Raul Miller wrote:
> I want to be able to talk about populations,
> distributions, samples, etc. using a consistent
> set of terminology regardless of whether or not
> the distribution of the population is known or
> unknown, or partially understood.
My impression is that one of the things John Randall
was pointing out is that the mathematics of statistics
is devised for dealing with uncertainty and other
limitations in what is, or can be, exactly known. This
contrasts with most of mathematics, where perfect
knowledge is presumed, axiomatically. He pointed
toward techniques from numerical analysis for those
cases where the subject matter falls, at least in
effect, within that axiomatic framework.
The implication of this is that we should not strive
for consistent terminology to deal with all things
that can be thought of in terms of populations.
(Consider applications of set theory.) We should
instead let statistics have its own terms, and
recognize that those terms apply where "normal" math
cannot reach, i.e. into hazardous estimations of
empirically encountered patterns.
Tracy Harms
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