Observational study design method vs hypothesis testing vs other? 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:


*

*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.

*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? 
 A: "[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 causal-inference).  
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.  
