Mike H:
>> There are reasons why the bell curve is used in intelligence testing -
>> population intelligence fits it.
Keith H:
> The Bell curve isn't 'used' in intelligence testing -- it's a consequence
> of it.
Stephen S:
No, it is a consequence of test design. It is **assumed**
that this thing ("IQ" or "g") occurs in a population
according to a Guassian distribution (which is *to assume*
that it has the same distribution as many biological traits
and thus is demonstrably just as real and a proper object of
measurement). This is the *rhetorical* force of IQ fitting a
bell curve. But this fit is not a fact; it's an artifact. An
IQ test that does NOT give a bell curve IS A FAULTY TEST and
must be REVISED. It has to be "normalized".
There are THREE kinds of Bell Curves according to Ian
Hacking (and it seems to me he's quite right).
Here is an excerpt from Hacking's review of Herrnstein &
Murray's _The Bell Curve_ (_London Review of Books_, 26 Jan.
1995, p. 5). Hacking offers the following "pedantic remarks"
to clarify H&M's assertion that "It makes sense that most
things will be arranged in bell-shaped curves. Extremes
tend to be rarer than the average."
"[The authors] do not note that there are three distinct
kinds of bell.
"1. THE CURVE OF ERRORS. Around 1800, some of the greatest
mathematicians of the day, such as Gauss and Laplace,
proposed a highly plausible mathematical model of the
distribution of errors made by an observer using an
instrument to determine the position of an object such as a
heavenly body. There was a real, true unknown value. If the
measurements were unbiased, their average, or mean, would be
that value, and the curve of error modelled the deviation
around that real true value.
"2. BIOMETRIC DISTRIBUTIONS. About fifty years later a
Belgian astronomer, Quetelet, noted that measurements of
many biological variables are distributed like the curve of
errors. His first example was the chest circumference of
soldiers in Highland regiments; Murray and Herrnstein use
the heights of boys in your high-school gym class... Notice
that the mean is no longer aiming at a measure of a real
quantity existing in nature, but is just an average, and
that the deviation around the mean is *not* produced by
physical or geometrical symmetries in the measuring device
plus observer. Karl Pearson, often called the founder of
biometrics, was so convinced that these distributions were
widespread that he called them *normal*. In most other
languages they are still called "Gaussian". Pearson's mentor
and patron, Francis Galton, inventor of regression and
correlation, long warned against trying to fit all
biometrical distributions into the 'Procrustean Bed' of the
error curve.
"3. NORMALISED TEST RESULTS. Because many real biometric
variables such as height are distributed like the curve of
errors, it was supposed that postulated quantities should
follow the same curve. IQ is the classic example.
Questions were chosen so that (in the simplest case) half
the population being tested would answer correctly, giving a
mean score of 100. The skill of designing a test was, in
part, to choose questions so that the results in the
population formed, roughly, a Gaussian curve. If they did
not, change the questions. The greatest designer of tests
was Lewis Terman, who invented the name IQ, and who did the
first massive testing, of US Army recruits in 1917. When
attention was turned to women, it emerged that female scores
were higher than male ones. Solution: find the questions
that women answer better than men and replace them.
Thus it is a fact of biometrics that males of the same
population are on average taller than females. But it was
*not* an empirically discovered fact of nature, revealed by
Terman's final tests, that females have the same average IQ
as men. It was a fact of test design. I do not mean this
observation to impugn the testing industry. I am saying only
that the bell curve of IQ is a logically different species
of beast from the bell curve of biometrics, in turn
logically different from the original bell curve of error. A
technicality? No, because *one ought to conceptualise
causality very differently in the three cases*..." [my
emphases -- SS]
-- END OF HACKING --
It seems clear to me that there are myriad difficulties
around the whole business of IQ (or "g") and especially the
question of its heritability.
An emerging "IQ divide" may be (or become) a social FACT.
But if it is (or does) it will still be very hard to know
the degree to which it is the result of biological
reproduction rather than social reproduction and it may well
be technically (if not conceptually) impossible to
distinguish between the two.
Alexis de Tocqueville observed that the "orders" in *ancien
regime* France (aristocrats, peasants) have the appearance
of different "races of men" because their ways of life are
so different. (On the basis of nutrition alone the peasant
will be noticeably shorter than the race of his superiors.)
In the early 19th Century, then, Tocqueville can *observe*
different races of Frenchmen. Doubtless, many of these
"racial" traits were highly heritable. But we would surely
ascribe all or the greatest part of that heritability to
*social* reproduction, would we not?
(I need to think more about what Keith has been saying about
the "IQ divide". My hunch is that any such divide can be
understood and explained in terms of social reproduction
alone. But I've not got the argument put together. This is
for another post, another time.)
best wishes,
Stephen Straker
<[EMAIL PROTECTED]>
Vancouver, B.C.
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