"William B. Ware" wrote:
>
> Robert,
>
> I don't think I understand your argument... Are you saying that the
> "descriptive statistic" should be invariant over scale?
Yes, of course. Otherwise it's a description of the process of
measuring, not of what is being measured.
>
> 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...
Yes, but not all data are integer test scores.
*If* you are given data that have been rounded or truncated to the
nearest multiple of some D (in your example, 1), then I suppose that an
unbiased estimator of the original range would be max + 1 - min or
something like that.
-Robert Dawson
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