Analysis of Large Scale Web Experiments Using Sequences of Estimators

Experimental testing is vital in the optimization of web applications, and as such A/B testing has been widely adopted as a methodology for determining optimal content for many web applications. While some testing platforms provide sequentially valid inferences, a large proportion of online tests still utilize traditional statistical tests that do not allow for interim "peeking" at the data or extending the test past its proposed sample size. In this paper we develop results useful for the sequential analysis of large scale experiments. In particular, the properties of sequences of maximum likelihood and generalized method of moments estimators are examined. This leads to new tests of odds ratios and relative risks for binary outcomes. For continuous and ordinal outcome we develop a test of mean difference and a non-parametric test of Area Under the Curve (AUC). Additionally, multivariate versions of these tests are proposed.