# Norms of a IQ-test: percent range (PR) and z-score

Discussion in 'Scientific Statistics Math' started by Pat, Aug 30, 2006.

1. ### PatGuest

Hi!

My norm table of the test is as following:

raw sc. percent range
62 100
60 99
58 98
56 96
... ..
28 50
.... ...

n, x and SD of the distribution are:

n=253

x=26.0
sd=16.6

the following equation provides a z-standardisation using x and SD:
z = (RW-x)/sd

the raw score of 28 for example should therefore result in the
following value:

z = (28-26)/16.6 = 0.12

However, according to the norm table a raw score of 28 results in a PR
of 50, which is equivalent to 0.0 and obviously not equal to 0.12.

How can this discrepancy be explained?
Which is the correct z-transformation, that leads to the correct PR?

thank you
pat

Pat, Aug 30, 2006

2. ### Richard UlrichGuest

Why do you think that they are using a z-transformation?

If they have set the median to 50, and the median is a couple
of points off from the mean, then
it appears that they are reporting the observed percentiles.

Richard Ulrich, Aug 30, 2006

3. ### Reef FishGuest

Different IQ tests are normed differently, and they don't always
have the same standard deviation of 15 for the IQ though the
mean is always normed to be 100.

Your example seems to have no relation to an IQ test, and your
x is the mean of the normed scores?

-- Reef Fish Bob.

Reef Fish, Aug 30, 2006
4. ### Herman RubinGuest

The educationists assume the true IQ is exactly normal,
and thus their norms are obtained by inverting the
cumulative distribution function.

Of course, this is stupid, but so is any other kind of
norming which depends on the population.

Herman Rubin, Sep 1, 2006
5. ### Richard UlrichGuest

There is no indication that *these* educationists
inverted anything. From what is shown, they just
reported the cumultive distribution for the raw scores.

- seems like a bit of an overstatement to me.

Richard Ulrich, Sep 1, 2006
6. ### Reef FishGuest

That's not quite correct.
That's not correct either.

http://www.eskimo.com/~miyaguch/his...lhttp://www.eskimo.com/~miyaguch/history.html

The web is titled "A Short (and Bloody) History ot the High IQ
Societies".

Actually the history is not short. Plenty bloody alright. The
"norming" and
"re-norming" of test scores and IQ requirements for the admission of
various
high IQ societies have repeatedly been done by the founders of two of
the
Hi IQ societies, Kevin Langdon (of the Triple Nine Society) and Ron
Hoeflin
(of the Mega Society) whose life ambition seemed to be one of making a
High IQ Society in which he is only qualified member.

Hoeflin failed in that goal (but not by much). But you'll have to dig
up his
writings on how he used test scores from members of other societies to
NORM the scores and IQ requirements for his Mega Society.

Ron Hoeflin was also unaware that the notion of QUOTIENT in IQ is
untenable, that is, the quotient of two NORMALLY distributed IQ
variables
(for different ages) cannot be NORMAL itself -- a recent thread in
sci.stat.math on the quotient of two normal r.v. (independent of the IQ
question). Ron Hoeflin and I had the only debate on that subject in
the
early issues of the Journal of the Triple Nine Society (VIDYA).

The interpretation of IQ as a quotient is limited to very young
children. That
was how Marilyn Vos Savant had her IQ rating of 228, as she took an IQ
test when she was 10 year old attaining the score of a 22 year old.
But
different IQ tests on her at the same age produced IQ score (on record
at her school) as long as 168.

http://en.wikipedia.org/wiki/Marilyn_vos_Savant

Of course the notion of an IQ being a QUOTIENT is patently absurd for
Adults. I used the example of how silly it would be to think that
Einstein
(who IQ was reported to be about 160), when he was 70 years old to
have the intelligence of a 102 year old.

At any rate, the IQ scores a approximately normal (up to about 3
standard
deviation -- thereafter, there is no reliable measure), and the
approximate
normality is accomplished by various methods of NORMING.
Overstatement to be sure. but not far from the truth.

-- Reef Fish Bob.

Reef Fish, Sep 2, 2006
7. ### Reef FishGuest

When I went back to try to take another look at the webpage to see if I
can find
more details about the NORMING of test scores by Ron Hoeflin, I was
surprised
that the link indicated an ambiguous reference (probably from the
truncation of the

http://www.eskimo.com/~miyaguch/

instead -- which was ONE of the webpages I was looking for!!! It
appeared
serendipidously!

The page was FULL of headlines about NORMING: The sixth, the fifth,
and
the first norming of the Mega Test. The norming of the Titan Test ...
the 2nd norming of Kevin Langdon's LAIT (The Triple Nine Society) test,

etc., etc.

It is a virtual jungle of the IQ Egghead's playing with statistics of
which they
know now the meaning nor the purpose. Ron Hoeflin and Kevin Langdon
can both say they belong to the Mega Society, when Hoeflin could hardly

write coherently about the IQ scores being a QUOTIENT in the lowly
Society of Triple Nine that admits anyone in the top 98% of the very
lowly
MENSA Society. The INTERNATIONAL membership of TNS never
exceeded 700 over its many years of existence (I was admitted a member
in
1979 as member #171) and have met more kooks like Ron Heflin and a
few who couldn't hold a regular job in society in that membership, and
the
TOTAL accomplishment of the majority members of that group were merely
memberships in OTHER high IQ societies.

It's a Society of Quacks on the measurement of Intelligence!

-- Reef Fish Bob.

Reef Fish, Sep 2, 2006
8. ### Reef FishGuest

Sorry I did not catch this non-obvious typo when it was written. The
lines
percent of recognized IQ tests. Scores above the 98th percentile.

TNS (Triple Nine Society) admits anyone who scored in the top 99.9
percentile of the general population, which is roughly equivalent to
Double M -- or top 98 percentile of the top 98 percentile.

These are the LOWEST of a dozen or more of the High IQ Societies.

-- Reef Fish Bob.

Reef Fish, Sep 2, 2006
9. ### Herman RubinGuest

No, they do not report the cumulative distribution
for the raw scores; they do not report the raw scores
at all. For each individual, only the quantile with
respect to the reference sample is reported, and not
always that directly.
This is NOT an overstatement. It is the kind of
misinterpretation which goes on continuously, and
which has destroyed the level of education.

It may be necessary to norm a test against known
individuals, but in any case, the scale should be
a direct scale, not a relative scale. Most IQ
tests never report a value of over 130, as their
sample is not large enough. But one can try to
find out the meaning of scores, and extrapolate.

What use would a temperature scale be, based on
relative values? Would you know what clothing to
wear? Similarly, you cannot properly advise
someone on mental ability with a relative scale.

Herman Rubin, Sep 3, 2006
10. ### Herman RubinGuest

Herman Rubin, Sep 3, 2006
11. ### Reef FishGuest

Reef Fish, Sep 3, 2006
12. ### Reef FishGuest

Herman, have you EVER taken an IQ test? If so, which one?

Your paragraph is completely counter to ALL the IQ tests I've
taken or administered, many of which for MENSA, as a
national Proctor of their IQ tests for qualification for admission
to MENSA.

The AGCT (Army General Intelligence Test) reports the RAW
score, which is NOT the IQ. The raw scores are converted
to IQ via some normal distribution formula. I am not aware of
any IQ test that reports the quantile with respect to "the reference
sample" -- WHICH reference sample?
RU > - seems like a bit of an overstatement to me.HR> This is NOT an overstatement. It is the kind of
HR> misinterpretation which goes on continuously, and
HR> which has destroyed the level of education.

Herman, you seemed to have stated MANY of your own
misinterpretation about IQ and IQ tests yourself, out of your
own unfamiliarity with the subject.

The last couple of statements are patently ABSURD!

How do you think the MENSA applicants qualify on IQ
tests if the minimum requirement is 131 and an IQ test
never reports a value over 130?

How do you think those societies that admit memberships
based on mininum IQs of 150, or higher, based their
admission on selective IQ tests, if the IQ tests do not
report a value over 130?

Have you EVER taken an IQ test? (This is second time
false!). Or was it that you've never scored over 130 on
the IQ tests you took, if they were IQ tests at all.
-- Reef Fish Bob.

Reef Fish, Sep 3, 2006
13. ### Herman RubinGuest

Herman Rubin, Sep 4, 2006
14. ### Reef FishGuest

Reef Fish, Sep 4, 2006
15. ### Reef FishGuest

I need to clarify ONE POINT I made which should have been stated
in a better way.

Reef Fish, Sep 4, 2006
16. ### Herman RubinGuest

Herman Rubin, Sep 5, 2006
17. ### Reef FishGuest

Herman Rubin wrote:

But you're now singing a different tune! You said NO IQ tests are
normed
and that none (hardly any) yield IQ scores greater than 130 because of
the
small sample size of tests taken.

THOSE are the points I challenged you to substantiate.
TWO different versions of IQ were represented by the Marilyn Vos Savant
discrepancies. ONE was the old idea of a Quotient, and Vos Savant was

estimated to have an IQ of 228 because she scored at age 10 (0 month)
the equivalent of a 22 year-old used for THAT score.

On the other hand, when she took the IQ test that are NORMED to the
normal scale, her scores were back to the 168 level.

I supported NONE of your claims because your claims were ALL WRONG.

Non sequitur.
But we were discussing IQ scores. The high IQ societies use the SAME
IQ tests and the SAME scoring as IQ tests for morons!

You are just evading the issue in which you seriously erred and is
doing
the mis-direction from your claim that IQ tests rarely (or never)
yielded a
score greater than 130.

That prompted me to ask WHICH IQ test you actually took.

So far, NO RESPONSE from you.
I believe you are getting farther and farther away from YOUR assertions
that are patently FALSE, and you failed to name a SINGLE IQ test
which either you took or are familiar with its scoring.

You kept bringing back the irrelevant issues, such as you CRT and
the CRT history, which are NOT the issue of how IQ test scores are
ACTUALLY normed to fit an approximate NORMAL scale!
HR >> And as I said before, one can produce a scale by successive
HR >> comparison to various standards, but NOT by using quantiles.
Read my comment above AGAIN, Herman. I asked you to name ONE
single IQ test that is not based on the normal quantiles!

You failed to name ANY. You finally mentioned the AGCT and your own
score. But that score is NOT IQ, far from it! That is a well-known
example.

And then you try to relate IQ scores to scores on Aptitude tests that
are
NOT intended to measure IQ.
But was it an IQ test? Or some kind of high school Aptitude test?
Or was it an AGCT often mistaken to be an IQ test, in which a score
of 159 would correspond to an IQ of substantially lower score, but
sufficient as a substitute for qualification to MENSA, as certain SAT
scores are.
Well, I even guessed it before I got to this paragraph. What you
had were the Aptitude tests, which are DEFINITELY NOT IQ tests.
I had explained that in my preceeding posts. And you even clipped
it BELOW, but gave your own unsubstantiated OPINION that IQ and
what constitute aptitude tests.
Schools do not screen candidates on their IQ, but on their aptitude
for those special areas of studies.

The tests are intended to measure entirely different things although
there is always some inevitable correlation because one who has
a high IQ is like to have high aptitude in certain areas. But the
CONVERSE is not true!

An extreme case of the failure of the CONVERSE are those who special
aptitudes are astounding, but their IQs are those of IDIOTS, and hence
they are called Idiot Savants. (No relation to Vos Savant. )

The rest are just REHASH of old points, and Herman Rubin's
unsubstantiated
OPINION about aptitude tests that are contrary to their use and
intended
use in ALL colleges, universities, and professional schools.

NONE even admit any IQ test score as the substitute, to the best of my
knowledge.

-- Reef Fish Bob.

Reef Fish, Sep 5, 2006