I've watched the many thoughtful "categorical or numerical"
messages with interest.
For many, many years I've proposed that IN THE BEGINNING
ALL RECORDED INFORMATION is BINARY, CATEGORICAL, NOMINAL -- (not DUMMY).
AFTER humans associate MEANING with the categories then the information
acquires various NAMES/TYPES. It is important to know the MEANING
that is associated with the recorded information. This is a problem with
all communication.
------
An interesting example is the discussion about GRADES GIVEN
FOR ASSESSING PERFORMANCE BY STUDENTS.
In some situations we observe grade names as:
C, D,B,F,A (CATEGORICAL, NOMINAL, BINARY, ...?)
THEN WE SOMETIMES THINK OF THEM AS BEING IN SOME "ORDER".
A,B,C,D,F
(we probably use "F" for Failure, but why don't we use "E" for Excellent?)
THEN WE MIGHT LIKE TO COMPUTE GRADE POINT AVERAGES AND
Let 4 = (another name for) "A"
3 = (another name for) "B"
2 = (another name for) "C"
1 = (another name for) "D"
0 = (another name for) "F"
(Why is the difference between D(1) and F(0) the same as ALL
other adjacent categories?)
And on the other hand we may have "SCORES" on a 100-point scale.
but someone might desire to have some "LETTERS". So we may
Let 90-100 = A
80-89 = B
70-79 = C
60-69 = D
00-59 = F
:-)
-- Joe
*************************************************************
Joe Ward Health Careers High School
167 East Arrowhead Dr 4646 Hamilton Wolfe
San Antonio, TX 78228-2402 San Antonio, TX 78229
Phone: 210-433-6575 Phone: 210-617-5400
Fax: 210-433-2828 Fax: 210-617-5423
[EMAIL PROTECTED]
http://www.ijoa.org/joeward/wardindex.html
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----- Original Message -----
From: Jan de Leeuw <[EMAIL PROTECTED]>
To: Paul Velleman <[EMAIL PROTECTED]>; Hankins <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Cc: Paul F Velleman <[EMAIL PROTECTED]>
Sent: Saturday, December 04, 1999 7:59 AM
Subject: RE: categorical or numerical
| It's nice to sort of disagree with Paul for a change.
|
| Students should be taught that ALL measurements are categorical and WHY
| we are usually pretty succesfull treating data AS IF it were measured on a
| continuous scale EVEN THOUGH WE KNOW IT IS NOT.
|
| Thus, on a minor point, it is neither a good nor a bad idea to "slice
| continuous
| measurements into categories". There are no continuous measurements, so
| the whole notion is irrelevant. We can just choose to make our categories more
| broad, and this is a choice which is part of the analysis. The argument
| that this "throws away information" seems to suggest that is inherently bad.
| But statistics is the art of throwing away information.
|
| Think about the shift of emphasis if the normal would be moved back to its
| rightful historical place: as a convenient and widely applicable numerical
| approximation tool. No more nonsense such as "Assume the data are a sample from
| a normal distribution ... ".
|
| Of course I agree with Paul that unnecessary discretizing is, well,
| unnecessary.
|
| At 11:46 PM -0500 12/3/99, Paul Velleman wrote:
| >At 11:14 PM 12/03/1999, Hankins wrote:
| > >We would not be able to measure anything, then not able to record the
| > >measurement, if slicing continuous measurements into categories is "almost
| > >always a bad idea"!
| >
| >Perhaps I should have been more precise. Of course every recorded
| >measurement is discretized to some degree. What I oppose is *unnecessary*
| >discretizing.
| >
| > >The students should rather be taught that ALL measurements are categorical.
| >
| >On this, however, I disagree. Calling a variable categorical usually
| >suggests a limited range of analysis possibilities. In fact, we are usually
| >pretty successful treating discretized data as if it were meausred on a
| >continuous scale even when we know it is not.
| >
| >-- paul
| >
| >Paul F. Velleman
| >Cornell University Data Description, Inc.
| >358 Ives Hall Box 4555
| >Ithaca, NY 14853 Ithaca, NY 14852-4555
| >(607) 255-4411 (607) 257-1000
| >(607) 255-8484 fax (607) 257-4146 fax
| >
| >
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| ===
| Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
| US mail: 8142 Math Sciences Bldg, Box 951554, Los Angeles, CA 90095-1554
| phone (310)-825-9550; fax (310)-206-5658; email: [EMAIL PROTECTED]
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