>I think you already do, John! Clearly, the results for
>a whole population are simply a statement of fact, with
>no sampling to inject the randomness required to underlie
>probabilistic statements of uncertainty,
Neatly put! But where is does the uncertainty come from? And why do we
want to make probabilistic statements?
A little bit more explanation is required.
Statisticians assume that the set of observations reported are one of an
infinite number of sets of observations that could be made. These infinite
number of observations are purely hypothetical. But they can be used to
generate a set of observed distributions that might be expected to be made
of a given set true distribution. From these hypothetical sets of
observations probabilistic statements about the relationship between the
observed and true distributions can be derived - and used to impress
clients.
If you can believe all that you have demonstrated enough faith to be on your
way to becoming a statistician! But you don't need to adopt this baggage in
order to be a successful statistician. You can keep such probabilistic
statements to where they belong in sampling populations rather than in
measuring populations. And keep in mind that when this probabilistic
methodology was adopted in the design of the so-called One Number Census of
2001, the result was that, for the first time in British history, the
estimate of the total population was not based primarily on the Census.
Put another way, the set of statistics quoted are the product of a variety
of data production processes. We know that in general these statistics are
produced carefully because they do relate to matters of life and death.
But these system are complex and many different people are involved in the
recording processes. People rarely act in random ways - something known to
social scientists. But because the processes are complex and it is
convenient for statisticians to assume that people do act in random ways and
so that variation can be attributed to 'noise'. But statisticians do that
for their own purposes as explained.
I have yet to find an example where this probabilistic approach adds
anything to understanding. But what it does do is divert attention away
from investigation of the statistics production processes than led to a
particular population estimate.
Ray Thomas
35 Passmore, Tinkers Bridge, Milton Keynes MK6 3DY
Email: [log in to unmask]
Tel/Fax 01908 679081
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