The Unreasonable Effectiveness of Monte Carlo Simulations in A/B Testing

Abstract: This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate statistical power, implementing variance reduction techniques and examining the effects of early stopping. By comparing frequentist and Bayesian approaches, we illustrate how simulations can clarify the relationship between p-values and posterior probabilities, and the validity of such approximations. The study also references how Monte Carlo simulations can be used to understand network effects in RCTs on social networks. Our findings show that Monte Carlo simulations are an effective tool for experimenters to deepen their understanding and ensure their results are statistically valid and practically meaningful.