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Let's say I have a series of previous year's weekly sales for a product $\{x_i\}$ and the series of sales for the same product this year $\{y_i\}$. How can I find out if the increase in sales are statistically significant?

Edit: Context: I have weekly sales of a group of items for the previous year. We ran a marketing campaign for that group and again recorded the weekly sales for the current year. I want to know whether running the campaign had any significant impact on sales. I've seen answers related to changepoint analysis, but I don't think that applies here. The item sales need not necessarily form a time series fit for regression and all. Since I want to get the broad impact of the campaign of sales on those items, I'm not worried about item-level impact.

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  • $\begingroup$ I think the first thing to do is ditch the term "statistically significant" and clearly define what question you hope statistical calculations will answer. P-values (and statistical significance) are used when you analyze a sample of data and want to make a conclusion about the population (or distribution) the data were sampled from. I don't see how that approach applies to your question. $\endgroup$ – Harvey Motulsky Jul 21 at 17:54
  • $\begingroup$ @HarveyMotulsky: You're right, I've phrased it in an ambiguous way - my bad. I guess a paired sample t-test should suffice (provided necessary assumptions are satisfied)? $\endgroup$ – user9343456 Jul 21 at 17:56
  • $\begingroup$ A t-test is used to test if there is a significant difference between the mean of two groups. I don't think this applies to what you're doing. It might be easier to help if you explain what you're trying to do in a little more detail. Are these your only two variables? Are you just trying to tell if sales increase significantly every week (which won't be possible). What data do you have? $\endgroup$ – Harry Jul 21 at 18:58
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    $\begingroup$ @Harry: I've edited the question to make it clearer. Thanks so much for your feedback! $\endgroup$ – user9343456 Jul 21 at 19:02
  • $\begingroup$ @user9343456 I have offered an answer to your question below. If it is useful, please consider accepting it :) $\endgroup$ – Harry Jul 22 at 16:25
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It sounds like you just want to look at if the change in the total number of sales (or income you could do the same with income) is significant. For this you will need a t test. For each week you should sum the number of sales (or income). So rather than the number of sales for each item, it should just say the number of sales. Then run a t test as you said earlier. Your two groups are "Before" and "After".

Remember the t test will tell you the significance of the difference in sales, not the magnitude. The magnitude is the difference between the mean of the two groups.

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