For a website CRO (conversion rate optimization) trajectory project of a client, I’m trying to setup a way that they can sequentially check whether an A/B test ‘reached’ significant results (i.e. Does website B lead to more transactions, than website A?). Much like clinical trials, data is coming in over time and the sooner a conclusion can be drawn the bigger the impact. I’ve been reading some papers on this subject (e.g. INTERIM ANALYSIS: THE ALPHA SPENDING FUNCTION APPROACH by DeMets and Lan, 1994). There, if I understand correctly, they mention some formulas for the alpha spending function to make sure that the type I error stays 5%, no matter how often you check the results in between. However, it is unclear to me if you can use these formulas also for chi square test of independence (the test statistic used by our client) since in rest of the paper they mention the Standardized Normal Statistic (i.e. Z-value for group sequential boundaries, which I’m not sure if this is the same statistic as in a T-test? ). Also, I see in the literature that the Z-test (which, I think, is not similar to the Z-value I mention before) is often used for this kind of questions but I’m not familiar with them.

So, my main question is:

Is there an alpha spending function that can be used for chi square test of independence?

In addition, I was wondering:

When should you use chi square test of independence and when a Z-test? What are the benefits/down sides etc?

Thank you all in advanced! Any help is highly appreciated.