Nominal characters

[Warren Lamboy]

                       Subject:                               Time:13:02
  OFFICE MEMO          Nominal characters                     Date:06/04/1995

Jerrold H. Zar, in his book Biostatistical Analysis, 2nd ed. (Prentice Hall)
describes "Types of Biological Data" in a way that might help to clarify the
definition of types of characters (p. 2-4).  He includes:

     data on a ratio scale - scale has a physically meaningful zero point,
         and there is a constant size interval between adjacent units on the
         scale, i.e., difference between 8 inches and 12 inches is the same
         as that between 20063 inches and 20067 inches.
     data on an interval scale - scale has a constant size interval between
         adjacent units, but zero point of the scale is arbitrary, e.g.,
Celsius
         temp scale or time of day or directions are interval scales
     data on an ordinal scale - differences are relative, and only the
         ordering or ranking of the values are possible
     data on a nominal scale - data values belong to categories, based on
         some observable quality

     continuous data - a variable for which there is a possible value
         between any other two possible values
     discrete data - a variable that can take on only certain specific
         values, often but not always integers or some subset of the integers

I can't help but think that some of the discussion has been the result of
disagreement over how data types are defined.  In addition, it seems that some
of the discussion has focused on whether characters are "really" nominal or
not.   It seems to me that some characters are 1) nominal and we know it, 2)
some are not nominal and we know it, 3) some are not but we don't realize it,
4) some are not and we realize it but we treat them as if they were nominal
anyway and a) no harm is done or b) we make a huge mistake.

As an aside, because our limits of resolution in measuring and reporting
results are always finite, we never have truly continuous characters
either--they are always discrete.  In many instances, however, nothing is lost
by treating them as if they were continuous.

Just my $0.01999995 worth.  Flame away!  -  Warren