  Bayes factors, in many cases, have been proven to bridge the classic -value
based significance testing and bayesian analysis of posterior odds. This paper
discusses this phenomena within the binomial A/B testing setup (applicable for
example to conversion testing). It is shown that the bayes factor is controlled
by the \emph{Jensen-Shannon divergence} of success ratios in two tested groups,
which can be further bounded by the Welch statistic. As a result, bayesian
sample bounds almost match frequentionist's sample bounds. The link between
Jensen-Shannon divergence and Welch's test as well as the derivation are an
elegant application of tools from information geometry.
