  AB testing aids business operators with their decision making, and is
considered the gold standard method for learning from data to improve digital
user experiences. However, there is usually a gap between the requirements of
practitioners, and the constraints imposed by the statistical hypothesis
testing methodologies commonly used for analysis of AB tests. These include the
lack of statistical power in multivariate designs with many factors,
correlations between these factors, the need of sequential testing for early
stopping, and the inability to pool knowledge from past tests. Here, we propose
a solution that applies hierarchical Bayesian estimation to address the above
limitations. In comparison to current sequential AB testing methodology, we
increase statistical power by exploiting correlations between factors, enabling
sequential testing and progressive early stopping, without incurring excessive
false positive risk. We also demonstrate how this methodology can be extended
to enable the extraction of composite global learnings from past AB tests, to
accelerate future tests. We underpin our work with a solid theoretical
framework that articulates the value of hierarchical estimation. We demonstrate
its utility using both numerical simulations and a large set of real-world AB
tests. Together, these results highlight the practical value of our approach
for statistical inference in the technology industry.
