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I'm working at a project in a distribution company. Let's say that in the beggining of this year some major change was made in the sale's area, and my job is to evaluate if this change actually increased the sales.

My thoughts were:

1 - I should do a hypothesis testing using data from 2 months before the change was applied versus the 2 first months of the change, then I shoud know if the change actually increased sales.

Or...

2 - Since I have all the complete sales data from these 4 months, there isn't really a need to use hypothesis testing, since it's only used when you have samples of the population, but in this case, the data I've got from these 4 months is the entire population. So all I needed to do is check the sales amount in the previous 2 months versus the 2 first months of the change.

My question is, which one of these 2 thoughts is correct?

I'm new to hypothesis testing so I'm still figuring it out.

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    $\begingroup$ Are you interested in the samples you happened to draw or in the process that generated the samples you happened to draw? It is reasonable to think of there being some data-generating process in nature about which you want to draw an inference. $\endgroup$
    – Dave
    Mar 27, 2021 at 3:22
  • $\begingroup$ I think it's the samples I happened to draw. The change I mentioned is a decrease in the sales' price of a specific product. My job is to evaluate if that change positively affected the sales. $\endgroup$
    – Caldass_
    Mar 27, 2021 at 3:32
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    $\begingroup$ I disagree. I suspect that you are interested in the latent process that generated the observations. In that case, you would be interested in some kind of inferential method, such as a hypothesis test. If you really are just interested in the observations you happened to see, then there is no inference. You have the entire population. There are no p-values or confidence intervals. $\endgroup$
    – Dave
    Mar 27, 2021 at 4:34
  • $\begingroup$ Imagine a table that contains date and sales value for each day of those 4 months I mentioned. The reason I think I'm interested in the samples is because I'm only going to look to the sales difference in these months, since I'm only interested in the impact that the major event will have on the sales volume. $\endgroup$
    – Caldass_
    Mar 27, 2021 at 4:55
  • $\begingroup$ If there is a seasonal effect or if there is a major change in the economy around the time of your change, the two months after the change might differ from the two months before just before--even if your change is completely inconsequential. Examples: In 2020, 2 mo. before Covid sequesters and 2 mo. after. In 2019 Sept-Oct vs. Nov-Dec. (holidays) // On comments above, I agree with @Dave: If you improve a highway to make it safer, are you only interested in accidents the month before vs. after the road work? Or do you hope before and after might serve as if random samples before vs. after. $\endgroup$
    – BruceET
    Mar 27, 2021 at 8:30

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