# How should I compare average store sales change across time?

I have what seems like a fairly common business statistics scenario: I need to compare one group of stores to another group of stores and be able to say if their difference in sales is statistically different.

For example: Group A ($n_A$ = 30 stores) participated in a promotion and saw an avg sales increase for this month compared to the same month last year of $\bar{x}_A$ and a standard deviation of $s_A$.

Group B ($n_B$ = 50 stores) did not participate in the promotion and had avg sales increase of $\bar{x}_B$ and corresponding $s_B$.

I realize there are a number of other variables but, in theory, I should be able to say with some certainty that there is or isn't any difference between stores that took or did not participate in a promotion, right?

Can I do a standard comparison of means test? Does it make a difference that these stores comprise of the entire population? Or is it not the entire population and I should be looking at average increase for multiple months and multiple years?

• I'd say it depends on what your goal is: 1)I want to describe the population I observed or 2)I would like to describe a population like the one I observed. For 1) you have no uncertainty at all, so statistics just reduces to describing differences and similarities. But beware: the "standard deviation" in this case does not describe the accuracy of a difference in means. In case 1) if the $\overline{x}_A$ and $\overline{x}_B$ are different, then the means are different, regardless of what the standard deviation is. – probabilityislogic Jan 28 '11 at 15:50
• ... just one point of clarification on my comment above, while the means are different, this alone tells us nothing about why they are different, apart from the labels of $A$ and $B$ (or equivalent synonyms of them). Anything beyond that is not answered by the means, but by the interpretation it is given (which will depend on your prior beliefs about what the potential causes of a difference may be - the obvious stand out being the promotion). – probabilityislogic Jan 28 '11 at 16:01