区组随机化

区组随机化的核心是：先按关键协变量把实验对象分成若干“相对同质”的区组（block/stratum），再在每个区组内部做随机分配。

一个标准流程：

1. 选定分块变量：选择会强烈影响结果、且实验前可观测的变量（如地区、性别、年龄段、历史转化率分层等）。

2. 构造区组：把样本按这些变量划分为互不重叠的区组（每个区组内样本更可比）。

3. 块内随机分配：在每个区组内按既定比例（例如 1:1 或 2:1）随机分配到 Treatment/Control。可用固定区组大小的随机化（如每块 4 人中 2 个进 Treatment），保证任何时点都大致平衡。

4. 分析时纳入区组信息：用“分块差分”的加权平均估计处理效应，或在回归中加入区组固定效应，以提高估计精度。

优点是能显著改善处理组与对照组在关键协变量上的平衡，并通常降低方差。

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英文解析

The core of block randomization is to first divide experimental subjects into several "relatively homogeneous" blocks (or strata) based on key covariates, and then perform random allocation within each block.

A standard procedure:

1. Select stratification variables: Choose variables that strongly influence the outcome and are observable prior to the experiment (e.g., region, gender, age group, historical conversion rate strata, etc.).

2. Construct blocks: Divide the sample into non-overlapping blocks based on these variables (samples within each block are more comparable).

3. Random allocation within blocks: Randomly assign subjects within each block to Treatment/Control according to a predetermined ratio (e.g., 1:1 or 2:1). Fixed block-size randomization (e.g., 2 out of 4 in each block go to Treatment) can be used to ensure approximate balance at any point in time.

4. Incorporate block information during analysis: Estimate the treatment effect using a weighted average of "stratified differences" or include block fixed effects in a regression model to improve estimation precision.

The advantages include significantly improved balance between the treatment and control groups on key covariates and typically reduced variance.