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

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

  1. Pat

    Pat Guest


    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:



    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, Aug 30, 2006
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  2. 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
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  3. Pat

    Reef Fish Guest

    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. Pat

    Herman Rubin Guest

    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. 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. Pat

    Reef Fish Guest

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

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

    Actually the history is not short. Plenty bloody alright. The
    "norming" and
    "re-norming" of test scores and IQ requirements for the admission of
    high IQ societies have repeatedly been done by the founders of two of
    Hi IQ societies, Kevin Langdon (of the Triple Nine Society) and Ron
    (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
    (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
    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.
    different IQ tests on her at the same age produced IQ score (on record
    at her school) as long as 168.

    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
    (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
    deviation -- thereafter, there is no reliable measure), and the
    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. Pat

    Reef Fish Guest

    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
    that the link indicated an ambiguous reference (probably from the
    truncation of the
    URL), but showed this page:

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

    The page was FULL of headlines about NORMING: The sixth, the fifth,
    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
    MENSA Society. The INTERNATIONAL membership of TNS never
    exceeded 700 over its many years of existence (I was admitted a member
    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
    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. Pat

    Reef Fish Guest

    Sorry I did not catch this non-obvious typo when it was written. The
    should read:
    Added footnote: MENSA admits anyone who scored in the top TWO
    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. Pat

    Herman Rubin Guest

    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. Pat

    Herman Rubin Guest

    Herman Rubin, Sep 3, 2006
  11. Pat

    Reef Fish Guest

    Reef Fish, Sep 3, 2006
  12. Pat

    Reef Fish Guest

    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
    I am asking because your mistaken notion is so astoundingly
    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. Pat

    Herman Rubin Guest

    Herman Rubin, Sep 4, 2006
  14. Pat

    Reef Fish Guest

    Reef Fish, Sep 4, 2006
  15. Pat

    Reef Fish Guest

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

    Reef Fish, Sep 4, 2006
  16. Pat

    Herman Rubin Guest

    Herman Rubin, Sep 5, 2006
  17. Pat

    Reef Fish Guest

    Herman Rubin wrote:

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

    And then you try to relate IQ scores to scores on Aptitude tests that
    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
    Aptitude Tests measure the same, or simply your opinion about
    what constitute aptitude tests.
    So what is your POINT? Colleges and Business Schools and Law
    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
    OPINION about aptitude tests that are contrary to their use and
    use in ALL colleges, universities, and professional schools.

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

    -- Reef Fish Bob.
    Reef Fish, Sep 5, 2006
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