Given a randomized experiment with binary outcomes, exact confidence intervals for the average causal effect of the treatment can be computed through a series of permutation tests. This approach requires minimal assumptions and is valid for all sample sizes, as it does not rely on large-sample approximations such as the central limit theorem. We show that these confidence intervals can be found in $O(n \log n)$ permutation tests in the case of balanced designs, where the treatment and control groups have equal sizes, and $O(n^2)$ permutation tests in the general case. Prior to this work, the most efficient known constructions required $O(n^2)$ such tests in the balanced case [Li and Ding, 2016], and $O(n^4)$ tests in the general case [Rigdon and Hudgens, 2015]. Our results thus facilitate exact inference as a viable option for randomized experiments far larger than those accessible by previous methods.

翻译：针对二元结果的随机化实验，可通过一系列置换检验计算处理组平均因果效应的精确置信区间。该方法无需依赖中心极限定理等大样本近似，仅需极少的假设条件，且适用于所有样本量。我们证明，在平衡设计（处理组与对照组样本量相等）条件下，可通过$O(n \log n)$次置换检验找到这些置信区间；在一般情形下则需$O(n^2)$次。在此项工作之前，已知最高效的构造方法在平衡情形下需要$O(n^2)$次检验[Li and Ding, 2016]，一般情形下需$O(n^4)$次[Rigdon and Hudgens, 2015]。因此，我们的研究成果使得精确推断成为远超先前方法所能处理的随机化实验的可行方案。