> > At 11:53 AM 2/28/2000 -0800, Judith A. Roberts wrote:
> > >Where did the mean of 100 and standard deviation of 15 for I.Q. come
> > >from? I did not have a clue about this one, and neither did one of the
> > >other statistics instructors.
To which Steven Specht replied:
> > My guess on this would be what Mark (not myself, but the other one) said
> > about keeping some consistency with the IQ=MA/CA*100 scoring system.
> > However, the issue of not having negative IQ scores is also a contributing
> > factor with most standardized scores that get reported to the general
> > public (SAT, GRE, etc.) How would you explain to a parent that their child
> > had a negative IQ or negative achievement? Just avoid the situation by
> > rescaling things to ease interpretation.
>
> I don't think folks are "rescaling" to prevent negative numbers or to avoid
> some situation. That strikes me as implying that, once again, statisticians
> are somehow arbitrarily manipulating numbers for some "convenience" rather
> than for some sound reason. I think most statisticians have better things to
> do (and get paid well for it).
> In order to get negative numbers with the IQ (Intelligence *Quotient*), one of
> the numbers in the ratio would have to be negative. Chronological age, for all
> intents and purposes, cannot be less than zero (unless you're referring to
> fetal age perhaps... but that could be included in the positive as well,
> technically). And mental age of less than zero really wouldn't make sense
> either, unless you're referring to some sort of Buddhist pre-life. Neither of
> these values makes any sense if they were negative. Therefore the quotient
> can't be negative, by definition of the concept, not by rescaling of the
> numbers.
Well, no. There are two approaches confused in the foregoing, it seems to me.
Early on, a "mental age" was calculated and a ratio of that MA to chronological
age was calculated and multiplied by 100 to get an IQ. The multiplication by
100 avoided having to deal with decimal fractions. Historically interesting;
currently not practiced, however.
Later that IQ calculation was abandoned, and IQ scores (so called) are
based on a distribution of scores with a known mean and standard deviation
(calculated from large numbers of tests administered). Individual scores in
that distribution can be converted easily to standard scores, which *truly can*
have negative values, because they are relative--in standard deviation units--
to the mean.
Standard scores (Z scores) can be converted to any mean and any standard
deviation one prefers. A mean of 100 recalls the "IQ" numbers of the early
years of the century and is readily comprehended as "normal." A standard
deviation of 15 is convenient, but simply arbitrary (some standard intelligence
tests, if I remember correctly, use 12 instead of 15).
Choosing a mean value low enough and a standard deviation value high
enough can indeed give negative numbers. No hint in any of that about
regression to past lives.
Pat Cabe
**************************************************
Patrick Cabe, Ph.D.
Department of Psychology
University of North Carolina at Pembroke
One University Drive
Pembroke, NC 28372-1510
(910) 521-6630
[EMAIL PROTECTED]
"Eternal vigilance is the price of liberty."
Thomas Jefferson
"There is the danger that everyone waits
idly for others to act in his stead."
Albert Einstein
"Majorities simply follow minorities.
Gandhi
