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I am trying to understand the following: do more customers purchase an item because it is discounted 'now' because they engaged with the product before (viewed it, added to a wishlist etc) vs just brought it because its on discount 'now'. Different products are discounted at different times, so I'm assuming a date range, and all discounted products in this range need to be considered.

I am confused how to set this up as a statistical test in order to prove / disprove the hypothesis.

My thoughts so far:

  1. T-Test of set 1 = customers engaged with product_i vs customers not engaged with product_i prior to product_i being on sale. Not sure this accounts for many products though or takes into account time.
  2. Logistic regression = probability of a customer purchasing product_i having engaged previous vs not. Again its limited to a product, and then there is an argument over what is a "good % of conversion".

Not sure how to solve this through a robust statistical method. Any thoughts?

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"[D]o more customers purchase an item because ..." is a causal question. I gather you have observational data. Neither a logistic regression model nor a t-test, when conducted in the standard way, will allow you to infer causality from observational data. There is a huge literature on inferring causality from observational data, which is too much to summarize here (on CV, you can peruse some of our threads categorized under ).

If you are just interested in whether there is a marginal association between a product being on sale and a customer buying it, you could run a logistic regression. You should probably account for the number of customer hours under observation for sale and non-sale periods during which a given customer could have made a purchase, because if items are not on sale 50% of the time not including that will bias the result.

Again, I'm not sure how much you are going to be able to really learn from this. This is a major topic in economics (you might just search the literature instead), and economists who try to figure this out use very sophisticated methods and structural models to do so.

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  • $\begingroup$ Interesting! Can you point me to the area of economics that answers this type of question? I will check out the causal-inference threads for sure meanwhile. Just to make sure - I am interested in the association of the product "now" being on sale causing the purchase (i.e. the customer wouldn't have brought it unless it was on sale, and I thought looking at if they were even interested in buying it would be a start). $\endgroup$
    – Dino Abraham
    Commented Jun 28, 2017 at 22:06
  • $\begingroup$ Edit: in a lot of those links they seem to use a regression of some sort. Is it wrong to? $\endgroup$
    – Dino Abraham
    Commented Jun 28, 2017 at 22:25
  • $\begingroup$ I was also reading about Markov models (hence posed here). Seems like the problem could be modelled around this? We could figure the probability of each state (interested --> purchase; not interested --> purchase; interested --> still don't purchase; not interested --> don't purchase). And perhaps attribute total sales for a given month across the states to see if there are significant differences. This would solve for the time issue I reckon. $\endgroup$
    – Dino Abraham
    Commented Jun 28, 2017 at 23:28
  • $\begingroup$ @DinoAbraham, I'm not an economist, so I don't quite know. It's a topic w/i microeconomics. I once talked w/ an econ grad student who was working on it (eg, how much does a sale on a brand of coffee at the grocery store bring in new consumers for the firm vs induce long-time consumers, who would be purchasing anyway, to stock up). You could ask about it on the Economics SE site, I suppose. For the most part, the methods to infer causality from observational data are built on top of regression methods, so regression per se isn't necessarily wrong, only the simple, naive application of it. $\endgroup$
    – gung - Reinstate Monica
    Commented Jun 29, 2017 at 0:52
  • $\begingroup$ I don't know enough about Markov models to comment, but I think they are a legitimate possibility. $\endgroup$
    – gung - Reinstate Monica
    Commented Jun 29, 2017 at 0:54

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