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M1 · 数学与统计基础 (Mathematics & Statistics Fundamentals)| 专题分类：实验设计 (A/B) (实验设计 (A/B))| 难度等级：Medium
一、核心一句话结论 (One-Sentence Summary)
实际分组比例显著偏离预期；用卡方检验检测，通常说明分流/埋点/过滤有 bug。
Sample Ratio Mismatch (SRM) occurs when the observed traffic split deviates significantly from the planned design ratio (e.g. 50:50), indicating severe selection bias that invalidates all experimental results.
二、核心考点要义 (Key Insights)
- 📌 SRM 是实验不可信的第一信号
- 📌 常见原因：重定向、bot 过滤、曝光时机差异
English Insights:
– Detection: Evaluated using a Chi-Square goodness-of-fit test comparing observed sample sizes $O_A, O_B$ to expected $E_A, E_B$; flagged if $p_{text{SRM}} < 0.001$.
– Consequence: Invalidates all causal conclusions; any observed lift could be an artifact of unequal user attrition rather than true product impact.
– Root Causes: Redirect performance lags, browser cache discrepancies, bot filtering asymmetries, and post-treatment tracking drops.
三、核心数学原理与机理推导 (Mathematical Principles & Derivation)
$$chi^2=sumfrac{(O_i-E_i)^2}{E_i},qquad p<0.001Rightarrowtext{SRM}$$
SRM 的检测：设预期分流比例为 p_i（如 50/50），实际观测样本量为 O_i，期望 E_i=p_i·N，则卡方统计量 χ²=Σ(O_i−E_i)²/E_i 在 H₀（分流正确）下服从 χ²(k−1)。实践中 SRM 的判定阈值比常规检验更严格（通常 p<0.001 甚至 p<0.0001），因为分流错误一旦存在就会持续影响所有实验，且会因大样本而轻易达到 p<0.05。为什么 SRM 是严重信号：若分流本身有偏，则组间差异可能来自分流偏差而非策略效果，实验结论完全不可信——所以 SRM 是’实验不可信的第一信号’，任何解读都应在确认无 SRM 之后进行。
📖 查看英文严格数学推导 (English Mathematical Derivation)
Let planned allocation ratio be $r_A : r_B$ (e.g. 0.5 : 0.5) with total observed traffic $N = O_A + O_B$. Expected counts are $E_A = N r_A$ and $E_B = N r_B$. The Chi-Square test statistic is: $chi^2 = frac{(O_A – E_A)^2}{E_A} + frac{(O_B – E_B)^2}{E_B} = frac{(O_A – N/2)^2}{N/2} + frac{(O_B – N/2)^2}{N/2} = frac{(O_A – O_B)^2}{N} sim chi^2_1$. For example, if $O_A = 502,000$ and $O_B = 498,000$ (a seemingly tiny 0.4% difference), $chi^2 = frac{(4000)^2}{1,000,000} = 16.0$. With 1 degree of freedom, critical value at $alpha=0.001$ is $10.83$; since $16.0 > 10.83$, $p_{text{SRM}} = 0.000063$, signaling catastrophic SRM.
四、工业级落地权衡与工程考量 (Industrial Trade-offs)
常见成因与排查：① 分流逻辑——哈希函数不均匀、盐值（salt）在不同服务间不一致、多层实验的流量冲突；② 埋点与日志——某组的事件上报丢失（如客户端版本差异）、曝光时机不同（处理组多一次渲染导致曝光计数不同）、日志采样不对称；③ 过滤逻辑——bot/爬虫过滤规则在两组执行不一致、异常值清洗依赖了组信息、重定向导致用户中途换组；④ 时序——两组上线时间不同导致覆盖的用户群不同（如处理组先上线，早期用户被排除）。排查顺序：先看原始分流日志（是否真的按预期分流）→ 再看埋点与曝光（是否对称）→ 最后检查下游过滤逻辑。发现 SRM 后的正确做法是废弃该实验并修复基础设施，而不是’校正’数据。
⚙️ 查看英文落地权衡分析 (English Systems & Trade-offs)
Systematic SRM troubleshooting protocol: (1) Segmented Chi-Square breakdown: Slice by Device (iOS vs Android), Browser (Chrome vs Safari), Country, and User State (New vs Returning). If SRM concentrates in a specific slice (e.g. Android only), inspect platform-specific client code. (2) Redirect vs In-line rendering: Redirect variants suffer from network drops before page load. (3) Bot filtering: If Treatment triggers bot defenses more frequently, bot scrapers are selectively removed from one variant.
五、常见面试避坑陷阱 (Common Pitfalls & Traps)
- ⚠️ 用 p<0.05 判定 SRM（应更严格，如 p<0.001）
- ⚠️ 发现 SRM 后仍强行解读指标差异
English Pitfalls:
– Attempting to ‘re-normalize’ or re-weight data to salvage an experiment with severe SRM (unobserved selection bias makes results irrecoverable).
– Using standard $p=0.05$ threshold for SRM checks (due to huge $N$, use stringent $p < 0.001$ to avoid false platform alarms).
六、高频深度面试追问与预测 (Follow-Up Questions)
- SRM 与指标不显著的混淆风险？
- Why does a heavy client-side JavaScript bundle in Treatment cause selective drop-off before impression logging?
- 发现 SRM 后应该怎么做？
- How does Simpson’s paradox manifest when changing allocation percentages mid-experiment?
七、知识图谱对齐 (Knowledge Graph Anchor)
- 🔗 关联底层卡片：
工业级 A/B 实验设计、分流正交、SRM 卡方排查与方差缩减(Industrial A/B Testing: Split, SRM & Variance Reduction) - 🗺️ 知识图谱模块：
数据科学与因果实验导图
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本题收录于 TalentMe 算法科学家深度考察真题库 (Science Depth)。全库共 856 道硬核考点，深度覆盖数学统计、经典ML、深度学习、Transformer、大语言模型、多模态、推荐系统与 MLOps。支持 Jev 面经智能匹配、一键离线单文件 HTML 手册导出并直连 Obsidian 本地记忆。