Tweet
Here is the announced summary of opinions about the correct
meaning and usage of the word "NORMALIZED", or "NORMALIZATION", in
reply to my message of Jun, 11 (enclosed below).
I received many interesting responses, and am really grateful
to all those who helped me to better understand this multi-faceted
word, that seems to be appliable to infinite cases, and (as some of you
suggested) will possibly be used in the future with other new meanings,
as the scientific terminology keeps evolving and changing.
One of the most surprising meanings of the word "normalized" was
suggested by an eminent psychoanalyst (you won't find his message
in this summary: he called me at the phone, and didn't want his
name be published :-). Here is his definitions:
NORMALIZED is the PATIENT WHO GAVE UP PUTTING THE MICROWAVE OVEN INTO
HIS COLD COFFEE!!!
Contrary to Edsko Hekman's suggestion (about re-heating old coffee),
the psychoanalist INSISTED that IT IS IRRELEVANT whether the oven
WAS ON OR OFF!
(please see the ensuing messages by Bryan Finlay and Edsko Hekman
if you want to understand the joke.)
Paolo de Leva
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Date: Sat, 11 Jun 1994 16:40:56 +0200
From: "Paolo de Leva - Sport Biom. Rome"
Subject: Standard terminology: "NORMALIZED"
To: Multiple recipients of list BIOMCH-L
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
stature).
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
Rome, ITALY
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
subscribers?
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From: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Sat, 11 Jun 94 12:02:27 EDT
Subject: Re: Standard terminology: "NORMALIZED"
Paolo writes:
NORMALIZED=RELATIVE to a yardstick selected to allow
meanigful comparisons between subjects. Let's call this the
"DEFINITION A" of the word "normalized".
That definition is the normal one ;-)
Definition B is a restricted
special case of Definition A and is
used mostly by some who are introduced
to measurement and transformation problems
through statistics and social science. I think that
physicists would never use definition B, except as a
special case of definition A.
One's reaction depends on one's experience.
Social scientists will react to "normalized" (Def A) as an odd
use of the concept within Def B, whereas physical
scientists will react to "normalized" (Def B) as
you did-as a special hokey kind of fudging
transformation, and "normalized" (Def B) data as
data that have to be decoded (denormalized) before they
could be "normalized" (Def A).
One more point:
The Gaussian distribution is very widely called the "normal
distribution." That customary usage is probably a significant source of
strength the tendency to use Definition B.
[Signature deleted according to the desire of the writer]
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>From deleva Sat Jun 11 23:26:54 1994
Date: Sat, 11 Jun 1994 23:26:49 +0200
To: [deleted according to the desire of the writer]
Subject: Re: Standard terminology: "NORMALIZED"
Thanks (I cannot see your name anywhere in your message),
I am released to know that Def. A, the one I have been using
so long, is not just an improper application of a different concept.
(By the way, I don't think that Def. B can be viewed as a special
case of Def. A: they are quite different concepts).
I was doubting because I have never seen the word NORMALIZED in
a book of physics or mathematics. I have just seen it for the first
time reading a sport biomechanics paper. So I wondered (after reading
the statistics book):
1) Did only sport biomechanists give Def. A to the word?
2) Did only biomechanists give def. A to the word?
3) Will everybody in the world understand Def. A without
explicit operational declaration?
Paolo
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Sender: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Sun, 12 Jun 94 00:22:02 EDT
Subject: Re: Standard terminology: "NORMALIZED"
Paolo,
I am bioengineer and a psychologist, and
I wrote and edited technical publications for many
years at [...omitted...]
I do not think that we quite agree, but that is not
bad, because you are picking up on usage that is
conventional and fluid; finding out how the twists on words are
used requires exploration and reflection. You do not
find this kind of stuff in dictionaries (which are ALWAYS
out of date in subtle ways).
An unambiguous (relatively!) term in this area is
"z-score". Are you familiar with that? It means
(roughly!) normalized (Def B). If social
science people just used "z-score" instead of
"normalized,' there would be less confusion.
However, the confusion itself can stimulate and
be instructive. With that in mind, I never
correct anyone's spelling or use of our
beautiful, expressive, deep, resourceful
language. And I wish others would do the same!
Regards,
[Signature deleted according to the desire of the writer]
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>From deleva Sun Jun 12 13:27:41 1994
Date: Sun, 12 Jun 1994 13:27:36 +0200
To: [deleted according to the desire of the writer]
Subject: Re: Standard terminology: "NORMALIZED"
Thanks [omitted name],
I appreciate your explanations. Of course I know what is a
z-score, and also a T-score. However, they are usually defined
STANDARD scores, and not normalized. See also Glass and Hopkins for that.
Def. B of "NORMALIZED" is quite different. You will realize that
if you read again my first message (or read the book). It's not
a linear transformation done to make the score comparable with
other scores. It's a NONLINEAR transformation of T-SCORES, which
makes the T-SCORES (usually T-SCORES and not z-SCORES undergo the process
of NORMALIZATION) perfectly fitting a normal curve. Thus, normalization is
a process tha comes after, and has different purposes with respect to
"standardization" (the latter being LINEAR transformation to z-scores
and T-scores).
Paolo de Leva
----------------------------------------------------------------------------
Sender: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Tue, 14 Jun 94 17:10:51 EDT
Subject: normalization
Paolo,
I think that you have opened a can of worms. The more I think about
"normalized", the more sure I am that I know more than the last time
I thought about it, and the more unsure I am that what I now think about
it is adequate.
The term (and related terms) has a lot of independent sources,
and the apparent independent sources may not really be independent.
For example, the mathematical meanings of "norm"
and "normalized function" are probably factors. I say "probably"
because there is no agreed way of deciding whether such
possible linguistic extensions and inductions are "real".
A normalized function has norm unity, and one meaning
of "normalize" is to transform the measure so
that it ranges from zero to one. However, "normalize" is
also used to mean constrain the measure to +/-1. And
a related common usage is Def A. Note that you could normalize
(constrain) measures and still not make them comparable
by Def A. But usually both things happen at once.
We now have several definitions of "normalize." I hope
that the intended meaning is clear from here on.
There is another word that is used in almost the same way:
"specific." as in specific gravity, specific charge, etc.
The intent is to adopt measures that are well-behaved
in certain environments. This is so familiar to us
that we barely think about it. For example, if we
want a strong space material, its mass is also important
(because it has to be lifted into orbit). So we use
specific strength (strength per kg). But specific
strength is better behaved in many ways, and would be used
even if we had no space program. If volume were a concern,
we would define A (not THE) specific strength as strength per cubic mm.
In these cases, we might "normalize" the measure by expressing it in
molecular bond strength units (so that a theoretical maximum
was unity).
We normalize measures in order to make them comparable for a
given purpose. We make up a normalized measure as
conditions require. Sometimes, the normalization
becomes pretty standard, and then it goes into common use,
and then it may get into dictionaries, as well as books
and journals and lectures. Naturally, normalized
measures are more common in use than in dictionaries.
I can't think of any in dictionaries offhand.
The main point I want to make is that there is not a
"correct" meaning of "normalize." There are familiar
meanings and unfamiliar meanings that extend the usage.
You can insist on a certain meaning, and many will agree,
but you won't stop new usages.
I suspect that for simple transformations of x, which imply
an easy-to-understand unit, people use the term "specific x",
and for more complex cases, where the implicit unit is
more exotic, people would tend to use the term "normalized"
(even when the range is not zero to unity).
If that's so, then nonlinear transformations would be
more likely to be called "normalizations". But I feel that I
am completely out of my depth now.
Regards,
[Signature deleted according to the desire of the writer].
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>From deleva Thu Jun 16 23:22:40 1994
Date: Thu, 16 Jun 1994 23:22:25 +0200
To: [deleted according to the desire of the writer]
Subject: Re: normalization
Am I right, in your opinion, if I say that only statisticians
use the term "normalization" referring to NONLINEAR transformations?
I would suggest you to neatly distinguish between the statistical
definition and the mathematical-physical definition.
Thanks,
Paolo de Leva
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From: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Fri, 17 Jun 94 21:00:11 EDT
Subject: Re: normalization
Dear Paolo,
You ask:
Am I right, in your opinion, if I say that only statisticians
use the term "normalization" referring to NONLINEAR transformations?
I would suggest you to neatly distinguish between the statistical
definition and the mathematical-physical definition.
No, no, Paolo. Statisticians are more likely than
other scientists and mathematicians
to use"normalized"
as meaning "linearized on the assumption that the
data being normalized are Gaussian (with parameters
so-and-so)." It is, I suggest, by mysterious cognitive
processes, that "normalize" is used by extension
for cases where the transformation is complex or nonlinear.
I pay more attention to the way the words are used, and
not so much to the way they "ought to be used"
for clarity, precision, etc. Words get carried beyond
their original meaning and domains, but the novel usages
bear some clues as to their provenance, at which I guess. That is the
theory that guides me. It's hard to disprove such a
vague theory.
Paolo, please do not identify me in your posting.
My remarks were only for you, and do not bear
scrutiny by the multitude. My theory deserves a
more powerful presentation!
Thanks,
[Signature deleted according to the desire of the writer]
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From: dapena@valeri.hper.indiana.edu
Date: Sun, 12 Jun 94 14:28:09 -0500
To: deleva@risccics.ing.uniroma1.it
Subject: Re: Standard terminology: "NORMALIZED"
Paolo,
The meaning "relative to a yardstick selected to allow
meaningful comparisons among subjects" for the word "normalized" is very
widespread among researchers. I would advise you to use it.
Jesus
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Date: Mon, 13 Jun 1994 10:22:23 +0800
To: deleva@risccics.ing.uniroma1.it
From: ikirtley@info.curtin.edu.au (Chris Kirtley)
Subject: Re: Standard terminology: "NORMALIZED"
Dear Paolo,
I also understand the term "normalised" to mean ensemble averaging of the
time axis to average several strides of different durations.
I agree that this term is badly defined - perhaps we could make it more
specific by qualifying its use with the parameter being "normalised", e.g.
"body-weight normalised", "stature-normalised", "time-normalised", etc.
Chris
from...
Dr. Chris Kirtley MB ChB, PhD,
Lecturer, bio-engineering,
School of Physiotherapy,
Curtin University of Technology,
GPO Box U1987,
Perth 6001
Western Australia.
Tel. (09) 381 0600
Fax (09) 381 1496
e-mail: c.kirtley@info.curtin.edu.au
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From: "TJ. Lawes"
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
Date: Mon, 13 Jun 1994 09:14:56 +0100 (BST)
'Normalised' is a term which has received a widespread beating over many
years of scientific endeavour in an attempt to produce comparable scores
between tests and/or subjects. So what is the basis for being able to perform
this systematically and with good logical mathematical argument.
The answer comes from the branch of analysis known as 'Dimensionless
Analysis' for I do not claim to have a fully comprehensive background.
The aim of the excercise in mathematical manipulation is to produce a
quantity which is not measurement based and therefore 'accounts' for
unwanted variables.
To describe by example, when measuring the stiffness of a fracture during
healing, we can measure the motion of the fragments relative to each other
at the fracture interface. However, we know that this is not the complete
story. If we can measure the motion at the fracture, it can only be
compared to motion at other fracture sites on individual patients if the
applied load is the same. We know this cannot be controlled in singular
patients normal gait, let alone in a distribution. Hence the motion and
the applied load are measured in order to 'normalise' the results. In
this way, different patient/fractures may be directly compared. This is
not a true Dimensionless Analysis as the resulting quantity still has
units, in this case N/m.
However, it can be seen that the normalised quantity is useful, wheras the
original measurement of motion provides no benefit. Then, it is a
sufficient definition to view normalised numbers as being transformed, by
either a second parameter (as in definition A of Normalised) or, equally
acceptably, by using a parameter model, (as I believe is your definition B
of Normalised, without having read the artcicle you reference).
Hence, normalised is applied more widely as a technique of analysis,
rather than a specific result.
I hope this is helpful to your enquiry.
(Hand written sig.) ->
Timothy J. Lawes
Biomedical Research Engineer,
Bristol University,
Dept. of Anatomy, Vet School.
Southwell St. Bristol BS2 8EJ
(0272) 303197
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Date: Mon, 13 Jun 1994 09:45:51 -0400 (EDT)
From: CRISCO@BIOMED.MED.YALE.EDU
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
As is often observed, the same word has different meanings when used in
different fields of study. I belive both are correct. We often used
"normalized", as in your Definition A, for any variable that has been non-
dimensionalized for comparative analysis.
Trey Crisco, Ph.D.
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Date: Mon, 13 Jun 1994 12:26:05 -0400 (EDT)
From: James Dowling
Subject: Re: Standard terminology: "NORMALIZED"
To: "Paolo de Leva - Sport Biom. Rome"
Dear Paolo,
I was certainly not the first to use the term "normalized" due to my
tender years but I have both used it and read it often and it has always
been in the context of your definition A. I believe that it would be too
difficult to change to a new term and since one must always state in the
methods how they normalized the data, authors can choose to either divide
by a constant, a variable such as mass, or use a transformation that
makes the data normally distributed about a mean. Please let me know
what others think.
Jim Dowling
Dept. of Kinesiology
McMaster University
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Date: Tue, 14 Jun 94 08:35:10 IST
From: Moshe
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
Dear Paolo:
I believe many words has multiple meaning, especially in English. So what?
Normalized, meaning corrected to get an independent value, is used for long
enough to become a legitimate word.
I could think of at least one more meaning to normalized, related to
psychiatry. And if I was an English expert, I'm sure I could find some more.
I believe language is for human use, and as long as the meaning is clear in
the specific context, one can use the word.
Sorry if I am not clear. As I said, I am not a real English speaking. I
reacted only because we have exactly the same problems with our language,
Hebrew. Some people try to prevent the use of certain words in certain
meanings. But it is a waist of time.
Moshe
********************************************!***** **********************
* MOSHE NISSAN, PHD ! FAX: 972-3-6974546 *
* BIO-MEDICAL ENGINEER ! TEL: 972-3-6974720 (WORK)*
* Dept. Orthopaedics B' ! : 972-4-371788 (home) *
* TEL-AVIV SOURASKY MEDICAL CENTER ! *
* 6 Weitzman st. Tel-Aviv 64239 ISRAEL ! Bitnet: RPRNISN@TECHNION *
************************************************** **********************
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Date: Tue, 14 Jun 1994 17:58:40 +0200
From: deleva
To: RPRNISN@TECHNION.TECHNION.AC.IL, deleva@risccics.ing.uniroma1.it
Subject: Re: Standard terminology: "NORMALIZED"
I am not trying to limit the use of the word "normalized".
On the contrary, I WOULD WANT TO USE IT!
I was just asking if Def. A was used by a large enough number
of people to be considered a standard definition. I asked because I
would want to be understood by everybody when I write my papers,
and I was not sure that the word normalized was understood by everybody
in the meaning I was interested in.
Paolo
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Date: Fri, 17 Jun 94 08:37:24 IST
From: Moshe
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
Dear Paolo:
I am sorry if my response seemed a bit aggressive. It is another prove to
my claim that there is no chance everyone will understand you the way you want.
I gave up on this hope long ago. I was teaching pure physics at university
and it always amaised me how could some of my students understand questions
in a different way from the one I meant,no matter the extent of clarifications,
explanations etc.
And to your question: yes, I believe "Normalized" is used and accepted world
wide, and it can be used freely in case the text is purely biomechanics. If
statistics is involved (beyond sd and significance), than one should define
"Normalized" in the paper.
Bye for now, yours, Moshe
********************************************!***** **********************
* MOSHE NISSAN, PHD ! FAX: 972-3-6974546 *
* BIO-MEDICAL ENGINEER ! TEL: 972-3-6974720 (WORK)*
* Dept. Orthopaedics B' ! : 972-4-371788 (home) *
* TEL-AVIV SOURASKY MEDICAL CENTER ! *
* 6 Weitzman st. Tel-Aviv 64239 ISRAEL ! Bitnet: RPRNISN@TECHNION *
************************************************** **********************
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Date: Tue, 14 Jun 1994 13:41:30 EDT
From: "J.B. FINLAY"
Subject: "NORMALIZATION..."
To: Multiple recipients of list BIOMCH-L
Paolo's question about "Normalization" highlights a common problem
that we have with communications. This problem arises from peoples'
(our) tendency to talk and write using abbreviated phrases. Such
phrases may have appropriately implied meanings ONLY among those
individuals who are accustomed to them and, even then, only when
the phrases are encountered in a clearly-defined context.
This problem is well-reflected in the statement:
I PUT THE COFFEE IN THE MICROWAVE
Without discussing any of the POSSIBLE meanings (Stupid, theoretical,
practical, or otherwise), suffice it to say that the probable
information intended to be conveyed by this statement is:
I PUT THE CUP/MUG OF COFFEE IN THE MICROWAVE OVEN
and we can still debate whether the coffee was in solution or not!
NORMALIZED DATA:
In terms of "Normalized Data", any potential problem should be avoided
by speaking or writing the complete implied phrase (using Reference
citations, if necessary):
THE PROBABILITY DISTRIBUTION OF the data was normalized by...
or
THE MAGNITUDES OF the data were normalized by...
In the first statement, "normalized" actually implies that the
Probability Distribution curve was converted to that of a statistically-
defined "Normal" curve and, for this statement to be properly understood
in a manuscript, it would be appropriate to cite a reference to a
textbook in Statistics.
Once this procedure of normalization has been established in the
conversation or manuscript, then an "abbreviated" reference to
"normalization" might be warranted.
Few, if any, reports of biomechanical data can be presented
meaningfully without the use of statistics. Consequently, as
Biomechanicians, we should be particularly attuned to this problem.
As participants in the multi-disciplinary field of Biomechanics
(Biology, with its coverage of both plants and animals, involves
Human Biology as only one small element of its activities), our
communications should be such as to minimize these potential
misunderstandings - i.e. rather than trying to justify the use of
ambiguous phrases based upon interpretations used within our own
limited circle-of-colleagues or discipline - e.g. fluid mechanics,
etc.
I hope this personal impression of the problem will help in the
ensuing discussion.
Best wishes:
Bryan Finlay, PhD 519-663-3063
Director of Orthopaedic Research 519-663-3904 FAX
University Hospital
P.O. Box 5339
London, Ontario, CANADA, N6A 5A5
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Date: Tue, 14 Jun 1994 23:41:39 +0200
From: "Paolo de Leva - Sport Biom. Rome"
Subject: NORMALIZED?
To: Multiple recipients of list BIOMCH-L
I appreciated Bryan Finlay's reply to my message about the
meaning of the word "NORMALIZATION", and I think it was useful for us
to be reminded that our language should be as much as possible explicit
and clear, to be understandable by the largest possible number of readers
with different backgrounds, although the need of synthesis often
prevents us from defining explicitly all the words and expressions we
use, and I am sure there's no way to avoid a large amount of implicit
concepts in any kind of communications (scientific papers included).
If I said to my wife that I AM PUTTING THE CUP CONTAINING COFFEE
IN SOLUTION INTO THE MICROWAVE OVEN, my wife would laugh at me. And the
same would happen if I used unduly and boringly explicit phrases in the
context of scientific communications.
Good writers or lecturers possess, I believe, the skill
to choose to be explicit whenever and only when the conveyed concepts
may be not familiar to any of the possible cathegories of readers or
listeners. On the other hand, they are master in the art of avoiding
wasting words whenever and only when the conveyed concepts may be
understood using standardized terminology and expressions.
I would add that probably the latter "art" is the most appreciated
and at the same time the most complex.
That's the reason why I wanted to know if my definition "A"
of the word "NORMALIZED" was widespread enough to have become a
standard definition: I need to use the concept of "normalized", according
to Def. A, in my next paper.
Paolo de Leva
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Date: Wed, 15 Jun 1994 07:53:34 GMT
From: Edsko Hekman
Subject: Re: NORMALIZED?
To: Multiple recipients of list BIOMCH-L
I would like to suggest that RE-HEATING OLD COFFEE should not become a
NORMALIZED procedure...
Edsko Hekman
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From: "J.B. FINLAY"
To: deleva@risccics.ing.uniroma1.it
Date: Wed, 15 Jun 94 08:28:58 EDT
Subject: Normalization and publications
Hi Paolo:
I guess you focussed on my attempted "humourous" introduction to my
answer to your question.
I believe the answer to your "restated question" is that, if the
Journal you propose to use is a Journal that publishes articles with
statistics in them, then you can expect that the word "normalized"
may be viewed in a statistical concept. Simply, any use of "meams"
(that should have been typed MEANS) and "standard deviations" have
implications to the existence of a "Normal" curve. Where a "normal"
curve did not exist in the original data, it is quite common (and
statistically acceptable) to apply a transform to the data so that
there probability distribution satisfies that of a normal curve.
Under such circumstances, the transforming equation (used to
normalize the data) would be expected to be quoted.
My original conclusion summarized this point. If the publication
is in a Biomechanics journal, then one definition cannot be assumed
over the other - since statistics are an essential tool in the
description of Biological systems.
I will be interested to see what other responses you get. Since
responses on the Bulletin Board are often seen as "Grandstanding",
I guess I should have addressed my original response to you and
let you summarize the responses.
Best of wishes with the publication.
Best wishes:
Bryan Finlay, PhD 519-663-3063
Director of Orthopaedic Research 519-663-3904 FAX
University Hospital
P.O. Box 5339
London, Ontario, CANADA, N6A 5A5
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>From deleva Wed Jun 15 23:43:58 1994
Date: Wed, 15 Jun 1994 23:43:44 +0200
To: bfinlay@uwovax.uwo.ca, deleva@risccics.ing.uniroma1.it
Subject: Re: Normalization and publications
Thanks, Bryan.
I will send the article to the Journal of Biomechanics, as soon as
my private reviewer (=friend) in USA will return it with the right english
words instead of my "ITALIANIZED" (how about this new word? :-)) words.
I disagree with you for a small detail: normalizing (statistical
meaning) the data, according to the definition of GLASS and HOPKINS, is
a quite questionable method, in my opinion.
I think you define the statistical "normalization" differently
from Glass and Hopkins. Probably you refer to the non-linear
transformations (such as changing the scale using square root,
or lgarithm of the observations) which help to correct the shape
of a skewed curve. The result of such transformations is usually to
a curve which is MORE NEARLY normal than the original.
The latter is a good method, I think. But the "normalization"
described by Glass and Hopkins introduces changes in the scores that
don't have a logic at all. They don't follow the square of the original
observations, or their logarithm. A normalized T score is obtained by
"first converting the orig. scores to percentiles, and then
converting each percentile to the score corresponding to that percentile
in a normal distribution". Do you see what I mean now? Let's suppose
I got an IQ score of 99.99, while the person immediately below me got
a score of 94, and the subject immediately above got just 100.0. When
the scores are normalized, I might end out with a normalized T-score of
96, while the other two persons might stay with their score! That's
rather questionable, I am sure you agree: my score was decreased just
because a "NOT SENSIBLE" statistician thought that his data would look
nicer if they had a PERFECTLY normal shape, while actually it is PERFECTLY
"NORMAL", and plausible that an observed distribution never be PERFECTLY
NORMAL (it never ever can be!!!), because of measurement errors,
and especially of SAMPLING ERRORS!
My score was decreased just because the statistician
did not get enough subjects with a score ranging between 94 and 99.9!
But sampling errors do exist, and I want my score to be closer
to 100 than to 94, because 99.99 is what I got, and I DESERVE it:
it was very hard for me to get it!!!!
Paolo de Leva
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From: "J.B. FINLAY"
To: deleva@risccics.ing.uniroma1.it
Date: Thu, 16 Jun 94 09:24:41 EDT
Subject: Re: Normalization and publications
Dear Paolo:
Thanks for the note.
You were correct about the "transformations" that I was trying to explain.
I appreciate the nonsensity of the process that you described which
actually "removes" information for the data set.
Best of luck with your submission to J.Biomech. This is the mut
multidisciplinary journal that I had in mind as I was writing. I
have just submitted a paper to them. On the basis of my submissions
to them in the past, the reviews depend entirely upon whether it
goes to physicians, surgeons, plant biologists, electrical engineers,
mechanical, etc... At least the new guidelines for submission to
J.Biomech. invite the author to suggest the names of some potential
reviewers.
Based on our communications, I find it hard to believe that you need
someone to check your English; however, you can never go wrong in
getting someone else to read your material - if deadlines permit!
Best wishes:
Bryan Finlay, PhD 519-663-3063
Director of Orthopaedic Research 519-663-3904 FAX
University Hospital
P.O. Box 5339
London, Ontario, CANADA, N6A 5A5
----------------------------------------------------------------------------
Date: Thu, 16 Jun 1994 23:58:25 +0200
From: "Paolo de Leva - Sport Biom. Rome"
Subject: "questionable" transformation
To: Multiple recipients of list BIOMCH-L
I would like to point out that in my first message to BIOMCH-L
about "Standard terminology: NORMALIZED", I defined questionable the
nonlinear transformation which is defined as "NORMALIZATION" in the
book by Glass and Hopkins (Statistical methods in Education and Psychology),
and not other kinds of nonlinear transformations which are used in
statistics to correct skewed distributions of data.
The latter transformations (simply defined by Glass & Hopkins
as "TRANSFORMATIONS" -see p.70- or "NONLINEAR TRANSFORMATIONS" -see
note, p.70) are changes of scale, for example replacement of scores
by the logarithm or square root of the raw scores themselves, WHICH
MAKE THE FREQUENCY DISTRIBUTION MORE NEARLY NORMAL.
And that's perfectly acceptable to me. What I defined qiestionable
(and I am sure many will agree) is the normalization defined as in my
"Definition B" (see previous message), that MAKES THE DISTRIBUTION
PERFECTLY NORMAL (P E R F E C T L Y). Glass and Hopkins explain that:
"NORMALIZED scores are obtained by first converting the original scores to
percentiles and then converting each percentile to the score corresponding to
that percentile in a normal distribution"...
If you are curious to know why I think the latter kind of
statistical normalization is questionable, read my summary of responses
to my previous posting ("Standard terminology: NORMALIZED"). I will
post the summary tomorrow.
With regards,
Paolo de Leva
Istituto Superiore di Educazione Fisica
Biomechanics Lab
Via di Villa Pepoli, 4
00153 ROME
ITALY
Tel: 39-6-575.40.81
FAX: 39-6-361.30.65
e-mail address: DELEVA@RISCcics.ing.uniRoma1.IT
----------------------------------------------------------------------------
Date: Thu, 16 Jun 1994 23:18:04 -0600 (CST)
From: "Steve Nordquist of Overland Park, KS"
Subject: NORMALIZATION (Biomch.)
To: DELEVA@risccics.ing.uniroma1.it
From seeing this issue addressed in _Science_ (english ed.) three or
so years ago, where there was a bit of fret on it, and previously, when
a few definitions were trotted out, I got these impressions:
The first goal of the normalization should be to show off the details of
your empirical data. Therefore, any fit to a log-log chart or so should
be done carefully as to preserve any deviation from simplistic forms
that would otherwise appear in the 4" wide by 322" high graph you would
have without logarithms...that sort of practice has to be done FIRST,
THEN you go and...
Normalize by:
a) Complying with the usual application in the journal, asuming you
aggree with it.
b) Clipping outliers, and making the corequisite disclaimers and thorough
explanation
c) Otherwise move samples around, explaining why the way is so agreeable.
I haven't seen 'Normalized' alone in a paper yet where it didn't have to be
commented on later in "errata" or the policy of the journal (inside the front
cover, next to: "Warning! Substantive, not editorial!")
Has biomechanics really progressed so that normalization makes it clear
when an 'outlying' group is clearly definable as an extraordinary effort on
the part of the subject?
Steve Nordquist
----------------------------------------------------------------------------
END OF SUMMARY
Paolo de Leva
Istituto Superiore di Educazione Fisica
Biomechanics Lab
Via di Villa Pepoli, 4
00153 ROME
ITALY
Tel: 39-6-575.40.81
FAX: 39-6-361.30.65
e-mail address: DELEVA@RISCcics.ing.uniRoma1.IT
meaning and usage of the word "NORMALIZED", or "NORMALIZATION", in
reply to my message of Jun, 11 (enclosed below).
I received many interesting responses, and am really grateful
to all those who helped me to better understand this multi-faceted
word, that seems to be appliable to infinite cases, and (as some of you
suggested) will possibly be used in the future with other new meanings,
as the scientific terminology keeps evolving and changing.
One of the most surprising meanings of the word "normalized" was
suggested by an eminent psychoanalyst (you won't find his message
in this summary: he called me at the phone, and didn't want his
name be published :-). Here is his definitions:
NORMALIZED is the PATIENT WHO GAVE UP PUTTING THE MICROWAVE OVEN INTO
HIS COLD COFFEE!!!
Contrary to Edsko Hekman's suggestion (about re-heating old coffee),
the psychoanalist INSISTED that IT IS IRRELEVANT whether the oven
WAS ON OR OFF!
(please see the ensuing messages by Bryan Finlay and Edsko Hekman
if you want to understand the joke.)
Paolo de Leva
----------------------------------------------------------------------------
Date: Sat, 11 Jun 1994 16:40:56 +0200
From: "Paolo de Leva - Sport Biom. Rome"
Subject: Standard terminology: "NORMALIZED"
To: Multiple recipients of list BIOMCH-L
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
stature).
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
Rome, ITALY
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
subscribers?
----------------------------------------------------------------------------
From: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Sat, 11 Jun 94 12:02:27 EDT
Subject: Re: Standard terminology: "NORMALIZED"
Paolo writes:
NORMALIZED=RELATIVE to a yardstick selected to allow
meanigful comparisons between subjects. Let's call this the
"DEFINITION A" of the word "normalized".
That definition is the normal one ;-)
Definition B is a restricted
special case of Definition A and is
used mostly by some who are introduced
to measurement and transformation problems
through statistics and social science. I think that
physicists would never use definition B, except as a
special case of definition A.
One's reaction depends on one's experience.
Social scientists will react to "normalized" (Def A) as an odd
use of the concept within Def B, whereas physical
scientists will react to "normalized" (Def B) as
you did-as a special hokey kind of fudging
transformation, and "normalized" (Def B) data as
data that have to be decoded (denormalized) before they
could be "normalized" (Def A).
One more point:
The Gaussian distribution is very widely called the "normal
distribution." That customary usage is probably a significant source of
strength the tendency to use Definition B.
[Signature deleted according to the desire of the writer]
----------------------------------------------------------------------------
>From deleva Sat Jun 11 23:26:54 1994
Date: Sat, 11 Jun 1994 23:26:49 +0200
To: [deleted according to the desire of the writer]
Subject: Re: Standard terminology: "NORMALIZED"
Thanks (I cannot see your name anywhere in your message),
I am released to know that Def. A, the one I have been using
so long, is not just an improper application of a different concept.
(By the way, I don't think that Def. B can be viewed as a special
case of Def. A: they are quite different concepts).
I was doubting because I have never seen the word NORMALIZED in
a book of physics or mathematics. I have just seen it for the first
time reading a sport biomechanics paper. So I wondered (after reading
the statistics book):
1) Did only sport biomechanists give Def. A to the word?
2) Did only biomechanists give def. A to the word?
3) Will everybody in the world understand Def. A without
explicit operational declaration?
Paolo
----------------------------------------------------------------------------
Sender: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Sun, 12 Jun 94 00:22:02 EDT
Subject: Re: Standard terminology: "NORMALIZED"
Paolo,
I am bioengineer and a psychologist, and
I wrote and edited technical publications for many
years at [...omitted...]
I do not think that we quite agree, but that is not
bad, because you are picking up on usage that is
conventional and fluid; finding out how the twists on words are
used requires exploration and reflection. You do not
find this kind of stuff in dictionaries (which are ALWAYS
out of date in subtle ways).
An unambiguous (relatively!) term in this area is
"z-score". Are you familiar with that? It means
(roughly!) normalized (Def B). If social
science people just used "z-score" instead of
"normalized,' there would be less confusion.
However, the confusion itself can stimulate and
be instructive. With that in mind, I never
correct anyone's spelling or use of our
beautiful, expressive, deep, resourceful
language. And I wish others would do the same!
Regards,
[Signature deleted according to the desire of the writer]
----------------------------------------------------------------------------
>From deleva Sun Jun 12 13:27:41 1994
Date: Sun, 12 Jun 1994 13:27:36 +0200
To: [deleted according to the desire of the writer]
Subject: Re: Standard terminology: "NORMALIZED"
Thanks [omitted name],
I appreciate your explanations. Of course I know what is a
z-score, and also a T-score. However, they are usually defined
STANDARD scores, and not normalized. See also Glass and Hopkins for that.
Def. B of "NORMALIZED" is quite different. You will realize that
if you read again my first message (or read the book). It's not
a linear transformation done to make the score comparable with
other scores. It's a NONLINEAR transformation of T-SCORES, which
makes the T-SCORES (usually T-SCORES and not z-SCORES undergo the process
of NORMALIZATION) perfectly fitting a normal curve. Thus, normalization is
a process tha comes after, and has different purposes with respect to
"standardization" (the latter being LINEAR transformation to z-scores
and T-scores).
Paolo de Leva
----------------------------------------------------------------------------
Sender: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Tue, 14 Jun 94 17:10:51 EDT
Subject: normalization
Paolo,
I think that you have opened a can of worms. The more I think about
"normalized", the more sure I am that I know more than the last time
I thought about it, and the more unsure I am that what I now think about
it is adequate.
The term (and related terms) has a lot of independent sources,
and the apparent independent sources may not really be independent.
For example, the mathematical meanings of "norm"
and "normalized function" are probably factors. I say "probably"
because there is no agreed way of deciding whether such
possible linguistic extensions and inductions are "real".
A normalized function has norm unity, and one meaning
of "normalize" is to transform the measure so
that it ranges from zero to one. However, "normalize" is
also used to mean constrain the measure to +/-1. And
a related common usage is Def A. Note that you could normalize
(constrain) measures and still not make them comparable
by Def A. But usually both things happen at once.
We now have several definitions of "normalize." I hope
that the intended meaning is clear from here on.
There is another word that is used in almost the same way:
"specific." as in specific gravity, specific charge, etc.
The intent is to adopt measures that are well-behaved
in certain environments. This is so familiar to us
that we barely think about it. For example, if we
want a strong space material, its mass is also important
(because it has to be lifted into orbit). So we use
specific strength (strength per kg). But specific
strength is better behaved in many ways, and would be used
even if we had no space program. If volume were a concern,
we would define A (not THE) specific strength as strength per cubic mm.
In these cases, we might "normalize" the measure by expressing it in
molecular bond strength units (so that a theoretical maximum
was unity).
We normalize measures in order to make them comparable for a
given purpose. We make up a normalized measure as
conditions require. Sometimes, the normalization
becomes pretty standard, and then it goes into common use,
and then it may get into dictionaries, as well as books
and journals and lectures. Naturally, normalized
measures are more common in use than in dictionaries.
I can't think of any in dictionaries offhand.
The main point I want to make is that there is not a
"correct" meaning of "normalize." There are familiar
meanings and unfamiliar meanings that extend the usage.
You can insist on a certain meaning, and many will agree,
but you won't stop new usages.
I suspect that for simple transformations of x, which imply
an easy-to-understand unit, people use the term "specific x",
and for more complex cases, where the implicit unit is
more exotic, people would tend to use the term "normalized"
(even when the range is not zero to unity).
If that's so, then nonlinear transformations would be
more likely to be called "normalizations". But I feel that I
am completely out of my depth now.
Regards,
[Signature deleted according to the desire of the writer].
----------------------------------------------------------------------------
>From deleva Thu Jun 16 23:22:40 1994
Date: Thu, 16 Jun 1994 23:22:25 +0200
To: [deleted according to the desire of the writer]
Subject: Re: normalization
Am I right, in your opinion, if I say that only statisticians
use the term "normalization" referring to NONLINEAR transformations?
I would suggest you to neatly distinguish between the statistical
definition and the mathematical-physical definition.
Thanks,
Paolo de Leva
----------------------------------------------------------------------------
From: [deleted according to the desire of the writer]
To: deleva@risccics.ing.uniroma1.it
Date: Fri, 17 Jun 94 21:00:11 EDT
Subject: Re: normalization
Dear Paolo,
You ask:
Am I right, in your opinion, if I say that only statisticians
use the term "normalization" referring to NONLINEAR transformations?
I would suggest you to neatly distinguish between the statistical
definition and the mathematical-physical definition.
No, no, Paolo. Statisticians are more likely than
other scientists and mathematicians
to use"normalized"
as meaning "linearized on the assumption that the
data being normalized are Gaussian (with parameters
so-and-so)." It is, I suggest, by mysterious cognitive
processes, that "normalize" is used by extension
for cases where the transformation is complex or nonlinear.
I pay more attention to the way the words are used, and
not so much to the way they "ought to be used"
for clarity, precision, etc. Words get carried beyond
their original meaning and domains, but the novel usages
bear some clues as to their provenance, at which I guess. That is the
theory that guides me. It's hard to disprove such a
vague theory.
Paolo, please do not identify me in your posting.
My remarks were only for you, and do not bear
scrutiny by the multitude. My theory deserves a
more powerful presentation!
Thanks,
[Signature deleted according to the desire of the writer]
----------------------------------------------------------------------------
From: dapena@valeri.hper.indiana.edu
Date: Sun, 12 Jun 94 14:28:09 -0500
To: deleva@risccics.ing.uniroma1.it
Subject: Re: Standard terminology: "NORMALIZED"
Paolo,
The meaning "relative to a yardstick selected to allow
meaningful comparisons among subjects" for the word "normalized" is very
widespread among researchers. I would advise you to use it.
Jesus
----------------------------------------------------------------------------
Date: Mon, 13 Jun 1994 10:22:23 +0800
To: deleva@risccics.ing.uniroma1.it
From: ikirtley@info.curtin.edu.au (Chris Kirtley)
Subject: Re: Standard terminology: "NORMALIZED"
Dear Paolo,
I also understand the term "normalised" to mean ensemble averaging of the
time axis to average several strides of different durations.
I agree that this term is badly defined - perhaps we could make it more
specific by qualifying its use with the parameter being "normalised", e.g.
"body-weight normalised", "stature-normalised", "time-normalised", etc.
Chris
from...
Dr. Chris Kirtley MB ChB, PhD,
Lecturer, bio-engineering,
School of Physiotherapy,
Curtin University of Technology,
GPO Box U1987,
Perth 6001
Western Australia.
Tel. (09) 381 0600
Fax (09) 381 1496
e-mail: c.kirtley@info.curtin.edu.au
----------------------------------------------------------------------------
From: "TJ. Lawes"
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
Date: Mon, 13 Jun 1994 09:14:56 +0100 (BST)
'Normalised' is a term which has received a widespread beating over many
years of scientific endeavour in an attempt to produce comparable scores
between tests and/or subjects. So what is the basis for being able to perform
this systematically and with good logical mathematical argument.
The answer comes from the branch of analysis known as 'Dimensionless
Analysis' for I do not claim to have a fully comprehensive background.
The aim of the excercise in mathematical manipulation is to produce a
quantity which is not measurement based and therefore 'accounts' for
unwanted variables.
To describe by example, when measuring the stiffness of a fracture during
healing, we can measure the motion of the fragments relative to each other
at the fracture interface. However, we know that this is not the complete
story. If we can measure the motion at the fracture, it can only be
compared to motion at other fracture sites on individual patients if the
applied load is the same. We know this cannot be controlled in singular
patients normal gait, let alone in a distribution. Hence the motion and
the applied load are measured in order to 'normalise' the results. In
this way, different patient/fractures may be directly compared. This is
not a true Dimensionless Analysis as the resulting quantity still has
units, in this case N/m.
However, it can be seen that the normalised quantity is useful, wheras the
original measurement of motion provides no benefit. Then, it is a
sufficient definition to view normalised numbers as being transformed, by
either a second parameter (as in definition A of Normalised) or, equally
acceptably, by using a parameter model, (as I believe is your definition B
of Normalised, without having read the artcicle you reference).
Hence, normalised is applied more widely as a technique of analysis,
rather than a specific result.
I hope this is helpful to your enquiry.
(Hand written sig.) ->
Timothy J. Lawes
Biomedical Research Engineer,
Bristol University,
Dept. of Anatomy, Vet School.
Southwell St. Bristol BS2 8EJ
(0272) 303197
----------------------------------------------------------------------------
Date: Mon, 13 Jun 1994 09:45:51 -0400 (EDT)
From: CRISCO@BIOMED.MED.YALE.EDU
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
As is often observed, the same word has different meanings when used in
different fields of study. I belive both are correct. We often used
"normalized", as in your Definition A, for any variable that has been non-
dimensionalized for comparative analysis.
Trey Crisco, Ph.D.
----------------------------------------------------------------------------
Date: Mon, 13 Jun 1994 12:26:05 -0400 (EDT)
From: James Dowling
Subject: Re: Standard terminology: "NORMALIZED"
To: "Paolo de Leva - Sport Biom. Rome"
Dear Paolo,
I was certainly not the first to use the term "normalized" due to my
tender years but I have both used it and read it often and it has always
been in the context of your definition A. I believe that it would be too
difficult to change to a new term and since one must always state in the
methods how they normalized the data, authors can choose to either divide
by a constant, a variable such as mass, or use a transformation that
makes the data normally distributed about a mean. Please let me know
what others think.
Jim Dowling
Dept. of Kinesiology
McMaster University
----------------------------------------------------------------------------
Date: Tue, 14 Jun 94 08:35:10 IST
From: Moshe
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
Dear Paolo:
I believe many words has multiple meaning, especially in English. So what?
Normalized, meaning corrected to get an independent value, is used for long
enough to become a legitimate word.
I could think of at least one more meaning to normalized, related to
psychiatry. And if I was an English expert, I'm sure I could find some more.
I believe language is for human use, and as long as the meaning is clear in
the specific context, one can use the word.
Sorry if I am not clear. As I said, I am not a real English speaking. I
reacted only because we have exactly the same problems with our language,
Hebrew. Some people try to prevent the use of certain words in certain
meanings. But it is a waist of time.
Moshe
********************************************!***** **********************
* MOSHE NISSAN, PHD ! FAX: 972-3-6974546 *
* BIO-MEDICAL ENGINEER ! TEL: 972-3-6974720 (WORK)*
* Dept. Orthopaedics B' ! : 972-4-371788 (home) *
* TEL-AVIV SOURASKY MEDICAL CENTER ! *
* 6 Weitzman st. Tel-Aviv 64239 ISRAEL ! Bitnet: RPRNISN@TECHNION *
************************************************** **********************
----------------------------------------------------------------------------
Date: Tue, 14 Jun 1994 17:58:40 +0200
From: deleva
To: RPRNISN@TECHNION.TECHNION.AC.IL, deleva@risccics.ing.uniroma1.it
Subject: Re: Standard terminology: "NORMALIZED"
I am not trying to limit the use of the word "normalized".
On the contrary, I WOULD WANT TO USE IT!
I was just asking if Def. A was used by a large enough number
of people to be considered a standard definition. I asked because I
would want to be understood by everybody when I write my papers,
and I was not sure that the word normalized was understood by everybody
in the meaning I was interested in.
Paolo
----------------------------------------------------------------------------
Date: Fri, 17 Jun 94 08:37:24 IST
From: Moshe
Subject: Re: Standard terminology: "NORMALIZED"
To: deleva@risccics.ing.uniroma1.it
Dear Paolo:
I am sorry if my response seemed a bit aggressive. It is another prove to
my claim that there is no chance everyone will understand you the way you want.
I gave up on this hope long ago. I was teaching pure physics at university
and it always amaised me how could some of my students understand questions
in a different way from the one I meant,no matter the extent of clarifications,
explanations etc.
And to your question: yes, I believe "Normalized" is used and accepted world
wide, and it can be used freely in case the text is purely biomechanics. If
statistics is involved (beyond sd and significance), than one should define
"Normalized" in the paper.
Bye for now, yours, Moshe
********************************************!***** **********************
* MOSHE NISSAN, PHD ! FAX: 972-3-6974546 *
* BIO-MEDICAL ENGINEER ! TEL: 972-3-6974720 (WORK)*
* Dept. Orthopaedics B' ! : 972-4-371788 (home) *
* TEL-AVIV SOURASKY MEDICAL CENTER ! *
* 6 Weitzman st. Tel-Aviv 64239 ISRAEL ! Bitnet: RPRNISN@TECHNION *
************************************************** **********************
----------------------------------------------------------------------------
Date: Tue, 14 Jun 1994 13:41:30 EDT
From: "J.B. FINLAY"
Subject: "NORMALIZATION..."
To: Multiple recipients of list BIOMCH-L
Paolo's question about "Normalization" highlights a common problem
that we have with communications. This problem arises from peoples'
(our) tendency to talk and write using abbreviated phrases. Such
phrases may have appropriately implied meanings ONLY among those
individuals who are accustomed to them and, even then, only when
the phrases are encountered in a clearly-defined context.
This problem is well-reflected in the statement:
I PUT THE COFFEE IN THE MICROWAVE
Without discussing any of the POSSIBLE meanings (Stupid, theoretical,
practical, or otherwise), suffice it to say that the probable
information intended to be conveyed by this statement is:
I PUT THE CUP/MUG OF COFFEE IN THE MICROWAVE OVEN
and we can still debate whether the coffee was in solution or not!
NORMALIZED DATA:
In terms of "Normalized Data", any potential problem should be avoided
by speaking or writing the complete implied phrase (using Reference
citations, if necessary):
THE PROBABILITY DISTRIBUTION OF the data was normalized by...
or
THE MAGNITUDES OF the data were normalized by...
In the first statement, "normalized" actually implies that the
Probability Distribution curve was converted to that of a statistically-
defined "Normal" curve and, for this statement to be properly understood
in a manuscript, it would be appropriate to cite a reference to a
textbook in Statistics.
Once this procedure of normalization has been established in the
conversation or manuscript, then an "abbreviated" reference to
"normalization" might be warranted.
Few, if any, reports of biomechanical data can be presented
meaningfully without the use of statistics. Consequently, as
Biomechanicians, we should be particularly attuned to this problem.
As participants in the multi-disciplinary field of Biomechanics
(Biology, with its coverage of both plants and animals, involves
Human Biology as only one small element of its activities), our
communications should be such as to minimize these potential
misunderstandings - i.e. rather than trying to justify the use of
ambiguous phrases based upon interpretations used within our own
limited circle-of-colleagues or discipline - e.g. fluid mechanics,
etc.
I hope this personal impression of the problem will help in the
ensuing discussion.
Best wishes:
Bryan Finlay, PhD 519-663-3063
Director of Orthopaedic Research 519-663-3904 FAX
University Hospital
P.O. Box 5339
London, Ontario, CANADA, N6A 5A5
----------------------------------------------------------------------------
Date: Tue, 14 Jun 1994 23:41:39 +0200
From: "Paolo de Leva - Sport Biom. Rome"
Subject: NORMALIZED?
To: Multiple recipients of list BIOMCH-L
I appreciated Bryan Finlay's reply to my message about the
meaning of the word "NORMALIZATION", and I think it was useful for us
to be reminded that our language should be as much as possible explicit
and clear, to be understandable by the largest possible number of readers
with different backgrounds, although the need of synthesis often
prevents us from defining explicitly all the words and expressions we
use, and I am sure there's no way to avoid a large amount of implicit
concepts in any kind of communications (scientific papers included).
If I said to my wife that I AM PUTTING THE CUP CONTAINING COFFEE
IN SOLUTION INTO THE MICROWAVE OVEN, my wife would laugh at me. And the
same would happen if I used unduly and boringly explicit phrases in the
context of scientific communications.
Good writers or lecturers possess, I believe, the skill
to choose to be explicit whenever and only when the conveyed concepts
may be not familiar to any of the possible cathegories of readers or
listeners. On the other hand, they are master in the art of avoiding
wasting words whenever and only when the conveyed concepts may be
understood using standardized terminology and expressions.
I would add that probably the latter "art" is the most appreciated
and at the same time the most complex.
That's the reason why I wanted to know if my definition "A"
of the word "NORMALIZED" was widespread enough to have become a
standard definition: I need to use the concept of "normalized", according
to Def. A, in my next paper.
Paolo de Leva
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Date: Wed, 15 Jun 1994 07:53:34 GMT
From: Edsko Hekman
Subject: Re: NORMALIZED?
To: Multiple recipients of list BIOMCH-L
I would like to suggest that RE-HEATING OLD COFFEE should not become a
NORMALIZED procedure...
Edsko Hekman
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From: "J.B. FINLAY"
To: deleva@risccics.ing.uniroma1.it
Date: Wed, 15 Jun 94 08:28:58 EDT
Subject: Normalization and publications
Hi Paolo:
I guess you focussed on my attempted "humourous" introduction to my
answer to your question.
I believe the answer to your "restated question" is that, if the
Journal you propose to use is a Journal that publishes articles with
statistics in them, then you can expect that the word "normalized"
may be viewed in a statistical concept. Simply, any use of "meams"
(that should have been typed MEANS) and "standard deviations" have
implications to the existence of a "Normal" curve. Where a "normal"
curve did not exist in the original data, it is quite common (and
statistically acceptable) to apply a transform to the data so that
there probability distribution satisfies that of a normal curve.
Under such circumstances, the transforming equation (used to
normalize the data) would be expected to be quoted.
My original conclusion summarized this point. If the publication
is in a Biomechanics journal, then one definition cannot be assumed
over the other - since statistics are an essential tool in the
description of Biological systems.
I will be interested to see what other responses you get. Since
responses on the Bulletin Board are often seen as "Grandstanding",
I guess I should have addressed my original response to you and
let you summarize the responses.
Best of wishes with the publication.
Best wishes:
Bryan Finlay, PhD 519-663-3063
Director of Orthopaedic Research 519-663-3904 FAX
University Hospital
P.O. Box 5339
London, Ontario, CANADA, N6A 5A5
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>From deleva Wed Jun 15 23:43:58 1994
Date: Wed, 15 Jun 1994 23:43:44 +0200
To: bfinlay@uwovax.uwo.ca, deleva@risccics.ing.uniroma1.it
Subject: Re: Normalization and publications
Thanks, Bryan.
I will send the article to the Journal of Biomechanics, as soon as
my private reviewer (=friend) in USA will return it with the right english
words instead of my "ITALIANIZED" (how about this new word? :-)) words.
I disagree with you for a small detail: normalizing (statistical
meaning) the data, according to the definition of GLASS and HOPKINS, is
a quite questionable method, in my opinion.
I think you define the statistical "normalization" differently
from Glass and Hopkins. Probably you refer to the non-linear
transformations (such as changing the scale using square root,
or lgarithm of the observations) which help to correct the shape
of a skewed curve. The result of such transformations is usually to
a curve which is MORE NEARLY normal than the original.
The latter is a good method, I think. But the "normalization"
described by Glass and Hopkins introduces changes in the scores that
don't have a logic at all. They don't follow the square of the original
observations, or their logarithm. A normalized T score is obtained by
"first converting the orig. scores to percentiles, and then
converting each percentile to the score corresponding to that percentile
in a normal distribution". Do you see what I mean now? Let's suppose
I got an IQ score of 99.99, while the person immediately below me got
a score of 94, and the subject immediately above got just 100.0. When
the scores are normalized, I might end out with a normalized T-score of
96, while the other two persons might stay with their score! That's
rather questionable, I am sure you agree: my score was decreased just
because a "NOT SENSIBLE" statistician thought that his data would look
nicer if they had a PERFECTLY normal shape, while actually it is PERFECTLY
"NORMAL", and plausible that an observed distribution never be PERFECTLY
NORMAL (it never ever can be!!!), because of measurement errors,
and especially of SAMPLING ERRORS!
My score was decreased just because the statistician
did not get enough subjects with a score ranging between 94 and 99.9!
But sampling errors do exist, and I want my score to be closer
to 100 than to 94, because 99.99 is what I got, and I DESERVE it:
it was very hard for me to get it!!!!
Paolo de Leva
----------------------------------------------------------------------------
From: "J.B. FINLAY"
To: deleva@risccics.ing.uniroma1.it
Date: Thu, 16 Jun 94 09:24:41 EDT
Subject: Re: Normalization and publications
Dear Paolo:
Thanks for the note.
You were correct about the "transformations" that I was trying to explain.
I appreciate the nonsensity of the process that you described which
actually "removes" information for the data set.
Best of luck with your submission to J.Biomech. This is the mut
multidisciplinary journal that I had in mind as I was writing. I
have just submitted a paper to them. On the basis of my submissions
to them in the past, the reviews depend entirely upon whether it
goes to physicians, surgeons, plant biologists, electrical engineers,
mechanical, etc... At least the new guidelines for submission to
J.Biomech. invite the author to suggest the names of some potential
reviewers.
Based on our communications, I find it hard to believe that you need
someone to check your English; however, you can never go wrong in
getting someone else to read your material - if deadlines permit!
Best wishes:
Bryan Finlay, PhD 519-663-3063
Director of Orthopaedic Research 519-663-3904 FAX
University Hospital
P.O. Box 5339
London, Ontario, CANADA, N6A 5A5
----------------------------------------------------------------------------
Date: Thu, 16 Jun 1994 23:58:25 +0200
From: "Paolo de Leva - Sport Biom. Rome"
Subject: "questionable" transformation
To: Multiple recipients of list BIOMCH-L
I would like to point out that in my first message to BIOMCH-L
about "Standard terminology: NORMALIZED", I defined questionable the
nonlinear transformation which is defined as "NORMALIZATION" in the
book by Glass and Hopkins (Statistical methods in Education and Psychology),
and not other kinds of nonlinear transformations which are used in
statistics to correct skewed distributions of data.
The latter transformations (simply defined by Glass & Hopkins
as "TRANSFORMATIONS" -see p.70- or "NONLINEAR TRANSFORMATIONS" -see
note, p.70) are changes of scale, for example replacement of scores
by the logarithm or square root of the raw scores themselves, WHICH
MAKE THE FREQUENCY DISTRIBUTION MORE NEARLY NORMAL.
And that's perfectly acceptable to me. What I defined qiestionable
(and I am sure many will agree) is the normalization defined as in my
"Definition B" (see previous message), that MAKES THE DISTRIBUTION
PERFECTLY NORMAL (P E R F E C T L Y). Glass and Hopkins explain that:
"NORMALIZED scores are obtained by first converting the original scores to
percentiles and then converting each percentile to the score corresponding to
that percentile in a normal distribution"...
If you are curious to know why I think the latter kind of
statistical normalization is questionable, read my summary of responses
to my previous posting ("Standard terminology: NORMALIZED"). I will
post the summary tomorrow.
With regards,
Paolo de Leva
Istituto Superiore di Educazione Fisica
Biomechanics Lab
Via di Villa Pepoli, 4
00153 ROME
ITALY
Tel: 39-6-575.40.81
FAX: 39-6-361.30.65
e-mail address: DELEVA@RISCcics.ing.uniRoma1.IT
----------------------------------------------------------------------------
Date: Thu, 16 Jun 1994 23:18:04 -0600 (CST)
From: "Steve Nordquist of Overland Park, KS"
Subject: NORMALIZATION (Biomch.)
To: DELEVA@risccics.ing.uniroma1.it
From seeing this issue addressed in _Science_ (english ed.) three or
so years ago, where there was a bit of fret on it, and previously, when
a few definitions were trotted out, I got these impressions:
The first goal of the normalization should be to show off the details of
your empirical data. Therefore, any fit to a log-log chart or so should
be done carefully as to preserve any deviation from simplistic forms
that would otherwise appear in the 4" wide by 322" high graph you would
have without logarithms...that sort of practice has to be done FIRST,
THEN you go and...
Normalize by:
a) Complying with the usual application in the journal, asuming you
aggree with it.
b) Clipping outliers, and making the corequisite disclaimers and thorough
explanation
c) Otherwise move samples around, explaining why the way is so agreeable.
I haven't seen 'Normalized' alone in a paper yet where it didn't have to be
commented on later in "errata" or the policy of the journal (inside the front
cover, next to: "Warning! Substantive, not editorial!")
Has biomechanics really progressed so that normalization makes it clear
when an 'outlying' group is clearly definable as an extraordinary effort on
the part of the subject?
Steve Nordquist
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END OF SUMMARY
Paolo de Leva
Istituto Superiore di Educazione Fisica
Biomechanics Lab
Via di Villa Pepoli, 4
00153 ROME
ITALY
Tel: 39-6-575.40.81
FAX: 39-6-361.30.65
e-mail address: DELEVA@RISCcics.ing.uniRoma1.IT