Setting the duration of online A/B experiments
如何设定在线 A/B 实验的持续时间AI 解读 ↓
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如何设定在线 A/B 实验的持续时间
- 研究问题
- 在线 A/B 实验的样本量与持续时间如何共同影响处理效应区间宽度，尤其当同一用户跨日保持分组、观测持续相关时？
- 方法与思路
- 作者基于含两个方差分量的混合效应模型，为比率处理效应估计量推导区间宽度公式，并引入用户特定时间相关参数。
- 材料陈述的贡献
- 摘要称，该公式揭示持续性方差对区间收窄的限制，考察实验前数据的作用，并较好解释 YouTube 真实实验中的区间宽度。
- 阅读关注点
- 应核对比率估计量、方差分解和历史相关参数估计，尤其辨清摘要所述时间衰减率对应区间宽度、方差还是其他量。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核实；摘要未给出完整公式及适用条件，所述衰减率也需结合正文推导核对。
原文摘要
In designing an online A/B experiment, it is crucial to select a sample size and duration that ensure the resulting confidence interval (CI) for the treatment effect is the right width to detect an effect of meaningful magnitude with sufficient statistical power without wasting resources. While the relationship between sample size and CI width is well understood, the effect of experiment duration on CI width remains less clear. This paper provides an analytical formula for the width of a CI based on a ratio treatment effect estimator as a function of both sample size (N) and duration (T). The formula is derived from a mixed effects model with two variance components. One component, referred to as the temporal variance, persists over time for experiments where the same users are kept in the same experiment arm across different days. The remaining error variance component, by contrast, decays to zero as T gets large. The formula we derive introduces a key parameter that we call the user-specific temporal correlation (UTC), which quantifies the relative sizes of the two variance components and can be estimated from historical experiments. Higher UTC indicates a slower decay in CI width over time. On the other hand, when the UTC is 0 -- as for experiments where users shuffle in and out of the experiment across days -- the CI width decays at the standard parametric 1/T rate. We also study how access to pre-period data for the users in the experiment affects the CI width decay. We show our formula closely explains CI widths on real A/B experiments at YouTube.