Interpretation of ANOVA when the entire population is under study

Hi, this is a sort of "philosophy of interpretation" question.

Suppose I have a variable of interest $PC = sales per customer. I have,
for $PC, the mean and variance for each of 5 stores A, B,C,D,E. These
statistics are based on ALL customers (say in a given month) in each
store, and there are ONLY the 5 stores.

Since we have data from the entire population, the null hypothesis
tested in ANOVA (that all the POPULATION means are equal) seems not to
be pertinent. We don't have a random sample of stores, maybe we
arguably have a random sample of customers (who chose to shop in a
given store in a given month .. sort of postulating some meta
population) but that is weak.

Nevertheless, there is variation of $PC within store across customers,
and it makes some intuitive sense to ask whether the stores "differ
significantly" in average sales per customer.

In the absence of variation due to sampling, we only have variation
arising from the "allocation of customers to stores". I guess there is
an analogy with treatments here, but customers are not assigned to
stores at random (unlike treatments) so that analogy breaks down.

I guess what I am asking is that in the situation of having data from
the entire population (of customers and sales) , does it make sense to
say that there are "significant differences" across some (co)variate
and to use ANOVA to test for this.

Some clarification would be appreciated.

.

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