No, theoretically, there's no cap on the number. Given the
equation I mentioned earlier, if, for example, a 5-year-old is able
to complete IQ test questions suited for a 50-year-old, the child's
IQ would be calculated as 1000.
HOWEVER....
There are a number of problems with this measure.
First and foremost, as mentioned earlier, nobody can work out
g in the first place. Any
current measure of intellectual ability is at best a corollary of
g. The WAIS is biased
because you'd need to know English, have had basic education in
mathematics and lived in a country with snow to have an even
chance. Did someone say Raven's matrices? Biased against women on
the visuospatial ability count. Bottom line, it's a whole load of
bovine excrement any way you cut it.
Secondly, there's the matter of IQ score distributions, which are
based around a mean of 100, with standard deviations of 15. Given
the normal distribution, anything above 165 represents such a tiny
number that unless you had census data on every single person
within that range, the probability of getting any particular score
in that range would be about as reliable as flipping a coin.
Most important is the fundamental flaw of classical test theory,
employed by the Stanford-Binet, WAIS and their clones. How does one
determine if a test item is indeed representative of a
50-year-old's level of function? The obvious answer is to test a
bunch of 50-year-old individuals to see how many of them can get
the answer right. However, this raises an interesting conundrum.
How do you know that this group of 50-year-olds is representative
of all 50-year-olds? The answer depends on their performance on the
test items, but the test items are themselves an unknown measure -
after all, you started out trying to find out how tough the
questions were in the first place.
We therefore have a vicious cycle of working out how tough the
question is based upon how many people of a certain group could get
the answer right, and conversely working out how bright this group
is, which in turn is influenced by how tough the question is.
Now, theoretically, there is a way out of this in the form of Item
Response Theory. Starting with a Poisson distribution, the
parameters of the individual's level of ability and the item
difficulty may be iteratively ascertained simultaneously using the
equation: Pi(q) = 1/(1 + e-Dai(q-bi)), where:
q is the examinee's ability level
i is the item
bi is the difficulty parameter for item i
D is a figure of 1.7
e is a transcendental constant of value 2.718
to determine Pi(q), which is the probability of a person of ability
level q getting item i correct. Note that the answer is specific to
the measured ability, not g, and requires a sample of at least a
few thousand for a reasonable goodness-of-fit statistic to be
achieved.
Let's face it, that's just too much work for determining something
as trivial as IQ.
