explicate the difference between intelligence and g is to
realise that, in principle, everything that can be known about
intelligence could be discovered with research on a single person,
i.e., with N = 1. Intelligence refers to a class of the various
behavioural capabilities common to all biologically normal members of a
given animal species, although here we are particularly interested in
Homo sapiens. These capabilities are behavioural, observable functions,
such as apprehension of a stimulus, perception, discrimination,
generalisation, conditioning, learning, memory, transfer of training,
language acquisition, thinking, reasoning, and problem solving. These
functions are possessed by all biologically normal human beings, that
is, all persons without serious diagnosable brain damage or major
genetic or chromosomal anomalies. The 'laws' of each of these functions
(also called 'abilities') can be discovered by studying a single
individual, just as Hermann Ebbinghaus discovered many 'laws' of
learning and memory with himself as his sole experimental subject.
Likewise, the brain mechanisms involved in these intelligence
behaviours could, in principle, also be studied with N = 1. With N = 1
it would also be possible to study what Sir Charles Sherrington called
the integrative function of the central nervous system, that is, those
brain processes that allow communication between different functionally
specialised modules to accomplish particular complex goal-directed
actions.
4. But if we wish to study the conspicuous individual differences in
any or all of these functions, we obviously need N 2. Then we will
find that measurements of these various "mental" functions do indeed
show reliable individual differences, and that these are also all
positively correlated to varying degrees across various abilities. And
then we discover that the matrix of all the intercorrelations among the
N 2 measures of individuals' performances on these ability variables
shows different degrees of generality; that is, we can discern
clusters, some larger than others, among all the different variables'
intercorrelations. Some variables are more strongly correlated with
each other and some are weakly correlated. By means of factor analysis
we can discover precisely how much of the variance in each measure is
independently associated with each of the clusters and how much is not
associated with any particular clusters (i.e., group factors or sources
of variance that only certain abilities have in common), but is a
source of variance common to all of the variables in the matrix -- in
other words, the g factor, which emerges from a hierarchical factor
analysis or as the first principal factor in a common factor analysis.
There is also some residual variance that is unique to each specific
ability measure. It should be noted that this g (and all other factors
as well) depends upon the existence of individual differences in
performance on the various mental abilities I listed above as
"intelligence." Thus the psychology of mental abilities (or
intelligence) and the psychology of individual differences in
intelligence are entirely different concepts. A causal explanation of
the one will not serve as the explanation for both.
5. The g factor represents the highest-order common factor among
individual differences in a variety of behavioural tests that reflect
all or at least a great many of these mental abilities. The g factor is
not a direct measure of these diverse abilities per se, but of the
individual differences variance they all have in common. An estimate of
an individual's level of g, relative to other individuals who took the
same battery of tests, is that individual's "factor score" on g, which
is a g-weighted average of the individual's standardised scores on each
of the tests in the battery, the weights being the tests' g loadings
(i.e., the test's correlation with the one source of variance that is
common to all of the tests in the battery). A g factor can be found in
every battery of tests that one can concoct, provided the test items
elicit one or more of the open-ended list of mental functions referred
to above as intelligence, and are (1) sufficiently diverse in the
psychometric sampling of these functions, and (2) sufficiently numerous
to allow reliable measurement. The better these two psychometric
conditions are met, the less error or variation there will be in the
estimates of g. For several reasons, the most important of them being
broad practical predictive validity, IQ is quite a good estimator of g
factor scores, and this is true whether or not the construction of the
IQ tests were based on factor analysis. But other factors, particularly
verbal, numerical, and memory factors, also constitute some part of the
total variance of most IQ tests.
6. Now back to the question of the biological basis for g, or more
loosely speaking, individual differences in IQ. The well established
fact that IQ (and g) has very substantial heritability, which increases
from about .40 in early childhood to about .80 in late adulthood,
averaging about .60 after the late teens, can only mean that a large
part of the variance in IQ (specifically its broad heritability) is
biologically based. This is certain, even though we don't know the
chain of biological, biochemical, anatomical, and physiological
processes by which the genotypic variance gets transformed into the
phenotypic variance in IQ. But we don't yet have this knowledge either
for other heritable traits, such as stature, blood pressure, longevity,
or the probability of giving birth to dizygotic twins. However, a
number of specific differences in the DNA between groups with average
IQ and very high IQ have been identified (studies cited in Jensen,
1998). Further, myself and others have shown that the degree to which
the various subtests that compose the IQ scores are g loaded predicts
(with correlation coefficients in the .60 to .80 range) the size of the
heritability coefficients of those subtests tests. This means that g
per se is more highly related to the tests' heritability coefficients
than are the other sources of variance in all the subtest scores. IQ
therefore also has a slightly lesser heritability than g factor
scores. The differing magnitudes of inbreeding depression (a wholly
genetic effect) on various mental test scores are predicted by the
tests' g loadings, with correlations around .80.
7. The evidence on IQ heritability and inbreeding depression
necessarily implies an evolutionary origin of the biological basis of
IQ or g. The mechanism of heritability consists of individual
differences in gene (or allele) frequencies, and such differences have
come about mainly through the chief mechanisms of evolution --
spontaneous genetic mutations and natural selection. Both genetics and
evolution are absolutely fundamental and essential for understanding
g. It might even be hypothesised that psychometric g is merely a
lower-order factor in an even more over-arching biological super-G
factor something like Darwinian fitness. Let's see what the
evolutionary psychologists will make of this!
8. There is no "essence" of g, which is only the first factor in a
common factor analysis or the highest-order common factor in a
hierarchical analysis. Both methods yield highly similar (i.e.,
correlated) g factors, and highly similar g factors appear in most test
batteries, provided the tests that compose them are numerous and highly
diverse in the kinds of knowledge, skills, and mental operations called
for. The obtained g factors vary only slightly across the different
methods of extraction, and also with the breadth of psychometric
sampling (i.e., number and diversity of tests included in the
analysis). These variations in tests all give highly intercorrelated
estimates of some "true" g, in the same psychometric sense that an
obtained measurement is an estimate of the true measurement (which
can't be known) but conceptually is the mean of an infinite number of
measurements of the thing being measured. The g factor obeys the same
logic, in this respect, as all other kinds of measurements, which are
merely estimates of some "true" but necessarily unknowable value. At
the present time, there are few ideal test batteries for measuring g
and I have had to use the evidence that is available, which, it should
be noted, is in some cases merely attenuated estimates of g, so that
more accurate measurements would have yielded even stronger
correlations with other, non-psychometric variables. With one
exception, I have never used a g estimate based on any test battery
that didn't include a variety of tests, as the first factor of a test
battery test with rather homogeneous subtests would reflect some
first-order or second-order group factor as much or more as it reflects
g. A vocabulary test, for example, measures g and a verbal factor. The
one exception I referred to is Raven's progressive matrices test (or
other tests like it), which, in most factor analyses, typically loads
only on g but not on any group factors.
9. Buckhalt is right that the frontier between psychometric g and its
undoubted biological and neurological underpinnings is necessarily
uncertain as to the specific mechanisms that mediate between physiology
and behaviour. But it has been only recently in the history of
psychology that the necessary tools have been available for research
into this subject -- DNA analysis, electrophysiology, and imaging
techniques like fMRI and PET. I have simply looked at the best evidence
presently at hand; I haven't gone beyond it, except to express my hope
that scientists will continue researching in this Galton-Spearman
research paradigm that continually increases our knowledge and seems
more promising than anything else on the scene in differential
psychology. It represents, I believe, what the philosopher of science
Imre Lakatos refers to as a "progressive" research program, in contrast
to a "degenerating" program. The contrast between the empiricism and
theoretical coherence of the Galton-Spearman paradigm and the
alternative behaviouristic, humanistic, mentalistic, and egalitarian
philosophies that claim to oppose it is brilliantly illustrated by
Peter Urbach (1974) in terms of Lakotos's philosophy of science. I
would urge everyone to read Urbach's article. The rapidly growing
systematic body of knowledge based on empirical studies and reported in
contemporary journals such as Behaviour Genetics, Intelligence, and
Personality and Individual Differences clearly exemplifies the Galton-
Spearman tradition. Other approaches have had nothing at all comparable
or competitive to show.
10. Overall, I find little if anything to argue with in Buckhalt's
well-written commentary, since for every critical point he makes, he is
usually able to anticipate what my own response to it would be and then
spells it out himself. Overall I find a high congruence between his and
my own thinking on all these issues and feel glad to realise that
someone else has so well understood the message of my book.
REFERENCES
Buckhalt, J. A. (1999). Defending the science of mental ability and its
central dogma. Review of Jensen on Intelligence-g-factor. PSYCOLOQUY
10(47). ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/
psyc.99.10.047.intelligence-g-factor.4.buckhalt
http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.47
Jensen, A. R. (1998). The g factor: The science of mental ability.
Westport, CT: Praeger.
Jensen, A. R. (1999). Precis of: "The g Factor: The Science of Mental
Ability" PSYCOLOQUY 10(23).
ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/
psyc.99.10.023.intelligence-g-factor.1.jensen
http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.23
Urbach, P. (1974). Progress and degeneration in the 'IQ debate' British
Journal of the Philosophy of Science, 25, 99-135 and 235-259.
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