I introduce a simple permutation procedure to test conventional (non-sharp) hypotheses about the effect of a binary treatment in the presence of a finite number of large, heterogeneous clusters when the treatment effect is identified by comparisons across clusters. The procedure asymptotically controls size by applying a level-adjusted permutation test to a suitable statistic. The adjustments needed for most empirically relevant situations are tabulated in the paper. The adjusted permutation test is easy to implement in practice and performs well at conventional levels of significance with at least four treated clusters and a similar number of control clusters. It is particularly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.

翻译：本文介绍了一种简单的置换检验程序，用于在存在有限数量且高度异质性的大规模聚类时，检验二元处理效应中关于传统（非精确）假设。该假设通过聚类间比较来识别处理效应。该程序通过对适当统计量应用水平调整的置换检验，在渐近意义上控制了检验尺度。文中列举了大多数实证相关情形所需的调整值。经验证，该调整后的置换检验易于实施，且在至少四个处理聚类和类似数量对照聚类的情况下，能在常规显著性水平下表现良好。它对某些聚类变异性远大于其他聚类的情形尤为稳健。文中还提供了示例和实证应用。