In Part I, I wrote,

FUQ -- Frequently Unasked Questions.

This ESSAY will be written in several parts, because of the vast
amount of SUBSTANCE in it, even though I appeal much to what can
readily be found on existing web sites.

It's the MISUNDERSTOOD CONCEPTS that I mostly address in my essay.
----------------------------------------------------------------------o

FUQ 2. Do different IQ tests measure the same IQ? Or, are IQ scores
from different IQ tests comparable?

Answer. Generally no.

Apart from the fact that different IQ tests place different emphasis
on different aspects of "general intelligence", such as verbal and
mathematical skills, spatial recognition, logical deduction/inference,
and analogies, etc., different IQ tests are normed slightly differently.

E.g., for qualification for membership to MENSA (Top 98 percentile of
the general population) here are the MINIMUM scores on various IQ tests:

IQ Test Minimum IQ required for MENSA

Otis Alpha 138
Otis Beta 128
Otis Gamma 131
Wechsler's WAIS-R 130
California Test of Mental Maturity 132
Stanford Binet (Form L-M) 132

and there are many other "equivalent" qualifying IQs based on other tests.

Thus, the IQ number, a measure of intelligence, is at best a discretized
(no fractional values used) measurement on a continuous scale of many
different "normal" (Gaussian) distribution, generally centered at 100,
with a standard deivation of approximately 15.



FUQ 3. Is qualification to membership in MENSA a fairly good indication
that a person is in the Top 98 %tile of the general population
in intelligence, as measured by IQ tests?

Answer. DEFINITELY no!

(a) The MENSA organization, by its admission standards, invalidates its
requirement (statistically speaking) that an admited member is in
the top 2-percentile of the generaly population in IQ.

Yes, even MENSA is not above an occasional self-contradiction!

For persons of age 14 or above, in an IQ test session "administered
by one of our proctors" (which I served for a couple of decades),
"should your score on one of the proctored tests indicate your IQ
to be in the top 2%, you will be offered membership in the Society,"
according to a MENSA pamphlet on admission requirements.

Since the FAILURE to admission is based on the FAILURE to be in the
top 2% of BOTH of TWO independent IQ tests, that puts a qualifier
approximately in the 1-(.98)(.98) or only the top 3.96% rather than
the top 2%. Furthermore, since there are no limitation to the
number of trials (re-tests) for qualification, a persistent person
of average intelligence (IQ = 100) has a non-negligible probability
of qualifying for MENSA through taking the same qualifying tests
(or different permitted tests) over and over again.

(b) MENSA permits the use of certain "aptitude" tests and college or
graduate "achievement" test scores as "alternative" qualification
scores for IQ -- a dubious "equivalence" since IQ is supposed to be
independent of age, achievement, or scholastic aptitudes.

Alternative Admission standards to MENSA

SAT (Verbal and Math combined, pre-9/77) 1,300
(Verbal and Math combined, post-9/77) 1,250
GRE (Verbal and Math combined) 1,250
LSAT (prior to 1982) 662
(since 1982) 39
ACT (composit) 29

A personal observation: A LARGE proportion of college students,
even in 2nd or 3rd rate universities had SAT scores higher than
1,250. Some of those are also genuine "morons" as are a few of
those easily identified in most newsgroups. :-))



FUQ 4. How well does the Gaussian (normal) distribution characterize
the categories of "intelligence" in a large population?

Answer. Quite well within 3 standard deviations. Very poorly outside
that range, which is why most "standard" normal tables go up
to about a Z value (in standard deviation units) of 3.49, or 4,
listing the Pr( Z > 4.00 )= 0.0000 meaning < 0.00005.

Thus, as we had seen in the answer to FUQ 1, the number of
"morons (or lower)"(@) in the world (based on a population
of 5 billion) is approximately Pr( Z < -2)*5,000,000,000 =
.0228 *5*10^9 = 114,000,000 or approx. 100,000,000.

(@) IQ .le. 70 = two standard deviations below the mean (approx.)
Note that for simplicity, all numbers are grossly rounded.

100,000,000 is also the number of people in the world eligible
for membership in MENSA. But less than 1% of the eligible
population are actually members of MENSA. American MENSA has
about 50,000 members; another 20,000 members are from 96
countries in the world.


Today, it is politically incorrect to label those who are
"mentally retarded" or "challenged" by terms "morons",
"imbecile", and "idiot" as defined by IQ. They WERE:

> IQ Range Classification
> 70-80 Borderline deficiency
> 50-69 Moron
> 20-49 Imbecile
> below 20 Idiot

given in, e.g., http://members.shaw.ca/delajara/IQBasics.html (Who's computer is this?)

If we use the definition for an "idiot" based on IQ of 20 or
less, that would be 5 1/3 standard deviations below the mean.
If we use the normal tables for Pr( Z < -5 1/3) to estimate
the number of "idiots", we would have (.00000004821) times
5,000,000,000, or approximately 241. There are almost that
many idiots in this newsgroup! :-))


The same phenomenon occurs at the other end of the spectrum also,
the IQs of the super-intelligent. The number would be be
grossly underestimated by the normal distribution, in part
because of the extreme-short-tailedness of the Gaussian distri-
bution, and in part because the IQ tests were not designed to
be able to measure the intelligence of the truly super-intelligent.

Marilyn Vos Savant supposedly had the highest tested IQ
of 228, according to the Guinness World Record. That would
be 8.5+ standard deviations above the mean. But according to the
normal tables, Pr( Z > 8.5 ) = 9.48*10^(-18), and you would have
to have a world population a billion times larger than the present
one to find ONE person in that IQ range.


The web site http://www.wiskit.com/marilyn/iq.html (Who's computer is this?) (*)

did a similar analysis but came to the erroneous conclusion
that is wrong by orders of magnitude!

*> The chances that any particular person on Earth (chosen at random)
*> has an IQ of 228 is about 1 in 9,800,000,000,000,000.

228 is 8.5333 standard deviations about the mean. The probability that
a normal deviate is that many standard deviation above the mean is

1 in 140,650,000,000,000,000.

Even as "low" as 8 standard deviations above the mean, you can find in
the National Bureau of Standards Handbook of Mathematical Functions the
probability, given as "-log Q(x) = 15.20614", from which you can get
the probability of 6.2209*10^(-16).


In short, the use of IQ to measure "intelligence" (based on a normal
distribution of scores) is very INACCURATE and UNREALIABLE for anything
that exceeds 3 or 4 standard deviations from the mean, in either
direction.

This concludes Part II of my Essay on
"FUQ: (opposite of FAQ) A serious Essay on IQ"


In the final episode, I shall address the question of how the IQ of
historical figures, such as Thomas Jefferson or George Washington
(who obviously had been dead before any IQ test or the notion of IQ
was "invented". I shall also share with you my personal experience of
the "smartest" person I know (whose IQ, just as that of Marilyn Vos
Savant) cannot be calibrated -- but I have every reason to believe
that this person was much "smarter" than Marilyn Vos Savant, Einstean,
or any of the usual personalities whom others thought were super
intelligent.

The concluding Part III may not appear till December, since I'll be
taking trips to California, Mexico, London, and Hong Kong this month.

Until then, ...................................... I would ask all,
whether you have serious questions, or wish to "flame" whatever I
say in this essay, to do so under the corresponding "subject" of
"Q and A on Part II of the serious subject of IQ", under which I'll
make this IDENTICAL post, so that anyone can refer to this Part II
without it being tangled in a possibly lengthy thread of Q & A and
possibly with much expected flame and/or noise.

-- Bob.