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In this paper, we provide a statistical testing framework to check whether arandom sample splitting in a multi-dimensional space is carried out in a validway, which could be directly applied to A/B testing and multivariate testing toensure the online traffic split is truly random with respect to the covariates.We believe this is an important step of quality control that is missing in manyreal world online experiments. Here, we propose a randomized chi-square testmethod, compared with propensity score and distance components (DISCO) testmethods, to test the hypothesis that the post-split categorical data sets havethe same multi-dimensional distribution. The methods can be easily generalizedto continuous data. We also propose a resampling procedure to adjust formultiplicity which in practice often has higher power than some existing methodsuch as Holm's procedure. We try the three methods on both simulated and realdata sets from Adobe Experience Cloud and show that each method has its ownadvantage while all of them establish promising power. To our knowledge, we areamong the first ones to formulate the validity of A/B testing into apost-experiments statistical testing problem. Our methodology is non-parametricand requires minimum assumption on the data, so it can also have a wide rangeof application in other areas such as clinical trials, medicine, andrecommendation system where random data splitting is needed.

Equivalence Test in Multi-dimensional Space with Applications in A/B Testing