Open Access: A fundamental problem of hypothesis testing with finite inventory in e-commerce

Each week, we select a recently published Open Access article to feature. This week’s article comes from Applied Stochastic Models in Business and Industry and looks at the problems that are faced by companies doing hypothesis testing in online environments. The article shows that high false-positive rates occur and offers strategies to design better tests. 
The article’s abstract is given below, with the full article available to read here.
Bohle, DMarynych, AMeiners, MA fundamental problem of hypothesis testing with finite inventory in e-commerceAppl Stochastic Models Bus Ind202137454– 474
We draw attention to a problem that is often overlooked or ignored by companies practicing hypothesis testing (A/B testing) in online environments. We show that conducting experiments on limited inventory that is shared between variants in the experiment can lead to high false-positive rates since the core assumption of independence between the groups is violated. We provide a detailed analysis of the problem in a simplified setting whose parameters are informed by realistic scenarios. The setting we consider is a two-dimensional (2D) random walk in a semiinfinite strip. It is rich enough to take a finite inventory into account, but is at the same time simple enough to allow for a closed form of the false-positive probability. We prove that high false-positive rates can occur, and develop tools that are suitable to help design adequate tests in follow-up work. Our results also show that high false-negative rates may occur. The proofs rely on a functional limit theorem for the 2D random walk in a semiinfinite strip.
More Details