Robert,

I don't think I understand your argument... Are you saying that the
"descriptive statistic" should be invariant over scale?

Anyway, more to the point... the "add one" is an old argument based on the
notion of "real limits."  Suppose the range of scores is 50 to 89.  It was
argued that 50 really goes down to 49.5 and 89 really goes up to
89.5.  Thus the range was defined as 89.5 - 49.5... thus the additional
one unit...

Personally, I don't subscribe to this position... It assumes that the low
score is always toward the low end of its value and that the upper value
is always toward the high end of its value... Sort of a maximum range... I
prefer not including the additional one unit...

Bill

__________________________________________________________________________
William B. Ware, Professor and Chair               Educational Psychology,
CB# 3500                                       Measurement, and Evaluation
University of North Carolina                         PHONE  (919)-962-7848
Chapel Hill, NC      27599-3500                      FAX:   (919)-962-1533
http://www.unc.edu/~wbware/                          EMAIL: [EMAIL PROTECTED]
__________________________________________________________________________


On Fri, 5 Oct 2001, Robert J. MacG. Dawson wrote:

> 
> 
> jeff rasmussen wrote:
> > 
> > Dear statistically-enamored,
> > 
> >         There was a question in my undergrad class concerning how to define the
> > range, where a student pointed out that contrary to my edict, the range was
> > "the difference between the maximum & minimum".  I'd always believed that
> > the correct answer was the "difference between the maximum & minimum plus
> > one"
> 
>       One what?  Any statistic that depends on the units used seems rather
> arbitrary to me.  If I compute the range of weights of a group of people
> (in kilograms) I ought to get the same actual *weight* as an American
> using pounds or a Brit using stones.  
> 
>       Suppose I have three meter sticks - are you telling us that the range
> of their lengths is a little over one meter?
> 
>       I'm afraid I vote with your students.
> 
>       -Robert Dawson
> 
> 
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