Re: Interpretation of ANOVA when the entire population is under study

Rich, thanks for the FPC references .. I am not sure how they bear on
the problem at hand, but that may become clearer to me as my
understanding of the problem unfolds.

I suspect my problem is about asking the right questions, or
alternatively, what can I reasonably conclude from the data at hand?

Suppose I have just 1 months worth of complete data (all customers)
from all stores and to make things simple assume that there are only 2
stores .. not a sample of 2 stores but a universe of 2 stores.

The data looks like
store A store B
N 1000 500 (N <> sample; N==all customers)
mean 10 25
sdev 5 5

What can I reasonably conclude from this .. what reasonable
generalizations might I make?

a) I can conclude that store B sold more per customer than store A in
that month. No generalization here, simply reportage. But
"uninformative".

b) Can I say that the observed differences are "unlikely to be due to
chance?" .. what would this mean? The question being asked is
tantamount to either

b1) if customers were randomly assigned to stores (which we know is not
true, but maybe is worth entertaining as a wedge to get a perspective
on the results) then we "might have observed" a different result? A
t-test would be appropriate here, no?

b2) if we can regard the month as being a random sample of 1 from all
months (and months being themselves interchangeable), then some other
month is/is not likely to show a similar result

It seems to me that there is information in the inter-customer
variability that we can use to give sensible answers to these and
similar questions.

To do this, it seems to me that we have to perform a "trick" .. to say
that the data that we have is really a sample from some loosely
specified universe. And then proceed with the usual ANOVA and
"significance tests". This seems defensible to me, or at least more
productive than saying "what you have here is population data and you
can only report it.. no generalization or sensible speculation possible
... a brick wall". So, what is the universe? perhaps - all purchases
over all future time (hence infinite and no FPC needed) for this set of
stores (not seen as a sample of all possible stores).

OK, is this sensible?

.

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