While there exists a large amount of literature on the general challenges and best practices for trustworthy online A/B testing, there are limited studies on sample size estimation, which plays a crucial role in trustworthy and efficient A/B testing that ensures the resulting inference has a sufficient power and type I error control. For example, when sample size is under-estimated, the statistical inference, even with the correct analysis methods, will not be able to detect the true significant improvement leading to misinformed and costly decisions. This paper addresses this fundamental gap by developing new sample size calculation methods for correlated data, as well as absolute vs. relative treatment effects, both ubiquitous in online experiments. Additionally, we address a practical question of the minimal observed difference that will be statistically significant and how it relates to average treatment effect and sample size calculation. All proposed methods are accompanied by mathematical proofs, illustrative examples, and simulations. We end by sharing some best practices on various practical topics on sample size calculation and experimental design.

When interpreting A/B tests, we typically focus only on the statistically significant results and take them by face value. This practice, termed post-selection inference in the statistical literature, may negatively affect both point estimation and uncertainty quantification, and therefore hinder trustworthy decision making in A/B testing. To address this issue, in this paper we explore two seemingly unrelated paths, one based on supervised machine learning and the other on empirical Bayes, and propose post-selection inferential approaches that combine the strengths of both. Through large-scale simulated and empirical examples, we demonstrate that our proposed methodologies stand out among other existing ones in both reducing post-selection biases and improving confidence interval coverage rates, and discuss how they can be conveniently adjusted to real-life scenarios.

On-line experimentation (also known as A/B testing) has become an integral part of software development. To timely incorporate user feedback and continuously improve products, many software companies have adopted the culture of agile deployment, requiring online experiments to be conducted and concluded on limited sets of users for a short period. While conceptually efficient, the result observed during the experiment duration can deviate from what is seen after the feature deployment, which makes the A/B test result biased. In this paper, we provide theoretical analysis to show that heavy-users can contribute significantly to the bias, and propose a re-sampling estimator for bias adjustment.

During the last decade, the information technology industry has adopted a data-driven culture, relying on online metrics to measure and monitor business performance. Under the setting of big data, the majority of such metrics approximately follow normal distributions, opening up potential opportunities to model them directly without extra model assumptions and solve big data problems via closed-form formulas using distributed algorithms at a fraction of the cost of simulation-based procedures like bootstrap. However, certain attributes of the metrics, such as their corresponding data generating processes and aggregation levels, pose numerous challenges for constructing trustworthy estimation and inference procedures. Motivated by four real-life examples in metric development and analytics for large-scale A/B testing, we provide a practical guide to applying the Delta method, one of the most important tools from the classic statistics literature, to address the aforementioned challenges. We emphasize the central role of the Delta method in metric analytics by highlighting both its classic and novel applications.

A/B tests (or randomized controlled experiments) play an integral role in the research and development cycles of technology companies. As in classic randomized experiments (e.g., clinical trials), the underlying statistical analysis of A/B tests is based on assuming the randomization unit is independent and identically distributed (\iid). However, the randomization mechanisms utilized in online A/B tests can be quite complex and may render this assumption invalid. Analysis that unjustifiably relies on this assumption can yield untrustworthy results and lead to incorrect conclusions. Motivated by challenging problems arising from actual online experiments, we propose a new method of variance estimation that relies only on practically plausible assumptions, is directly applicable to a wide of range of randomization mechanisms, and can be implemented easily. We examine its performance and illustrate its advantages over two commonly used methods of variance estimation on both simulated and empirical datasets. Our results lead to a deeper understanding of the conditions under which the randomization unit can be treated as \iid In particular, we show that for purposes of variance estimation, the randomization unit can be approximated as \iid when the individual treatment effect variation is small; however, this approximation can lead to variance under-estimation when the individual treatment effect variation is large.

A/B testing is one of the most successful applications of statistical theory in the Internet age. A crucial problem of Null Hypothesis Statistical Testing (NHST), the backbone of A/B testing methodology, is that experimenters are not allowed to continuously monitor the results and make decisions in real time. Many people see this restriction as a setback against the trend in the technology toward real time data analytics. Recently, Bayesian Hypothesis Testing, which intuitively is more suitable for real time decision making, attracted growing interest as a viable alternative to NHST. While corrections of NHST for the continuous monitoring setting are well established in the existing literature and known in A/B testing community, the debate over the issue of whether continuous monitoring is a proper practice in Bayesian testing exists among both academic researchers and general practitioners. In this paper, we formally prove the validity of Bayesian testing under proper stopping rules, and illustrate the theoretical results with concrete simulation illustrations. We point out common bad practices where stopping rules are not proper, and discuss how priors can be learned objectively. General guidelines for researchers and practitioners are also provided.

Relational databases hold a vast quantity of information and making them accessible to the web is an big challenge. There is a need to make these databases accessible with as little difficulty as possible, opening them up to the power and serendipity of the Web. Our work presents a series of patterns that bridge the relational database model with the architecture of the Web along with an implementation of some of them. The aim is for relational databases to be made accessible with no intermediate steps and no extra metadata required. This approach can vastly increase the data available on the web, therefore making the Web itself all the more powerful, while enabling its users to seamlessly perform tasks that previously required bridging multiple domains and paradigms or were not possible.