Interestingly, L. L. Thurstone used this issue (Thurstone, 1947) to
illustrate the uses of Factor Analysis -- he introduced a data set that
consisted of the intercorrelations of many different possible measures
of the "size" of a set of cardboard boxes: e.g. volume, sum of edges,
etc.

Then he showed that you can extract factors from the data that can be
related to box height, width, and depth.

_______________________________________
James E. Corter
Associate Professor of Statistics and Education
Chair, Department of Human Development
Teachers College, Columbia University
525 W. 120th St.
New York, NY 10027
Email: [log in to unmask]
Tel: (212) 678-3843
FAX: (212) 678-3837


>That choice is "unusual" because most workers do not use that method.
One reason >is probably that one would not measure the size of a box by
adding its length and >width - most would rather multiply them together.

>
>The problem with "size" is that simple word hides a large diversity of
possible >measures. One cannot decide what is size without specifying
some model and what >desired properties the measure of size is supposed
to optimize. One should not use >some measure just because it seems
"reasonable" intuitively. As I said previously, it >is fortunate that in
most biological applications the various choices are usually highly
>correlated.
>
>----------------------
>F. James Rohlf, Distinguished Professor & Graduate Program Director
State >University of New York, Stony Brook, NY 11794-5245
>www: http://life.bio.sunysb.edu/ee/rohlf  
>