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arXiv · 2606.24871

Sequential Probability Ratio Test using Z-Statistics (SPRT-z): A Practical Approach for Online Experimentation

Derek L. Ho·Emma G. Thomas
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Abstract

Modern online experimentation platforms produce data at scale and continuously. However, practitioners routinely apply Fixed Horizon Testing (FHT) under repeated peeking, inflating Type I error and reducing decision quality. Popular always valid sequential methods control Type I error under peeking and enable early stopping for efficacy, but do not natively support early futility stopping, launch criteria tied to a business-relevant minimum detectable effect, or Type II error control. As an alternative that satisfies these useful properties, we revive Wald's Sequential Probability Ratio Test (SPRT) for online experimentation with three novel contributions: (1) SPRT-z, an adaptation of Hajnal's sequential $t$-test, leverages large sample normal approximation to eliminate computational bottlenecks inherent to the scale of modern A/B tests and enables the Brownian motion-based methods used in (2) and (3); (2) Scale-Free Horizon Calibration (SFHC) is a Monte Carlo bisection procedure on the standardised $Z$-scale that sets a maximum sample size preserving nominal power under discrete monitoring with futility stopping; (3) A Brownian Median Unbiased Estimator and accompanying confidence intervals correct the upward bias induced by early stopping across all stopping regions via a six-region stagewise ordering of the sample space. A simulation study shows this workflow appropriately controls Type I and II error, reduces sample size relative to FHT, and ameliorates estimation bias from early stopping with close-to-nominal confidence interval coverage in most scenarios studied.

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BibTeXRIS

Derek L. Ho, Emma G. Thomas. 2026-06-23. Sequential Probability Ratio Test using Z-Statistics (SPRT-z): A Practical Approach for Online Experimentation. https://arxiv.org/abs/2606.24871

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