IQ tests
IQ (intelligence quotient) tests come in all styles and shapes. Some require
special knowledge, i.e., proficiency in a particular language or knowledge of
basic mathematics. Others aim to be culture fair and use only knowledge that is
supposed to be known in all cultures and do not require formal education. Some
give the test-taker plenty of time to answer the questions, others restrict the
time allowed to accomplish the test.
If you take an IQ test it may run something like this.
First you take what resembles a written exam of about an hour of duration,
during which you have to answer a bunch of questions. Having handed in your
answers your job is now over. The psychologist responsible for correcting the
test will now tally the number of correct answers. This number is your raw
score. After doing so he converts the raw score into an IQ. In this
conversion he may take into account your age and sex.
IQ scores are distributed according to a normal
distribution with a mean of 100. A
normal distribution is characterized by its mean and its standard deviation
(SD). Most people score close to the mean. The further we go from the mean, the
less people obtain those scores. A score of 100 + 1 SD corresponds to being in the top 15.9%, a score of
100 + 2 SD corresponds to being in the top 2.2%, while a score of 100 + 3 SD
corresponds to being in the top 0.1%. Typically tests use SD=16, but tests with SD=15 and SD=24 can also be
found.
The g factor
IQ tests are interesting because they provide good
estimates of the g factor.
Before explaining what this factor is about, let us recall the concept of correlation.
The correlation is a number between -1 and 1 that measures the linear relationship
between two variables. If the correlation is 1 then the variables have a
positive linear relationship A correlation of 0 indicates that they do not have
any linear dependency. A correlation of -1 means that they have a negative
linear relationship.
The g factor emerges in factor
analysis of tests that are varied and balanced. By varied I
mean that there are many different types of questions in the tests, i.e.,
verbal, logical, spatial, etc. By balanced I mean that there are several
questions of each type in the test. In other words we have a test consisting of
several subtests with specific types of questions.
When a large number of people take such a test we may compute the
correlation of the raw scores for each pair of subtests. If the correlation between two
subtests
is high it means that a test-taker doing well on the first is likely to do well
also on the second. Factor analysis allows us to form groups of subtests that are highly correlated. That a group of
subtests are positively
correlated means that there is some common skill involved in solving those
questions. Using factor analysis we may compute how much the subtests rely on
this common or primary factor.
Interestingly the primary factors are usually not
independent. Again we may find groups of primary factors that are correlated and
use factor analysis to extract common or secondary factors for these. Usually already in the
second round a single general factor emerges.
Amazingly it is usually the same general factor that arises
for different tests and a variety of culturally and ethnically different groups
of test-takers. We can therefore speak of the general factor, the g
factor (the g stands for general.)
We note that the g factor is something we came about
in an indirect way. It cannot be seen and measured directly, and it cannot be
put on a ratio scale. It is therefore not the case that somebody with an IQ of
200 is twice as intelligent as somebody with an IQ of 100. From IQs we can only
infer relative information, namely where on the distribution somebody lies in
comparison with the rest of the population.
Biological correlates of g
The physical causes for high or low g are not well known.
Several correlations with biological phenomena have been found. Examples are the
sex hormone balance, brain glucose metabolism, brain size and to a lesser extend
head size.
Significance of g
Many things of real life importance are correlated with g.
Positively correlated with g are for instance length of formal education,
occupational success, income, altruism, creativity and social skills. Negatively
correlated are for instance crime, psychoticism, racial prejudice, authoritarianism and
number of children.
Can g be altered?
It is possible to increase scores on IQ tests through
practice. However, when analyzing such results it turns out that the increases
are not in g. Rather such increases mean that people have increased their
test taking skill. Various school projects have been made attempting to increase
g but they have in general been unsuccessful.
Twin studies show that g is around 80% inherited and
20% environmental. This leaves little hope of increasing g, unless we
find out a way to produce larger environmental difference than the one
experienced by monozygotic twins reared apart.
We should, however, mention the mysterious Flynn effect. In
the last decades IQ scores have increased by 0.2 SDs per decade.
Considering that people with low IQ tend to have more children we would expect a
decrease in IQ over these years, not an increase.
Politically dangerous topics
It is well established that men and women differ in some of
the primary factors. In particular men outperform women in terms of spatial
reasoning, while women outperform men on some verbal tasks. Jensen says in his
book that
there is no difference between men and women's mean g, or in the variance of
g. Some researchers claim there is a small difference favoring males.
Races do differ in IQ scores. Highest scoring are
Ashkenazim Jews (100 + 1 SD) and some groups of Asians. Lowest
scoring are black Africans (100 - 2 SD).
Lynn has considered the connection between nations' GNPs
and their average IQs. It turns out that there is a positive correlation. It
therefore seems like g does not only have consequences on the individual
level but can also be used in explanations of demographical phenomena.
Intelligence
So far I have not considered the word "intelligence"
in its everyday use at all. A critique sometimes raised is that one cannot
measure intelligence. Another critique sometimes raised is that intelligence has
not been appropriately defined. My take on this issue is that I believe that
there is a high positive correlation between who people label as intelligent and
IQ scores of those persons. I am therefore willing to accept IQ scores as a
measure of intelligence, even if they may not correspond perfectly to whom I
would label as being intelligent.
Other factors
Attempts have been made to make tests that measure
creativity. This field has not been as successful as the field of making IQ
tests. IQ scores and creativity scores do have some positive correlation.
Emotional intelligence has enjoyed success in terms of
selling books.
To the best of my knowledge there are no tests of EQ that rest on a solid
scientific basis.
Eysenck used factor analysis on personality tests and found
three general factors: introversion/extroversion, psychoticism and neuroticism.
Neuroticism in particular has some predictive power in terms of occupational
success.
Gardner has a theory of "multiple
intelligences". Originally he had seven such intelligences mathematical/logical, verbal, spatial, musical, kinesthetic, interpersonal,
intrapersonal, but more have been added. A misunderstanding that I see from time to time is that IQ tests
are intended to measure the mathematical/logical intelligence that Gardner is
referring to. This is not correct; the g factor is a more general factor.
My guess is that if one-dimensional tests of Gardners' intelligences are ever
constructed then IQ scores will be highly correlated with the first three of
Gardners' original seven intelligences and moderately correlated with the latter
four.
Sternberg has a "triarchic" theory of intelligence. As
far as I understand he does not find IQ to be a sufficient measure for
intelligence. His goal is to find a better theory that subsumes the present
theory of intelligence.
Literature and links
A. Jensen: "The g Factor: The Science of Mental Ability". An
excellent and thorough book.
Much of the information in this article has been taken from this book.
H. Eysenck: "Intelligence: A New Look". A good book on IQ that is easier to
read than Jensen's book.
C. Brand: "The g Factor -
General Intelligence and its Implications". Online book which was never
published in paper due to political correctness.
R. Lynn, T. Vanhanen: "Intelligence and the Wealth and Poverty of Nations".
An article on the correlation between average national IQs and GNPs.
D. Kimura: "Sex Differences in the Brain" [PDF]. An article on sex differences in
mental abilities, and the effect of hormones on mental abilities.
Interview with Jensen. A Mega Society interview with A. Jensen from 2001.
Interview with Sternberg. An interview in Skeptic with R. Sternberg from 1995.
No title.
An article on the Flynn effect. Judging from data obtained from Danish
conscripts IQs may have peaked and started declining.
The Role of Intelligence in Modern Society. An article in American Scientist by
E. Hunt from 1995.
Mainstream Science on Intelligence. A statement on intelligence signed by 52 researchers. Originally published in Wall Street Journal in 1994.
APA Task Force Examines the Knowns and Unknowns of Intelligence. Press release from American Psychological Association on a task force report on intelligence in
1996.
Intelligence:
Knowns and Unknowns. The APA task force report on intelligence from 1996.
Deals with many of the issues treated in the present article.
Intelligence Theory and
Testing. University of Indiana site containing brief descriptions of
scientists involved in intelligence research as well as some short articles on
intelligence.
Disclaimer
I am not a psychologist, psychometrician or a statistician.
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