# Find out if increase in a series of values is statistically significant

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.

• 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. – Harvey Motulsky Jul 21 '20 at 17:54
• @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)? – user9343456 Jul 21 '20 at 17:56
• 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? – Harry Jul 21 '20 at 18:58
• @Harry: I've edited the question to make it clearer. Thanks so much for your feedback! – user9343456 Jul 21 '20 at 19:02
• @user9343456 I have offered an answer to your question below. If it is useful, please consider accepting it :) – Harry Jul 22 '20 at 16:25