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

In article <fm7hf2dkpr8a167c0tiq71ll5fbg61uvgk@xxxxxxx>,
Richard Ulrich <Rich.Ulrich@xxxxxxxxxxx> wrote:
On 1 Sep 2006 11:08:13 -0400, hrubin@xxxxxxxxxxxxxxxxxxxx (Herman
Rubin) wrote:

In article <1156962274.421938.297290@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pat <pat.mueller@xxxxxxxxxxxxxx> wrote:
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

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

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

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.

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

- seems like a bit of an overstatement to me.

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.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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