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

On 10 Dec 2005 23:21:55 -0800, "Sullivan2000" <jaitchis@xxxxxxxxxx>
wrote:

> 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.

The situation for Population statistics is like taking a vote.
What you observe is what you get. (Only occasionally are
there provisions for saying that the counting of votes can
be inaccurate....)

Once you start trying to *generalize* to anything -
tendencies for next year, random Universes, anything
of any interest (by and large) for the future, you have
that "meta population." And you have the conventional
tests.

You can google groups, <group:sci.stat.* FPC >
or "finite population correction" to see past discussions.
There might be some comments in my stats-FAQ.

>
> 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.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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