通过重采样A/A测试验证t检验的正态性假设,提升A/B测试可靠性。
$t$-Testing the Waters: Empirically Validating Assumptions for Reliable A/B-Testing
- 用重复抽样的A/A测试生成p值,检验其是否服从均匀分布。
- 发现当样本量不足时,正态性假设不成立,导致假阳性率上升。
- 适合数据科学家和产品团队在上线前验证A/B测试有效性。
A/B测试是网页实验设计的核心方法,广泛应用于各类场景。最常见的统计方法是基于均值差异的t检验,通常由中心极限定理(CLT)支持:随着样本量增大,平均处理效应的抽样分布趋于正态,从而保证t检验的有效性。然而,当结果变量存在偏斜或非正态时,'足够大'的样本量难以界定。为确保置信区间覆盖正确且p值准确反映假阳性率,必须验证正态性假设。本文提出一种实用方法:通过反复重采样进行A/A测试,若正态性假设成立,则生成的p值应服从均匀分布,可使用Kolmogorov-Smirnov检验进行验证。该方法能高效评估t检验前提是否满足,避免无效测试。我们展示了该方法的应用,并揭示了易引发假阳性错误的场景,为提升A/B测试的可靠性和稳健性提供实证框架。
原文摘要 · Abstract (English)
A/B-tests are a cornerstone of experimental design on the web, with wide-ranging applications and use-cases. The statistical $t$-test comparing differences in means is the most commonly used method for assessing treatment effects, often justified through the Central Limit Theorem (CLT). The CLT ascertains that, as the sample size grows, the sampling distribution of the Average Treatment Effect converges to normality, making the $t$-test valid for sufficiently large sample sizes. When outcome measures are skewed or non-normal, quantifying what "sufficiently large" entails is not straightforward. To ensure that confidence intervals maintain proper coverage and that $p$-values accurately reflect the false positive rate, it is critical to validate this normality assumption. We propose a practical method to test this, by analysing repeatedly resampled A/A-tests. When the normality assumption holds, the resulting $p$-value distribution should be uniform, and this property can be tested using the Kolmogorov-Smirnov test. This provides an efficient and effective way to empirically assess whether the $t$-test's assumptions are met, and the A/B-test is valid. We demonstrate our methodology and highlight how it helps to identify scenarios prone to inflated Type-I errors. Our approach provides a practical framework to ensure and improve the reliability and robustness of A/B-testing practices.
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