View Full Version : Standard terminology: "NORMALIZED"

unknown user
06-11-1994, 12:40 AM
Until I read p. 72 of the "Bible" of statistics (Glass and
Hopkins, 1970. Statistical methods in education and Psychology),
I had always used the term "NORMALIZED" to indicate the angular
momentum of the human body, when expressed relative to the product of
body mass and square stature. (While the unit of angular momentum is
Kg*m*m/s, that of the normalized angular momentum is just 1/s).
The underlying rationale was that "normalized" meant "RELATIVE"
to an appropriate yardstick (body mass times square stature) selected
to make possible and meaningful the comparison of the "normalized"
values determined for different subjects (having different mass and
In brief: NORMALIZED=RELATIVE to a yardstick selected to allow
meanigful comparisons between subjects. Let's call this the
"DEFINITION A" of the word "normalized".

After reading p.72 of Glass & Hopkins's book, I learned that
the term was first used by statisticians to indicate the result of
a relatively complex (and I would say somewhat questionable) form of
nonlinear transformation of the observed values (scores) of a given
variable. The effect of the transformation is that the distribution
curve of NORMALIZED scores is perfectly normal, while the curve of
the observed scores in not. Let's call this the "DEFINITION B" of
the word "normalized".

The latter definition (B) respects the ethimological meaning
of the word "normalized" (=become or made normal), while
the previous definition (A) doesn't. However, I learned definition "A"
from other resarchers, who used it in their works.

Concluding, I would like to know your opinion about definition
"A" (Normalized=relative... and comparable...):

1) Do you think it's correct?

2) Do you think it has been used long enough and by a large
enough number of reasearchers to become all over the world a
conventional and widely known operational definition?

With regards,

Paolo de Leva
Sport Biomechanics Lab
Istituto Superiore di Educazione Fisica

P.S.: I wonder who was the first author who used the term normalized
to mean "relative and comparable...". Is he or she among the