The survey experiment is widely used in economics and social sciences to evaluate the effects of treatments or programs. In a standard population-based survey experiment, the experimenter randomly draws experimental units from a target population of interest and then randomly assigns the sampled units to treatment or control conditions to explore the treatment effect of an intervention. Simple random sampling and treatment assignment can balance covariates on average. However, covariate imbalance often exists in finite samples. To address the imbalance issue, we study a stratified approach to balance covariates in a survey experiment. A stratified rejective sampling and rerandomization design is further proposed to enhance the covariate balance. We develop a design-based asymptotic theory for the widely used stratified difference-in-means estimator of the average treatment effect under the proposed design. In particular, we show that it is consistent and asymptotically a convolution of a normal distribution and two truncated normal distributions. This limiting distribution is more concentrated at the true average treatment effect than that under the existing experimental designs. Moreover, we propose a covariate adjustment method in the analysis stage, which can further improve the estimation efficiency. Numerical studies demonstrate the validity and improved efficiency of the proposed method.

翻译：调查实验在经济学和社会科学中被广泛用于评估处理或项目的效果。在标准基于总体的调查实验中，实验者从感兴趣的目标总体中随机抽取实验单元，然后将抽样单元随机分配到处理组或对照组，以探究干预的处理效应。简单随机抽样和处理分配可以在平均意义上平衡协变量。然而，在有限样本中，协变量不平衡问题常常存在。为解决不平衡问题，我们研究了一种在调查实验中平衡协变量的分层方法。进一步提出了一种分层拒绝抽样与再随机化设计以增强协变量平衡。我们为所提设计下广泛使用的平均处理效应的分层均值差估计量建立了基于设计的渐近理论。具体而言，我们证明该估计量具有一致性，且渐近服从一个正态分布与两个截断正态分布的卷积。与现有实验设计下的极限分布相比，该极限分布在真实平均处理效应处更为集中。此外，我们提出了一种分析阶段的协变量调整方法，可进一步提升估计效率。数值研究验证了所提方法的有效性及其改进的效率。