From the end of TFA:<p>>The book is not without its weak moments, although they are few. One in particular which I recall is the treatment of A/B testing. Essential to any hypothesis testing is the matter of how to reduce the sampling mechanism to a simple probabilistic model, so that a quantitative test may be derived. The book emphasizes one such model: simple random sampling from a population, which then involves the standard probabilistic ideas of binomial and multinomial distributions, along with the normal approximation to these. Thus, one obtains the z-test.<p>>In the context of randomized controlled experiments, where a set of subjects is randomly assigned to either a control or treatment group, the simple random sampling model is inapplicable. Nonetheless, when asking whether the treatment has an effect there is a suitable (two-sample) z-test. The mathematical ideas behind it are necessarily different from those of the previously mentioned z-test, because the sampling mechanism here is different, but the end result looks the same. Why this works out as it does is explained rather opaquely in the book, since the authors never developed the probabilistic tools necessary to make sense of it (here one would find at least a mention of hypergeometric distributions). Given the emphasis placed in the beginning of the book on the importance of randomized, controlled experiments in statistics, it feels like this topic is getting short-shrift.<p>Can anyone recommend good resources to fill this alleged gap?