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I have a project where I have access to entire populations' records. I'm not trying to generalize knowledge to a larger population; rather, I'm trying to compare the prevalence of an event happening in one whole population to the next (think comparing what percent of shoppers buy a certain product at Walmart versus Target, where you have records on every single shopper at both).

But, to continue using this example, some stores are very small--maybe only 5 customers in a month, as opposed to 500 at another.

I want to figure out what my minimum population size should be to include in the comparison. I have to keep stores separate and not lump them together. I've tried to use sample size power estimations, but it doesn't seem like the right fit for the dilemma. But perhaps I'm wrong.

Any advice?

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    $\begingroup$ Whether you are dealing with a finite population or an infinite population, if you want to make an inference about the population the sample size is important, But you say that you are not interested in drawing inference to a larger population. If that is the case I don't understand your question. The fact that some stores are small and others are large should not matter. You ought to be able to adjust for this . Also from your question I get the feeling that you are talking about comparing two finite populations. Maybe you can clarify this for me and one of us will be able to answer. $\endgroup$ – Michael Chernick Dec 29 '16 at 21:55
  • $\begingroup$ Yes, comparing finite populations. This is the entire possible population--there are no more people in this population in the world. But the populations are very, very different in size from one another, which makes me wonder if saying that 80% of Walmart customers experienced the desired outcome and 20% of Local Mom & Pop Store customers experienced the desired outcome, therefore Walmart is better, is fair if Walmart had 1,000 customers and Local Mom & Pop had 10. Is this a fair commentary on the smaller store's services? Does that help? $\endgroup$ – ShannonC Dec 29 '16 at 22:17
  • $\begingroup$ I suppose in a way it is trying to generalize, but only to a hypothetical larger population that doesn't truly exist? What we want to know is which store is better at doing this. But the small store, whether they have good or bad outcomes, could just have a couple odd customers that really skew the whole mix. $\endgroup$ – ShannonC Dec 29 '16 at 22:21
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From questions and comments, it seems that you don't want to do inference but you want to generalize your conclusions. However, inference is just generalizing. Then, either you don't need to generalize because you have data on the whole population, or what seems the entire population is a sample from the population you are actually interested in.

If you are interested in comparing the percent of customers in every store that bought a given product, with the whole population it's easy to compute both percents and tell the larger one. For example: "10 out of 1000 (1%) customers of Walmart have bought the product, while 1 out of 102 (0.98%) customers of Target have bought it; therefore, in that period Walmart performed better at selling the product".

However, we are usually more interested in knowing which store have been more effective, if there is a significant difference. Here we are interested in the probability of a customer buying the product, not just on the proportion of customers having bought it, and now our population is the pool of all possible customers that could have visited the stores, and the customers actually visiting them are just a sample of that population - the "hypothetical larger population" in your comment.

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